SSC CGL Tier-I 05 March 2020 Shift-II Previous Year Paper

SSC CGL Tier-I 05 March 2020 

Q. 1 Vineet, Rajesh and Kriti have different amounts of money with them. Rajesh has just double the amount of money than Vineet. The total amount of money that Rajesh and Kriti have is ₹147. Kriti has ₹6 more than the amount Vineet has. How much money does Kriti have ? 

A. ₹64 

B. ₹53 

C. ₹50 

D. ₹72 

Answer: B. 

Explanation: 

Amount of Rajesh = 2×amount of Vineet 

Amount of Kriti = 6 + amount of Vineet —(1) 

Total amount of Rajesh and Kriti = 147 

Amount of Rajesh + amount of Kriti = 147 

2×amount of Vineet + 6 + amount of Vineet = 147 

Amount of Vineet = 141/3 = 47 

From eq (1), 

Amount of Kriti = 6 + 47 = Rs. 53 

∴ The correct answer is option B. 

 

Q. 2 The sequence of folding a piece of paper and the manner in which the folded paper has been cut is shown in the following figures. How would this paper look when unfolded? 

Answer: C. 

 

Q. 3 Select the letter-cluster that can replace the question mark(?) in the following series. SAT, VEW,YIZ, ? , EUF 

A. BOC. 

B. BUK 

C. FIC. 

D. COD. 

Answer: A. 

Explanation: 

In the series, middle letter of the letter-cluster is vowels so, 

(S + 3)(A)(T + 3) = VEW 

(V + 3)(E)(W + 3) = YIZ 

(Y + 3)(I)(Z + 3) = BOC. 

(B. + 3)(O)(C. + 3) = EUF 

∴ The correct answer is option A. 

 

Q. 4 Select the option in which the numbers are related in the same way as are the numbers in the given set. (7, 98, 196) 

A. (15, 190, 380) 

B. (18, 185, 360) 

C. (11, 154, 308) 

D. (20, 267, 520) 

Answer: C. 

Explanation: 

In (7, 98, 196), 

7×14 = 98 

98×2 = 196 

Similarly, 

In (11, 154, 308), 

11×14 = 154 

154×2 = 308 

∴ The correct answer is option C. 

 

Q. 5 Select the dice that can be formed by folding the given sheet along the lines.

A. Only A. and B. 

B. Only A. 

C. Only B. 

D. Only C. and D. 

Answer: B. 

 

Q. 6 Arrange the following words in the order in which they would appear in an English dictionary. 

1. Category 

2. Caption 

3. Captain 

4. Capsule 

5. Capacity 

A. 5,4,3,1,2 

B. 5,4,3,2,1 

C. 4,5,3,2,1 

D. 5,4,1,3,2 

Answer: B. 

Explanation: 

Order of the words according to the English dictionary, 

Capacity, Capsule, Captain, Caption, Category 

∴ The correct answer is option B.

 

Q. 7 Study the given pattern carefully and select the number that can replace the question mark (?) in it?

A. 14 

B. 24 

C. 30 

D. 28 

Answer: A. 

Explanation: 

(299+100)/21 = 399/21 = 19

(296+100)/18 = 396/18 = 14

Similarly,

(348+100)/32 = 448/32 = 14

∴ The correct answer is option A. 

 

Q. 8 Four Letter-clusters have been given, out of which three are alike in some manner and one is different. Select the odd letter-cluster. 

A. NRW 

B. PTY 

C. ADL 

D. LPU 

Answer: C. 

Explanation: 

N + 4 = R + 5 = W 

P + 4 = T + 5 = Y 

A + 3 = D + 8 = L 

L + 4 = P + 5 = U 

∴ The correct answer is option C. 

 

Q. 9 Four words have been given. out of which three are alike in some manner and is different. 

Select the odd word. 

A. Rabies 

B. Schizophrenia 

C. Polio 

D. Measles 

Answer: B. 

Explanation: 

Except option B, remaining all are the disease which is caused by the virus. 

∴ The correct answer is option B. 

 

Q. 10 Pointing to the photograph of Sanchi, Nitin said, “Her mother’s father’s son’s wife is my mother-in-law’s only daughter”. How is Nitin related to Sanchi’s mother ? 

A. Paternal uncle 

B. Paternal grandfather 

C. Maternal uncle 

D. Brother 

Answer: D. 

Explanation: 

In the diagram, square shows the males, circle shows the females, vertical lines shows the generation, single horizontal lines shows the brother/sister and double horizontal lines shows the couples. 

From the diagram, 

Nitin is the brother of Sanchi’s mother. 

∴ The correct answer is option D. 

 

Q. 11 Which of the following Venn diagram best represents the relationship between the following classes? 

Income tax payers, Employees, Males 

A.

B.

C.

D.

Answer: B. 

 

Q. 12 ‘Vertebrate’ is related to ‘Monkey’in the same wayas ‘Invertebrate’is related to ‘ ……..’ 

A. Starfish 

B. Snake 

C. Deer 

D. «Frog 

Answer: A. 

Explanation: 

‘Vertebrate’ is related to ‘Monkey’in the same wayas ‘Invertebrate’is related to ‘starfish’. 

∴ The correct answer is option A. 

 

Q. 13 Select the option that is related to the third number in the same way as the second number is related to the first number. 

4:69:: 11:2 

A. 1029 

B. 198 

C. 176 

D. 1336 

Answer: D. 

Explanation: 

(4)3 + 3 = 64 + 5 = 69 

(11)3 + 3 = 1331 + 5 =1336 

∴ The correct answer is option D. 

 

Q. 14 In a certain code language. ‘CAUGHT’ is coded as ‘326212087’. How will ‘SOLDER’ be coded asin that language? 

A. 2012152358 

B. 1912122359 

C. 1915124359 

D. 1812122459 

Answer: B. 

Explanation: 

‘CAUGHT’ is coded as ‘326212087’, 

C = 3 

A = 27 – 1 = 26 

U = 21 

G = 27 – 7 =20 

H = 8 

T = 27 – 20 = 7 

Similarly, 

S = 19 

O = 27 – 15 = 12 

L = 12 

D = 27 – 4 = 23 

E = 5 

R = 27 – 18 = 9 

‘SOLDER’ is coded as ‘1912122359’ 

∴ The correct answer is option B. 

 

Q. 15 Which two signs and two numbers should be interchanged to make the given equation correct? 

11 × 7 ÷ 35 − 64 + 56 = 47

A. + and −; 7 and 11

B. × and ÷; 35 and 11

C. × and ÷; 35 and 56

D. + and −; 35 and 11 

Answer: B. 

Explanation: 

11 × 7 ÷ 35 − 64 + 56 = 47 

From the option B, 

on changing the sign, 

35 ÷ 7 × 11 − 64 + 56 = 47 

55 – 64 + 56 = 47 

47 = 47 

∴ The correct answer is option B. 

 

Q. 16 Select the correct mirror image of the given figure when a mirror is placed on its right side. 

Answer: B. 

 

Q. 17 Select the letter-cluster that can replace the question mark (?) in the following series. 

AR, CP, ?, GL, IJ, KH 

A. DM 

B. DN 

C. EN 

D. EM 

Answer: C. 

Explanation: 

(A + 2)(R – 2) = CP 

(C + 2)(P – 2) = EN 

(E + 2)(N – 2) = GL 

(G + 2)(L – 2) = IJ 

(I + 2)(J – 2) = KH 

∴ The correct answer is option C. 

Q. 18 Select the number that can replace the question mark (?) in the following series. 

61, 63, 65, 77, 89, ? , 149, 205 

A. 115 

B. 123 

C. 119 

D. 132 

Answer: C. 

Explanation: 

61 +(1)2 + 1 = 61 + 2 = 63 

63 +(2)2 – 2 = 63 + 2 = 65  

65 +(3)2 + 3 = 65 + 12 = 77 

77 +(4)2 – 4 = 77 + 12 = 89 

89 +(5)2 + 5 = 89 + 30 = 119 

119 +(6)2 – 6 = 119 + 30 = 149 

149 +(7)2 + 7 = 149 + 56 = 205 

∴ The correct answer is option C. 

Q. 19 Four number-pairs have been given, out of which three are alike in some manner and one is different. Select the number-pair that is different from therest 

A. 17:323 

B. 23: 575 

C. 19:475 

D. 11: 143 

Answer: C. 

Explanation:

17 × (17 + 2) = 17 × 19 = 323 

23 × (23 + 2) = 23 × 25 = 575 

19 × (19 + 2) = 19 × 21 = 399 

11 × (11 + 2) = 11 × 13 = 143 

∴ The correct answer is option C. 

Q. 20 Select the figure that can replace the question mark (?) in the following series. 

Answer: C. 

Q. 21 In a certain code language, ‘SANCTION’ is written as ‘XFSHODIT’. How will ‘PROFOUND’ be written as in that language ? 

A. UWTKJPHJ 

B. UWTKKPIJ 

C. UWTKNQIY 

D. VWUKMPIY 

Answer: A. 

Explanation: 

S + 5 = X 

A + 5 = F 

N + 5 = S 

C + 5 = H 

T – 5 = O 

I – 5 = D. 

O – 6 = I 

N + 6 = T 

Similarly, 

P + 5 = U 

R + 5 = W 

O + 5 = T 

F + 5 = K 

O – 5 = J 

U – 5 = P 

N – 6 = H 

D + 6 = J 

‘PROFOUND’ is written as ‘UWTKJPHJ’. 

∴ The correct answer is option A. 

Q. 22 Select the option in which the words share the same relationship as that shared by the given pair of words. Examination: Invigilator 

A. Election : Observer 

B. Bank : Loan 

C. Film : Comedian 

D. Inspection : Approval 

Answer: A. 

Explanation: 

Examinations are conducted by the invigilator. 

Similarly, 

Elections are conducted by the observer. 

∴ The correct answer is option A. 

Q. 23 How many triangles are there in the given figure? 

A. 34 

B. 33 

C. 32 

D. 35 

Answer: C. 

Q. 24 Select the option that is embedded in the given figure X (rotation is not allowed). 

Answer: C. 

Q. 25 Read the given statements and conclusions carefully. 

Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow from the statements. Statements: 

1. Some papers are copies. 

2. No copy is an eraser. 

Conclusions: 

I. Some copies are papers. 

II. Some papers are erasers. 

III. No paper is an eraser. 

A. Only conclusion II and either conclusion I or III follow. 

B. Only conclusions I and II follow. 

C. Only conclusion I and either conclusion II or III follow. 

D. Only conclusions I and III follow. 

Answer: C. 

Explanation: 

From the Venn diagram, 

Only conclusion I and either conclusion II or III follow 

∴ The correct answer is option C. 

General Awareness 

Instructions 

For the following questions answer them individually 

Q. 26 The Indian Army is set to commission the first batch of women soldiers by year ……. 

A. 2020 

B. 2022 

C. 2021 

D. 2023 

Answer: C. 

Q. 27 Part VIII of the Constitution of India deals with ______. 

A. States 

B. Municipalities 

C. Union Territories 

D. Panchayats 

Answer: C. 

Q. 28 Which of the following is NOT located in Odisha? 

A. Mayurbhanj Elephant Reserve 

B. Sambalpur Elephant Reserve 

C. Sonitpur Elephant Reserve 

D. Mahanadi Elephant Reserve 

Answer: C. 

Q. 29 Which of the following is NOT an ore of iron? 

A. Cuprite 

B. Haematite 

C. Magnetite 

D. Siderite 

Answer: A. 

Q. 30 The National Commission for Backward Classes (NCBC) was formed by insertion of Article ______ in the Constitution of India. 

A. 328B 

B. 328A 

C. 338A 

D. 338B 

Answer: D. 

Q. 31 

Name the first female amputee to climb Mount Everest. 

A. Premlata Agarwal 

B. Arunima Sinha 

C. Poorna Malavath 

D. Anshu Jamsenpa 

Answer: B. 

Q. 32 Pernicious anaemia is caused by the deficiency of vitamin ……. 

A. B2 

B. B6 

C. B1 

D. B12 

Answer: D. 

Q. 33 India won its ______ successive title at the South Asian Football Federation Women’s Championship in March 2019 

A. fourth 

B. sixth 

C. second 

D. fifth 

Answer: D. 

Q. 34 The excavated remains of ______ found near Patna in Bihar was inscribed as a World Heritage Site by UNESCO in July 2016. 

A. Ashoka Pillar 

B. Ellora Caves 

C. Sanchi Stupa 

D. Nalanda Mahavihara 

Answer: D. 

Q. 35 The headquarters of the Board of Control for Cricket in India (BCCI) are located in 

A. Bengaluru 

B. Mumbai 

C. Kolkata 

D. Delhi 

Answer: B. 

Q. 36 Name the first Lieutenant Governor of the Union Territory of Jammu and Kashmir. 

A. Arif Mohammad Khan 

B. Bhagat Singh Koshyari 

C. Satya Pal Malik 

D. Girish Chandra Murmu 

Answer: D. 

Q. 37 ______ is also known as the ‘Golden City 

A. Dungarpur 

B. Jodhpur 

C. Bundi 

D. Jaisalmer 

Answer: D. 

Q. 38 The aggregate value of goods and services produced in an economy can be calculated by three methods: income method, expenditure method and ______ method. 

A. product / value added 

B. spending 

C. deposit 

D. lending 

Answer: A. 

Q. 39 ……. renounced his knighthood in protest for Jalianwalla Bagh mass killing 

A. Jamsetjee Jejeebhoy 

B. Rabindranath Tagore 

C. Shivajirao Holkar 

D. Surendranath Banerjee 

Answer: B. 

Q. 40 ‘Dharmaraja (Yudhishthir) Ratha’, ‘Bhima Ratha’, ‘Arjuna Ratha’ and ‘Nakula Sahadeva Ratha’ are four of the Panch Rathas at Mahabalipuram. What is the name of the fifth Ratha? 

A. Bhishma Ratha 

B. Krishna Ratha 

C. Karna Ratha 

D. Draupadi Ratha 

Answer: D. 

Q. 41 The ______ in China is the world’s longest man-made waterway 

A. Suzhou Canal 

B. Kiel Canal 

C. Corinth Canal 

D. Grand Canal 

Answer: D. 

Q. 42 The Gadar (or Ghadar) Party was formed in the year ……. 

A. 1921 

B. 1918 

C. 1915 

D. 1913 

Answer: D. 

Q. 43 Alai-Darwaza, the southern gateway of the Quwwat-ul-Islam mosque in Delhi, was constructed by ….. 

A. Mu’izz ad-Din Muhammad Ghori 

B. Ahmad Shāh Durrani 

C. Ala-ud-din Khilji 

D. Muhammad bin Tughlu 

Answer: C. 

Q. 44 The Indus Waters Treaty was signed between India and Pakistan on ……. 

A. 19 September 1960 

B. 12 November 1959 

C. 16 December 1963 

D. 18 October 1969 

Answer: A. 

Q. 45 ______ are homogeneous mixtures of two or more components. 

A. Amalgams 

B. Solutions 

C. Enzymes 

D. Emulsions 

Answer: B. 

Q. 46 The total number of images formed by two mirrors inclined at 120° to each other is …… 

A.

B.

C.

D.

Answer: C. 

Q. 47 Depreciation is an annual allowance for the wear and tear of ………. 

A. work in progress 

B. land 

C. finished goods 

D. capital goods 

Answer: D. 

Q. 48 The Padma Awards are announced around ______ every year. 

A. Republic Day 

B. Sadbhavana Diwas 

C. Independence Day 

D. Hindi Diwas 

Answer: A. 

Q. 49 Which of the following can be used as a catalyst in Hydrogenation reaction? 

A. Barium 

B. Iron 

C. Tungsten 

D. Palladium 

Answer: D. 

Q. 50 The ‘Hyderabad Fund’ had been held by the ______ in the account of the High Commissioner of Pakistan to the UK, Habib Ibrahim Rahimtoola 

A. Bank of England 

B. National Westminster Bank 

C. Butterfield Private Bank 

D. Kingdom Bank 

Answer: B. 

Quantitative Aptitude 

Instructions 

For the following questions answer them individually 

Q. 51 In ABC, ∠B = 90, If the points D and E are on the side BC such that BD = DE = EC then which of the following is true? 

A. 5AE2 = 2AC2 + 3AD2

B. 8AE2 = 5AC2 + 3AD2 

C. 8AE2 = 3AC2 + 5AD2

D. 5AE2 = 3AC2 + 2AD2

Answer: C. 

Explanation: 

Let the BD, BE and BC. be x, 2x and 3x respectively. 

In △ABD, 

(AD)2 = (AB)2 + (BD)2 

(AD)2 = (AB)2 + (x)2  —-(1)

In △ABE,

(AE)2 = (AB)2 + (BE)2 (AE)2 = (AB)2 + (2x)2 

(AE)2 = (AB)2 + 4x2    —(2)

In △ABC,

(AC)2 = (AB)2 + (BC)2 

(AC)2 = (AB)2 + (3x)2 

(AC)2 = (AB)2 + 9x2 —(3)

Eq(1) multiply by 4, 

4AD2 = 4AB2 + 4x2   —(4)

Eq(4) – (2), 

4AD2 AE2 = 3AB2  —(5)

Eq(1) multiply by 9, 

9AD2 = 9AB2 + 9x2   —(6)

Eq(6) – (3),

9AD2 AC2 = 8AB2  —(7) 

Eq(5) multiply by 8 and Eq(7) multiply by 3, 

32AD2 − 8AE2 = 24AB2 —(8)

27AD2 − 3AC2 = 24AB2 —(9)

From eq(8) and (9), 

32AD2 − 8AE2 = 27AD2 − 3AC2 

8AE2 = 5AD2 + 3AC2 

Q. 52 When a positive integer is divided by d, the remainder is 15. When ten times of the same number is divided by d. the remainder is 6. The least possible value of d is: 

A.

B. 16 

C. 18 

D. 12 

Answer: B. 

Explanation: 

When a positive integer is divided by d, the remainder is 15 and When ten times of the same number is divided by d. the remainder is 6. So, 

15 will be also ten times so, 

Remainder = 150 

By the option B) 

When 150 is divided by 16 then remainder will be 6. 

Hence, correct answer is option B) 16. 

Q. 53 Reema sold 48 articles for ₹ 2,160 and suffered a loss of 10%. How many articles should she sell for ₹2,016 to earn a profit of 12%? 

A. 36 

B. 40 

C. 28 

D. 32 

Answer: A. 

Explanation: 

Selling price of 48 articles when loss of 10% = 2160 

Cost price of 48 articles = 2160 / 90 ×100 = 2400 

Cost price of 1 article = 2400/48 = 50 

Selling price of when profit of 12% = 2016 

Cost price = 2016 / 112 ×100 = 1800 

Number of articles = 1800/50 = 36 

Q. 54 A and B together borrowed a sum of ₹51,750 at an interest rate of 7%p.a. compound interest in such a way that to settle the loan, A paid as much amount after three years as paid by B after 4 years from the day of borrowing. The sum (in ₹) borrowed by B was: 

A. 25,650 

B. 26,750 

C. 25,000 

D. 24,860 

Answer: C. 

Explanation: 

let A borrow be Rs.x. 

Borrowed by B = 51,750 – x 

compound interest rate(r) = 7% 

Amount paid by A after 3 year = amount paid by B after 4 year 

Amount = principal(1 + r/100)t

x(1 + 7/100)3 = (51, 750 − x)(1 + 7/100)4 

x = (51, 750 − x) × 107/100 

100x = 5537250 – 107x 

x = 5537250/207 = 26750 

Borrowed by B = 51,750 – x = 51,750 – 26750 = 25000 

Q. 55 is equal to 

A. (x−4)/(x+4)

B. (x+4)/x(4−x)

C. (x+4)/x(x−4)

D. (x+4)/(x−4)

Answer: C. 

Explanation: 

Q. 56 The marked price of an item is 25% above its cost price. A shopkeeper sells it, allowing a discount of x % on the marked price. If he incurs a loss of 8%, then the value of x is 

A. 25.6% 

B. 26.8% 

C. 26.4% 

D. 25.2% 

Answer: C. 

Explanation: 

Let the cost price of an article be 100. 

Marked price = 100 × 125/100 = 125 

Discount = x% 

Loss = 8% 

Selling price = 100 × 92/100 = 92 

Selling price = marked price – discount 

Discount = 125 – 92 = 33 

x% = 33/125×100 = 26.4% 

Q. 57 What x is added to each of 10, 16, 22 and 32, the numbers so obtained in this order are in proportion? What is the mean proportional between the numbers (x + 1) and (3x + 1)? 

A. 12 

B.

C. 15 

D. 10 

Answer: C. 

Explanation: 

If x is added to each of numbers, the numbers so obtained in this order are in proportion 

so, (10 + x)/(16 + x) = (22 + x)/(32 + x) 

(10 + x)(32 + x) = (16 + x)(22 + x) 

320 + 10x + 32x + x2 = 352 + 16x + 22x + x2 

320 + 42x = 352 + 38x 

4x = 32 

x = 8 

(x + 1) = 8 + 1 = 9 

(3x + 1) = 24 + 1 = 25 

Mean proportional = √(9×25) = 15 

Q. 58 What is the value of  

A.

B.

C.

D. -1 

Answer: B. 

Explanation: 

Q. 59 The average of some numbers is 54.6. If 75% of the numbers are increased by 5.6 each, and the rest are decreased by 8.4 each, then what is the average of the numbers so obtained? 

A. 55.6 

B. 55.8 

C. 56.7 

D. 56.3 

Answer: C. 

Explanation: 

New average of the numbers = (average + increment/decrements) 

The average of some numbers = 54.6 

75% of the numbers are increased by 5.6 each, and the rest are decreased by 8.4 each so, 

New average of the numbers = 54.6 + (5.6 × 75/100 – 8.4 × 25/100) = 54.6 + 4.2 – 2.1 = 56.7 

Q. 60 Diameter AB of a circle with centre O is produced to a point P such that PO = 16.8 cm. PQR is a secant which intersects the circle at Q and R such that PQ = 12 cm and PR = 19.2 cm.The length of AB (in cm) is : 

A. 14.2 

B. 15.2 

C. 15.8 

D. 14.4 

Answer: D. 

Explanation: 

Q. 61 A boat can go 3.6 km upstream and 5.4 km downstream in 54 minutes, while it can go 5.4 km upstream and 3.6 km downstream in 58.5 minutes. The time (in minutes) taken by the boat in going 10 km downstream is: 

A. 48 

B. 50 

C. 45 

D. 54 

Answer: B. 

Explanation: 

Let the speed of speed of stream be u and speed of boat in still water be v. 

Speed of boat in upstream = u – v 

Speed of boat in downstream = u + v 

A boat can go 3.6 km upstream and 5.4 km downstream in 54 minutes so, 

Time = distance/speed 

3.6/(u – v) + 5.4/(u + v) = 54/60 

3.6/(u – v) + 5.4/(u + v) = 9/10 

36/(u – v) + 54/(u + v) = 9

4(u + v) + 6(u – v) = u2 – v2 

10u – 2v = u2 – v2 —(1) 

Boat can go 5.4 km upstream and 3.6 km downstream in 58.5 minutes so, 

5.4/(u – v) + 3.6/(u + v) = 58.5/60 

54/(u – v) + 36/(u + v) = 585/60 

6/(u – v) + 4/(u + v) = 13/12

72(u + v) + 48(u – v) = 13(u2 – v2

120u + 24v = 13(u2 – v2

Put the value of eq(1), 

120u + 24v = 13 × (10u – 2v) 

120u + 24v = 130u – 26v 

10u = 50v 

u = 5v —(2) 

put the value of u in eq(1), 

50v – 2v = 25v2 – v2 

48v = 24v2 

v = 2 

put the value of v in eq(2), 

u = 5 × 2 = 10 

Speed of boat in downstream = u + v = 10 + 2 = 12 

The time taken by the boat in going 10 km downstream = distance/speed = 10/12 hours = 60  × 10/12 = 50 min 

Q. 62 If 5cosθ – 12sinθ = 0, then what is the value of (1 + sinθ + cosθ)/(1-sinθ + cosθ

A. 5/4 

B. 3/2 

C. 3/4 

D. 5/2 

Answer: B. 

Explanation: 

5cosθ – 12sinθ = 0

tan θ =5/12 

We know that tanθ = perpendicular/base 

so, 

By the triplet 5-12-13, 

Hypotenuse = 13 

sin  θ = 5/13 

cos  θ= 12/13 

(1 + sin  θ + cos  θ)/(1 – sin  θ + cos θ

= (1 + 5/13 + 12/13)/(1 – 5/13 + 12/13)

= 30/20=3/2

Q. 63 The given table represents the sale (in thousands) of cars by four companies A, B, C and D in six years. Study the table and answer the question that follows. 

The total number of cars sold by companies A in 2017 and C in 2013 is what percentage of the total number of cars sold by all four companies in 2013 and 2016? (correct to one decimal place) 

A. 23.8 

B. 24.2 

C. 25.6 

D. 23.3 

Answer: D. 

Explanation: 

The total number of cars sold by companies A in 2017 and C in 2013 = 52 + 65 = 117 

The total number of cars sold by all four companies in 2013 = 45 + 63 + 65 + 67 = 240 

The total number of cars sold by all four companies in 2016 = 72 + 58 + 70 + 63 = 263 

The total number of cars sold by all four companies in 2013 and 2016 = 240 + 263 = 503 

Required percentage = 117/503 × 100 = 23.26% ~ 23.3% 

Q. 64 If 11sin2θ – cos2θ + 4sin θ – 4 = 0, 00<   θ < 900, then what is the value of (cos 2θ + cot 2θ) / (sec 2θ – tan 2θ)

A. (12+7√3)/6 

B. (12+5√3)/3 

C. (10+5√3)/3 

D. (10+7√3)/6 

Answer: A. 

Explanation: 

11sin2θ – cos2θ + 4sinθ – 4 = 0 

11sin2θ – (1-sin2θ) + 4sinθ – 4 = 0 

12sin2θ + 4sinθ – 5 = 0 

12sin2θ + 10sinθ –6sinθ – 5 = 0 

2sinθ (6sinθ+5)−1(6sinθ+5)= 0

(2sinθ −1) (6sinθ+5) = 0

For  00<   θ < 900

sinθ= ½

θ = 300

(cos 2θ + cot 2θ) / (sec 2θ – tan 2θ

On putting the value of θ

Q. 65 If the radius of a right circular cylinder is decreased by 10%, and the height is increased by 20%, then the percentage increase/decrease in its volume is: 

A. increase by 2.8% 

B. decrease by 1.8% 

C. increase by 1.8% 

D. decrease quadrilateral by in 2.8% 

Answer: D. 

Explanation: 

Volume of right circular cylinder = π r2

Radius of a right circular cylinder is decreased by 10%, and the height is increased by 20% so, 

r1 = r × 90/100 = 0.9r 

h1 = h × 120/100 = 1.2h 

Volume of new right circular cylinder =π r12h1 = π (0.9r)2(1.2h) = 0.972 π r2

Decrements in volume = π r2h – 0.972π r2h = 0.028π r2

Percentage Decrements in volume = (0.028π r2h)/(π r2h) × 100 = 2.8% 

Q. 66 ABCD is a cyclic quadrilateral which sides AD and BC are produced to meet at P, and sides DC and AB meet at Q when produced. If ∠A = 600 and ∠ABC = 720,then ∠PDC – ∠DPC = ? 

A. 240

B. 300 

C. 360 

D. 400 

Answer: A. 

Explanation: 

In ΔABP, 

∠A + ∠ABC + ∠APB = 1800 

∠APB = 1800 – 600 – 720 = 480 

∠ADC = 1800 – ABC = 1800 – 720 = 1080 

∠PDC = 1800 – ∠ADC = 1800 – 1080 = 720 

∠PDC – ∠DPC = 72 – 48 = 240 

Q. 67 The given table represents the sale (in thousands) of cars by four companies A, B, C and D in six years. Study the table and answer the question that follows. 

The Total number of cars sold by company C in 2018 exceeds the average number of cars sold by company A during 2014 to 2018 by: 

A. 15,000 

B. 14,000 

C. 16,000 

D. 12,000 

Answer: C. 

Explanation: 

Total number of cars sold by company C. in 2018 = 76000 

Total number of cars sold by company A during 2014 to 2018 = 52000 + 61000 + 72000 + 52000 + 63000 = 300000 

Average number of cars sold by company A during 2014 to 2018 = 300000/5 = 60000 

Required number = 76000 – 60000 = 16000 

Q. 68 A and B spend 60% and 75% of their incomes, respectively. If the savings of A are 20% more than that of B then by what percentage is the income of A less than the income of B? 

A. 15 

B. 20 

C. 10 

D. 25 

Answer: D. 

Explanation: 

Let the income of A. and B. be X and Y respectively. 

Saving of A = X – 60/100 × X = 0.4X 

Saving of B = Y – 75/100 × Y = 0.25Y 

If the savings of A are 20% more than that of B. then, 

Saving of A = 0.25Y × 120/100 = 3Y/10 

0.4X = 3Y/10 

4X = 3Y 

Ratio of income of A. and B. = 3 : 4 

Required percentage = (4 – 3)/4 × 100 = 25% 

Q. 69 The given table represents the sale (in thousands) of cars by four companies A, B, C and in six years. Study the table and answer the question that follows. 

The total number of cars sold by company B. during 2015, 2017 and 2018 is what percentage less than the total number of cars sold by company C. in 2013, 2015, 2017 and 2018? 

A. 16⅔  

B. 33⅓ 

C. 50 

D. 40 

Answer: B. 

Explanation: 

The total number of cars sold by company B during 2015, 2017 and 2018 = 60 + 53 + 67 = 180 

The total number of cars sold by company C in 2013, 2015, 2017 and 2018 = 65 + 66 + 63 + 76 = 270 

Required percentage = (270 – 180)/270 × 100 = 33⅓% 

Q. 70 To complete a certain task, X is 40 % more efficient than Y, and Z is 40% less efficient than Y. Working together, they can complete the task in 21 days. Y and Z together worked for 35 days. The remaining work will be completed by X alone in: 

A. 8 days 

B. 4 days 

C. 6 days 

D. 5 days 

Answer: D. 

Explanation: 

Efficiency of X = 140% of Y = 1.4Y 

Efficiency of Z = 60% of Y = 0.6Y 

Efficiency of X, Y and Z = 1.4 : 1 : 0.6 = 7 : 5 : 3 

They can complete the task in 21 days so, 

Total work = sum of efficiency ratio × times = (7 + 5 + 3) × 21 = 315 

Y and Z together worked for 35 days so, 

Work done by Y and Z = (5 + 3) × 35 = 280 

Remaining work = 315 – 280 = 35 

Remaining work complete by X = work/efficiency = 35/7 = 5 days 

Q. 71 The given table represents the sale (in thousands) of cars by four companies A, B, C and D in six years. Study the table and answer the question that follows. 

What is the ratio of the total number of cars sold by companies A, B and D in 2017 to the total number of cars sold by all four companies in 2018? 

A. 3:4 

B. 6:13 

C. 9:14 

D. 18:23 

Answer: C. 

Explanation: 

The total number of cars sold by companies A, B and D in 2017 = 52 + 53 + 75 = 180 

The total number of cars sold by all four companies in 2018 = 63 + 67 + 76 + 74 = 280 

The ratio of the total number of cars sold by companies A, B and D in 2017 to the total number of cars sold by all four companies in 2018 = 180 : 280 = 9 : 14 

Q. 72 The value of is: 

A. 4⅓  

B. 5⅚ 

C. 4 5/12 

D. 5 5/12 

Answer: C. 

Explanation: 

=> 4 5/12 

Q. 73 In ΔPQR, PQ = 24 cm and Q = 580 S and T are the points on side PQ and PR, respectively, such that STR = 1220 and If PS = 14 cm and PT = 12 cm, then the length of RT is : 

A. 14.8 cm 

B. 16 cm 

C. 15 cm 

D. 16.4 cm 

Answer: B. 

Explanation: 

∠PTS + ∠ STR = 1800 

∠PTS = 180 – 122 = 580 

∠P is a common angle. 

Δ PQR and ∠PTS are similar triangle. SO, 

PT/PQ = PS/PR 

12/24 = 14/PR 

PR = 28 cm 

RT = PR – PT = 28 – 12 = 16 cm 

Q. 74 If then the value of xy is : 

A.

B. 10 

C.

D.

Answer: A. 

Explanation: 

Q. 75 If 20x2 — 30x + 1 = 0, then what is the value of 25x2+1/16x2 

A. 58¾  

B. 53¾ 

C. 53½   

D. 58½ 

Answer: B. 

Explanation: 

English Comprehension 

Instructions 

For the following questions answer them individually 

Q. 76 Select the correctly spelt word. 

A. Beaureacracy 

B.  Recrutment 

C. Reimbursement 

D. Surveliance 

Answer: C. 

Q. 77 Select the appropriate meaning of the given idiom. 

To take the bull by the horns 

A. To speak arrogantly 

B. To murder someone 

C. To surrender to the enemy 

D. To handle difficulties 

Answer: D. 

Q. 78 Given below are four jumbled sentences. Select the option that gives their correct order. 

A. Although I had a fear of water, I thought it was an important skill I should learn. 

B. However, what I didn’t realize was that it would also make me a more confident person. 

C. I also thought it would be a good exercise that would make me physically stronger. 

D. One of the hardest things I’ve had to do was to learn how to swim. 

A. DCBA 

B. ACDB 

C. DACB 

D. BADC 

Answer: C. 

Q. 79 Select the correctly spelt word 

A. Definition 

B. Competiter 

C. Proliferete 

D. Beneficiery 

Answer: A. 

Q. 80 Select the correct synonym of the given word. 

Erudite 

A. Learned 

B. Strong 

C. Fashionable 

D. Illiterate 

Answer: A. 

Q. 81 Select the passive form of the given sentence. 

They are constructing a residential youth hostel. 

A. A residential youth hostel is constructed by them 

B. A residential youth hostel was constructed by them. 

C. A residential youth hostel has been constructed by them 

D. A residential youth hostel is being constructed by them 

Answer: D. 

Instructions 

In the following passage some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each blank. 

Comprehension: 

Drug addiction is the continued use of a particular drug (1)______ harmful consequences. Drug addiction not only affects an individual’s health and relationship, but also (2)______ the society and the environment. Prevention of a particular list of drugs can be possible by (3)______ their sale without a prescription. Drug addicts should be given proper medical treatment and (4)______ facilities. Motivational and awareness camps should be organized to scale down the consumption (5)______ drugs. 

Q. 82 Select the most appropriate option for blank No. 1 

A. despite of 

B. though 

C. in spite 

D. despite 

Answer: D. 

Q. 83 Select the most appropriate option for blank No. 2 

A. .imparts 

B. impacts 

C. reflects 

D. reduces 

Answer: B. 

Q. 84 Select the most appropriate option for blank No. 3 

A. conducting 

B. restricting 

C. performing 

D. promoting 

Answer: B. 

Q. 85 Select the most appropriate option for blank No. 4 

A. regeneration 

B. resignation 

C. rehabilitation 

D. regression 

Answer: C. 

Q. 86 Select the most appropriate option for blank No. 5 

A. for 

B. of 

C. from 

D. by 

Answer: B. 

Instructions 

For the following questions answer them individually 

Q. 87 Select the correct antonym of the given word. 

Allure 

A. Revive 

B. Rewind 

C. Repulse 

D. Attract 

Answer: C. 

Q. 88 Select the word which means the same as the groups of words given. 

A. long and aggressive speech 

A. Harangue 

B. Eloquence 

C. Prologue 

D. Discussion 

Answer: A. 

Q. 89 Select the word which means the same as the groups of words given. 

The school or college in which one has been educated 

A. Alma mater 

B. Alumni 

C. Graduate 

D. Mentor 

Answer: A. 

Q. 90 Given below are four jumbled sentences. Select the option that gives their correct order. 

A. During the celebration, many people display a set of ornamental dolls known as ‘Hina’ dolls. 

B. Hinamatsuri is a celebration of the girls in Japan wishing them a bright future. 

C. These royal-looking dolls are dressed in the clothing of the Heian period. 

D. These dolls represent the Emperor, Empress and other royal representatives. 

A. CDBA 

B. ACBD 

C. DBAC 

D. BADC 

Answer: D. 

Q. 91 In the sentence identify the segment which contains the grammatical error. 

The old man did not wanted to eat any food. 

A. to eat 

B. did not wanted 

C. any food 

D. The old man 

Answer: B. 

Q. 92 Select the most appropriate word to fill in the blank. 

All students should express their ______ views in the group discussion without any fear 

A. outspoken 

B. guarded 

C. candid 

D. secluded 

Answer: C. 

Q. 93 Select the most appropriate word to fill in the blank. 

All his endeavors to win his teacher’s favour proved ______ and did not bring the desired results. 

A. perpetual 

B. futile 

C. apparent 

D. prosperous 

Answer: B. 

Q. 94 In the sentence identify the segment which contains the grammatical error. 

No least than fifty participants were present for the singing competition. 

A. No least than 

B. the singing competition 

C. fifty participants wer 

D. present for 

Answer: A. 

Q. 95 Select the correct antonym of the given word. 

Bizarre 

A. Strange 

B. Usual 

C. Happy 

D. Weird 

Answer: B. 

Q. 96 Select the most appropriate option to substitute the underlined segment in the given sentence. If no substitution is required, select No improvement. 

Many of a students were not shortlisted for the personal interview 

A. No improvement 

B. Many of students 

C. The many student 

D. Many of the students 

Answer: D. 

Q. 97 Select the appropriate meaning of the given idiom. 

To flog a dead horse 

A. To waste the efforts 

B. To accept the challenge 

C. To complete the work 

D. To make the best use of resources 

Answer: A. 

Q. 98 Select the most appropriate option to substitute the underlined segment in the given sentence. If no substitution is required, select No improvement. 

When I was working in a software company, it was mandatory to register my legally as an authorized software developer. 

A. register me legal 

B. register myself legally 

C. register mine legally 

D. No improvement 

Answer: B. 

Q. 99 Select the correct indirect form of the given sentence. 

“Hello”, he said to his friend. “What can I do for you?”” 

A. He said hello and asked his friend what can do for him 

B. He asked and greeted his friend that what he can do for him 

C. He greeted his friend and asked what he could do for him 

D. He told hello and asked his friend what he could do for him 

Answer: C. 

Q. 100 Select the correct synonym of the given word. 

Violent 

A. Kind 

B. Mild 

C. Calm 

D. Aggressive 

Answer: D. 

SSC CGL Tier-I 05 March 2020 Shift-I Previous Year Paper

SSC CGL Tier-I Exam 05 March 2020

Q. 1 Select the option that is related to the third number in the same way as the second number is related to the first number and the sixth number is related to the fifth number. 

72 : 108 :: 84 : ? :: 102 : 153 

A. 144 

B. 126 

C. 117 

D. 135 

Answer: B. 

Explanation: 

72 + 72/2 = 72 + 36 = 108 

102 + 102/2 = 102 + 51 = 153 

Similarly, 

84 + 84/2 = 84 + 42 = 126 

∴ The correct answer is option B. 

 

Q. 2 Shaan has a total of ₹5,500 with him. He buys product ‘Z’ at ₹5,000 from this sum and then sells it to another person, thus making a profit of 15% onit. With all the money he has now, he buys product ‘X’ and then sells it to another person making a profit of 25% onit. What is the total money Shaan has now? 

A. ₹7,812.50 

B. ₹7,815.50 

C. ₹6,325.50 

D. ₹7,187.50 

Answer: A. 

Explanation: 

Cost price of product ‘Z’ = 5000 

Profit = 15% 

Selling price = 5000×115/100= 5750 

Cost price of product ‘X’ = 5750 + 500 = 6250 

Profit = 25% 

Selling price = 6250×125/100 = 7812.5 

Shaan has rs. 7812.5. 

∴ The correct answer is option A. 

 

Q. 3 Select the option figure in which the given figure is embedded (rotation is NOT allowed).

Answer: B. 

Q. 4 Select the letter-cluster that can replace the question mark (?) in the following series. aYd, fTi, kOn, pJs, ? 

A. VeX 

B. uEw 

C. uFw 

D. uEx 

Answer: D. 

Explanation: 

so, next letter-cluster is ‘uJx’. 

∴ The correct answer is option D. 

Q. 5 Four Letter-clusters have been given, out of which three are alike in some manner, while one is different. Select the odd letter-cluster. 

A. TVW 

B. FHJ 

C. LNP 

D. DFH 

Answer: A. 

Explanation: 

Except option A. remaining all options have the difference of 1 in each letter. 

So, ‘TVW’ is odd. 

∴ The correct answer is option A. 

Q. 6 Select the option in which the words share the same relationship as that shared by the given pair of words. 

Blunder : Error 

A. Euphoria : Happiness 

B. War : Peace 

C. Speak : Hear 

D. Anger : Rage 

Answer: A. 

Explanation: 

Blunder is similar to error. 

Similarly, 

Euphoria is similar to happiness. 

∴ The correct answer is option A. 

Q. 7 Arrange the following in a logical sequence from small to big. 

1. Crocodile 

2. Lizard 

3. Whale 

4. Housefly 

5. Monkey 

A. 4, 3, 2, 1, 5 

B. 3, 5, 4, 1, 2 

C. 4, 2, 5, 1, 3 

D. 4, 5, 2, 1, 3 

Answer: C. 

Explanation: 

Sequence from small to big, 

Housefly, Lizard, Monkey, Crocodile, Whale 

∴ The correct answer is option C. 

Q. 8 Four words have been given, out of which three are alike in some manner, while one is different. Select the odd word. 

A. Plenty 

B. Indigence 

C. Destitution 

D. Penury 

Answer: A. 

Explanation: 

Except the ‘Plenty’ remaining all have similar meaning. 

∴ The correct answer is option A. 

Q. 9 Select the option in which the numbers are related in the same way as are the numbers in the given set. 

(13, 65, 117) 

A. (15, 75, 135) 

B. (12, 55, 109) 

C. (14, 70, 127) 

D. (17, 85, 163) 

Answer: A. 

Explanation: 

13×5 = 65 

13×9 = 117 

Similarly, 

15×5 = 75 

15×9 = 135 

∴ The correct answer is option A. 

Q. 10 Four positions of the same dice are shown. Select the number that will be on the face opposite to the one showing ‘3’.

A.

B.

C.

D.

Answer: B. 

Q. 11 Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow from the statements. 

Statements: 

1. All parakeets are cuckoos. 

2. All cuckoos are rabbits. 

3. All rabbits are snakes. 

Conclusions: 

I. All parakeets are snakes. 

II. All snakes are cuckoos. 

III. All rabbits are parakeets. 

IV. All cuckoos are snakes. 

A. Only conclusions II and III follow. 

B. Only conclusions I and II follow. 

C. Only conclusions I and IV follow. 

D. All the conclusions follow. 

Answer: C. 

Explanation: 

From the Venn diagram, 

Only conclusions I and IV follow. 

∴ The correct answer is option C. 

Q. 12 Four number-pairs have been given, out of which three are alike in some manner and one is different. Select the number-pair that is different. 

A. 169-197 

B. 121-145 

C. 289-325 

D. 225-241 

Answer: D. 

Explanation: 

In 169 – 197, 

  (13)2 = 169 

(14)2 + 1 = 196 + 1 = 197

In 121-145, 

(11)2 = 121 

(12)2 + 1 = 144 + 1 = 145 

In 289-325, 

(17)2 = 289 

(18)2 + 1 = 324 + 1 = 325 

In 225-241 

(15)2  = 225 

(16)2 − 15 = 256 – 15 = 241 

∴The correct answer is option D. 

Q. 13 If each letter of the English alphabet is assigned an odd numerical value in increasing order, such as A = 1, B = 3 and so on, then what will be the code of HONEY? 

A. 132725747 

B. 152927949 

C. 132725745 

D. 152927947 

Answer: B. 

Explanation: 

H = 8 + 7 = 15 

O = 15 + 14 = 29 

N = 14 + 13 = 27 

E = 4 + 5 = 9 

Y = 25 + 24 = 49 

So, Code for ‘HONEY” = 152927949 

∴ The correct answer is option B. 

Q. 14 Select the number that can replace the question mark (?) in the following series. 

40, 37, 43, 34, 46, ? 

A. 31 

B. 41 

C. 51 

D. 61 

Answer: A. 

Explanation: 

The series follows the pattern as, 

40 – 3 = 37 

37 + 6 = 43 

43 – 9 = 34 

34 + 12 = 46 

46 – 15 = 31 

∴ The correct answer is option A. 

Q. 15 Which of the option figures is the exact mirror image of the given figure when the mirror is held at the right side?

A.

B.

C.

D.

Answer: D. 

Q. 16 Select the option that is related to the third word in the same way as the second word is related to the first word. Ministers : Council :: Sailors : ? 

A. Sea 

B. Ship 

C. Captain 

D. Crew 

Answer: D. 

Explanation: 

As ministers is related to council similarly, 

Sailors are related to crew. 

∴ The correct answer is option D. 

Q. 17 The sequence of folding a piece of paper and the manner in which the folded paper has been cut is shown in the following figures. How would this paper look when unfolded? 

Answer: B. 

Q. 18 

Study the given pattern carefully and select the number that can replace the question mark (?) in it. 

A.

B.

C.

D.

Answer: C. 

Explanation: 

(10×14) ÷ 35 = 140/35 = 4 

(15 ×5) ÷ 25= 75/25 = 3 

(14 ×6) ÷ 12 = 84/12 = 7 

(18 ×8) ÷ 16= 144/16 = 9 

∴ The correct answer is option C. 

Q. 19 How many triangles are present in the given figure? 

A. 22 

B. 20 

C. 23 

D. 21 

Answer: C. 

Q. 20 There is a family of five members: K, L, M,N and O. Among them,there is one married couple. O is unmarried and is the brother of K. is the sister of O. M is the only married female and the mother of N. L and O are the only males in the group. Who is the father of K? 

A.

B.

C.

D.

Answer: B. 

Explanation: 

In the diagram, circle shows the female, the square shows the male, vertical line son the generation, horizontal line shows the brother/sister and double horizontal lines show the couple. 

From the diagram, L is the father of K. 

∴ The correct answer is option B. 

Q. 21 Select the figure that can replace the question mark (?) in the following series. 

Answer: C. 

Q. 22 In the given Venn diagram,the triangle represents students playing table tennis, the rectangle represents students playing badminton, the circle represents female students, and the pentagon represents students playing football. The numbers given in the diagram represent the number of persons in that particular category. 

How many female students play both table tennis and badminton? 

A. 22 

B. 18 

C.

D.

Answer: C. 

Q. 23 The two given expressions on both the side of the ‘=’ sign will have the same value if two numbers from either side or both side are interchanged. Select the correct numbers to be interchanged from the given options. 

3 + 5 × 4 − 24 ÷ 3 = 7 × 4 − 3 + 36 ÷ 6 

A. 6, 3 

B. 5, 7 

C. 4, 7 

D. 24, 36 

Answer: B. 

Explanation: 

3 + 5 × 4 − 24 ÷ 3 = 7 × 4 − 3 + 36 ÷ 6 

From option B, 

On interchanging 5 and 7, 

3 + 7 × 4 − 24 ÷ 3 = 5 × 4 − 3 + 36 ÷ 6 

3 + 28 − 8 = 20 − 3 + 6 

23 = 23 

∴ The correct answer is option B. 

Q. 24 Select the set of letters that when sequentially placed in the blanks of the given letter series will complete the series.

f_hg_fh_gf_hg_fh_g 

A. f, g, h, f, g, h 

B. g, h, f, g, h, f 

C. g, f, g, f, h, f 

D. h, f, g, h, f, g 

Answer: B. 

Explanation: 

Sequence, 

fghghf/hfgfgh/ghfhfg 

∴ The correct answer is option B. 

Q. 25 In certain code languages. U is written as C, K is written as H, L is written as U, N is written as E, S is written as L, E is written as K, and C. is written as N. How will ‘KNUCKLES’ be written as in that language? 

A. KECNKUHL 

B. CHUECKN 

C. HECNHUKL 

D. HECNHULK 

Answer: C. 

Explanation: 

‘KNUCKLES’ is written as ‘HECNHUKL’. 

∴ The correct answer is option C. 

General Awareness 

Instructions 

For the following questions answer them individually 

Q. 26 Pongal festival is celebrated for four days in Tamil Nadu. What is the fourth day of Pongal called? 

A. Thai Pongal 

B. Kaanum Pongal 

C. Bhogi Pongal 

D. Mattu Pongal 

Answer: B. 

Q. 27 Name the law in Physics which states that equal volume of all gases under the same conditions of temperature and pressure contain equal number of molecules. 

A. Avogadro’s Law 

B. Boyles’s Law 

C. Charles’s Law 

D. Ohm’s Law 

Answer: A. 

Q. 28 Which of the following rivers flows through Tiruttani a famous pilgrimage place of South India? 

A. Nandi 

B. Kaveri 

C. Palar 

D. Vaigai 

Answer: A. 

Q. 29 In which year was the Nahargarh Fort in Jaipur built by Maharaja Sawai Jai Singh II ? 

A. 1800 

B. 1734 

C. 1805 

D. 1780 

Answer: B. 

Q. 30 As per the government rules, how much percentage of advance tax needs to be paid by 15th June by an individual who is liable to pay advance tax? 

A. 10% 

B. 25% 

C. 15% 

D. 30% 

Answer: C. 

Q. 31 Which dynasty built the pancha rathas of Mahabalipuram? 

A. Satavahana 

B. Pallava 

C. Chola 

D. Chera 

Answer: B. 

Q. 32 In which of the following locations was the Quit India Movement launched by Mahatma Gandhi in 1942? 

A. August Kranti Maidan 

B. Shivaji Park 

C. Pragati Maidan 

D. Jallianwala Bagh 

Answer: A. 

Q. 33 What was the theme of the 107th Indian Science Congress held in Bengaluru? 

A. Science and Technology: Rural Development 

B. Reaching the Unreached through Science and Technology 

C. Future India : Science and Technology 

D. Science and Technology for National Development 

Answer: A. 

Q. 34 The researchers of which academic institution employed the nanoscale phenomenon called ‘Electrokinetic streaming potential’ to harvest energy from flowing water on a small scale like water flowing through household water taps? 

A. IIT Guwahati 

B. IIT Delhi 

C. IIT Bombay 

D. IIT Madras 

Answer: A. 

Q. 35 In January 2020, B Sai Deepak set a Guinness World Record for most side lunges in 60 seconds. How many lunges did he do? 

A. 50 

B. 40 

C. 30 

D. 59 

Answer: D. 

Q. 36 Which National Park among the following is the largest protected area in the Eastern Himalayan sub-region? 

A. Jim Corbett National Park 

B. Namdapha National Park 

C. Keibul Lamjao National Park 

D. Bandipur National Park 

Answer: B. 

Q. 37 Chiropody is a branch of science related to which part of the body? 

A. Liver 

B. Kidney 

C. Feet 

D. Lungs 

Answer: C. 

Q. 38 G. Babita Rayudu took charge as an Executive Director for which of the following organisations in January 2020? 

A. The Securities and Exchange Board of India 

B. Insurance Regulatory and Development Authority of India 

C. Small Industries Development Bank of India 

D. Bombay Stock Exchange 

Answer: A. 

Q. 39 Which is the first Indian company to hit the ₹10 lakh crore mark in market capitalisation? 

A. HDFC. Bank 

B. ICICI Bank 

C. Tata Consultancy Services 

D. Reliance Industries 

Answer: D. 

Q. 40 The 23rd National Youth Festival (NYF) 2020 was celebrated in Lucknow to commemorate the birth anniversary of ______. 

A. Jawaharlal Nehru 

B. Sardar Vallabhbhai Patel 

C. Swami Vivekananda 

D. Mahatma Gandhi 

Answer: C. 

Q. 41 The Indian Railways has integrated its helpline numbers into a single number. What is the number? 

A. 139 

B. 145 

C. 150 

D. 160 

Answer: A. 

Q. 42 The police of which state was honoured with the President’s Colours award in December 2019? 

A. Maharashtra 

B. Kerala 

C. Tamil Nadu 

D. Gujarat 

Answer: D. 

Q. 43 In which year was the Currency Building in the BBD. Bagh or Dalhousie area of Kolkata constructed? 

A. 1833 

B. 1910 

C. 1850 

D. 1900 

Answer: A. 

Q. 44 In terms of area, which state has the largest forest cover in India? 

A. Maharashtra 

B. Odisha 

C. Madhya Pradesh 

D. Kerala 

Answer: C. 

Q. 45 VISHWAS, which is a major e-governance initiative launched by the government in January 2020, is the acronym for which of the following? 

A. Video Interface and State Wide Advanced Security 

B. Video Integration and System Wide Advanced Security 

C. Video Integration and State Wide Advanced Security 

D. Video Integration and State Wide Advanced System 

Answer: C. 

Q. 46 What is the colour of the light emitted by the Sun? 

A. Red 

B. White 

C. Orange 

D. Yellow 

Answer: B. 

Q. 47 The famous 11-day long ‘Dhanu Jatra’, considered as the largest open-air theatre of the world is celebrated in which state? 

A. Meghalaya 

B. Assam 

C. Odisha 

D. Manipur 

Answer: C. 

Q. 48 Which district has been awarded the Plastic Waste Management Award – 2020 for being the best district of India in the plastic waste management category during Swachhta Hi Seva 2019? 

A. Hojai 

B. Majuli 

C. Dibrugarh 

D. Jorhat 

Answer: C. 

Q. 49 Jasprit Bumrah has been selected to receive which of the following awards for his performance in international cricket in the 2018- 19 season? 

A. C.K. Nayudu 

B. Polly Umrigar 

C. M.A. Chidambaram 

D. Madhavrao Scindia 

Answer: B. 

Q. 50 Ishwar Sharma has been honoured with the Global Child Prodigy Award 2020. What is this award associated with? 

A. Sports 

B. Yoga 

C. Science 

D. Literature 

Answer: B. 

Quantitative Aptitude 

Instructions 

For the following questions answer them individually 

Q. 51 In an examination in which the full marks were 500, A scored 25% more marks than B, B scored 60% more marks than C and C scored 20% less marks than D. If A scored 80% marks, then the percentage of marks obtained by is: 

A. 65% 

B. 60% 

C. 50% 

D. 54% 

Answer: C. 

Q. 52 The given table represents the exports (in ₹crores) of four items A, B, C and D over a period of six years. Study the table and answer the question that follows. 

In which year, the exports of item D were 1.4 times the average exports of item B during six years? 

A. 2013 

B. 2012 

C. 2011 

D. 2014 

Answer: A. 

Explanation: 

Average exports of item B. during six years ={128 + 134 + 138 + 169 + 182 + 209}/6 

(Average = sum of the terms/no. of terms) 

= 960/6 = 160 

1.4 times the average exports of item B. during six years = 1.4×160 = 224 

In 2013, the exports of item D were 1.4 times the average exports of item B during six years. 

Q. 53 If x2 − 2√5x + 1 = 0, then what is the value of x5 + 1/x5

A. 610√5

B. 406√5

C. 408√5

D. 612√5

Answer: A. 

Explanation: 

x2 − 2√5x + 1 = 0 Divide by x, 

x − 2√5 + 1/x = 0 

x + 1/x = 2√5  —(1)

(x +1/x)2  = (2√5)2

x2 + (1/x)2 + 2 = 20

x2 + (1/x)2 = 18 —-(2)

From eq(1), 

(x +1/x)3  = (2√5)3

x3 + (1/x)3 + 3(x +1/x) = 40√5

x3 + (1/x)3 = 40√5 – 3(2√5)

x3 + (1/x)3 = 34√5

From eq(2) and (3), 

{x2 + (1/x)2}{x3 + (1/x)3}=(18) (34√5)

x5 + 1/x + x 1/x5 = 612√5

x5 + 1/x5 = 612√5 – 2√5 = 610√5

Q. 54 Sudha sold an article to Renu for ₹576 at a loss of 20%. Renu spent a sum of ₹224 on its transportation and sold it to Raghu at a price which would have given Sudha profit of 24%. The percentage of gain for Renu is: 

A. 13.2% 

B. 10.5% 

C. 12.9% 

D. 11.6% 

Answer: D. 

Explanation: 

Cost price for Sudha = 576/80 ×100 = 720 

Cost price for Renu = 576 

Final cost price for Renu = 576 + 224 = 800 

Selling price for Renu = 24% profit of sudha 

= 720 × 124/100 = 892.8 

Profit for Renu = 892.8 -800 = 92.8 

The percentage of gain for Renu = 92.8 / 800 ×100 = 11.6% 

Q. 55 If the nine-digit number 708x6y8z9 is divisible by 99, then what is the value of x + y + z? 

A.

B. 27 

C. 16 

D.

Answer: C. 

Explanation: 

To be divisible by 99, the number has to be divisible by 11 and 9 both. 

For divisibility by 11, 

7 + 8 + 6 + 8 + 9 – 0 + x + y + z 

(38 – x + y + z) has to be divisible by 11. 

For divisibility by 9, 

(38 + x + y + z) has to be divisible by 9. 

By option C), 

x + y + z = 16 

(38 – x + y + z) = 38 – 16 = 22 is divisible by 11. 

(38 + x + y + z) = 38 + 16 = 54 is divisible by 9. 

Q. 56 The ratio of the ages ofA. and B, 8 years ago, was 2 : 3. Four years ago,the ratio of their ages was 5 : 7. What will be the ratio of their ages 8 years from now? 

A. 4 : 5 

B. 5 : 6 

C. 7 : 8 

D. 3 : 4 

Answer: A. 

Explanation: 

8 years ago the ratio of the ages of A and B = 2 : 3 

Let the 8 years ago ages of A and B be 2x and 3x respectively. 

4 years age of A = 2x + 4 

4 years age of B = 3x + 4 

Four years ago,the ratio of their ages = 5 : 7 

(2x+4)/(3x+4) = 5/7

14x + 28 = 15x + 20 

x = 8 

8 years from now, Age of A = 2x + 16 = 2×8 + 16 = 32 

8 years from now, Age of B = 3x + 16 = 3×8 + 16 = 40 

Ratio of their ages 8 years from now = 32 : 40 = 4 : 5 

Instructions 

The given table represents the exports (in ₹crores) of four items A, B, C and D over a period of six years. Study the table and answer the question that follows. 

Q. 57 The total exports of item A. from 2012 to 2014 is what percentage less than the total exports of all the four items in 2015? (Correct to one decimal place) 

A. 16.7% 

B. 15.2% 

C. 14.3% 

D. 13.8% 

Answer: C. 

Explanation: 

The total exports of item A. from 2012 to 2014 = 225 + 370 + 425 = 1020 

The total exports of all the four items in 2015 = 400 + 209 + 306 + 275 = 1190 

Required percentage =(1190−1020)/ 1190×100 =170/ 1190×100 

= 14.28%≈14.3% 

Q. 58 What is the ratio of the total exports of item A in 2014 and 2015 to the total exports of item C in 2011 and 2015? 

A. 7 : 5 

B. 3 : 2 

C. 4 : 3 

D. 5 : 4 

Answer: B. 

Explanation: 

Total exports of item A. in 2014 and 2015 = 425 + 400 = 825 

Total exports of item C. in 2011 and 2015 = 244 + 306 = 550 

Ratio of the total exports of item A. in 2014 and 2015 to the total exports of item C. in 2011 and 2015 = 825 : 550 = 3 : 2 

Instructions 

For the following questions answer them individually 

Q. 59 The average of 24 numbers is 56. The average of the first 10 numbers is 71.7 and that of the next 11 numbers is 42. The next three ½ :⅓ :5/12 numbers (i.e. 22nd , 23nd, and 24th ) are in the ratio . What is the average of the numbers 22nd and  24th

A. 58 

B. 49.5 

C. 55 

D. 60.5 

Answer: D. 

Explanation: 

The average of 24 numbers = 56 

Sum of the numbers = 56×24 = 1344 

The average of the first 10 numbers = 71.7 

Sum of the first 10 numbers = 71.7×10 = 717 

The average of the next 11 numbers = 42 

Sum of the next 11 numbers = 42×11 = 462 

Ratio of the next three numbers (i.e.22nd , 23nd, and 24th ) = ½ :⅓ :5/12

Sum of next three numbers (i.e., and ) = 1344 – 717 – 462 = 165 

Q. 60 If , then what is the value of (P ÷ Q) × R

A. 2(x2 + y2)

B. x2 + y2

C. 4xy

D. 2xy 

Answer: A. 

Explanation: 

(P ÷ Q) ×

Q. 61 A shopkeeper bought 80 kg of rice at a discount of 10%. Besides 1 kg rice was offered free to him on the purchase of every 20 kg rice. If he sells the rice at the marked price, his profit percentage will be: 

A. 16⅔%

B. 15⅓ % 

C. 153/7 %

D. 142/7 %

Answer: A. 

Explanation: 

Let the Price of 1 kg rice be Rs.1. 

Total rice bought = 80 kg 

He offered 1 kg rice free on the purchase of every 20 kg rice. Free rice = 80/20 = 4 kg 

Rate of 80 kg rice = Rs.80 

Discount = 10% 

Cost price of rice for shopkeeper = 80×90/100= Rs.72 Selling price of rice for shopkeeper = 80 + 4 = Rs.84 Profit = 84 – 72 = Rs. 12 

 Profit percentage = 12/72×100 =16⅔  % 

Q. 62 D is the mid point of side BC of ABC. Point E lies on AC such that CE =⅓AC. BE and AD. intersect at G. What is AG/GD

A. 5 : 2 

B. 8 : 3 

C. 3 : 1 

D. 4 : 1 

Answer: D. 

Explanation: 

D is mid point of BC. 

To apply the mid poingt theorem in ADM, 

Q. 63 Two chords AB and CD of a circle with centre O intersect each other at P. If BOC = 70and AOD = 100, then APC is: 

A. 95

B. 70

C. 65

D. 55

Answer: A. 

Explanation: 

Q. 64 A train takes hours less for a journey of 300 km, if its speed is increased by 20 km/h from its usual speed. How much time will it take to cover a distance of 192 km at its usual speed? 

A. 3 hours 

B. 2.4 hours 

C. 4.8 hours 

D. 6 hours 

Answer: C. 

Explanation: 

Let the usual speed of the train be x km/hr. 

Distance = 300 km 

Time = 2½  hours = 5/2 hr = 2.5 hr 

Time = distance/speed 

According to question, 

300/x – 300(x + 20) = 2.5 

(x + 20)×120 – 120x = x(x + 20) 

120x + 2400 – 120x = x2 + 20x 

x2 + 20x – 2400 = 0 

x2 + 60x – 40x – 2400 = 0 

x(x + 60) – 40(x + 60) = 0 

(x + 60)(x- 40) = 0

x = 40 

Distance = 192 km 

Time taken to cover distance by usually speed = 192/40 = 4.8 hours 

Q. 65 If 12cos2θ−2sin2θ+3cosθ=3, 0<θ<90, then what is the value of (cosecθ + secθ)/(tanθ + cotθ)? 

A. (4 +√3)/4 

B. (1 +2√2)/2 

C. (1 +√3)/2 

D. (2 +√3)/4 

Answer: C. 

Explanation: 

12cos2θ−2sin2θ+3cosθ=3 

12cos2θ−2(1-cos2θ)+3cosθ=3 

14cos2θ+3cosθ=5

Put the value of θ = 60

14cos2 60+3cos 60=5 

14×1/2 + 3 ×1/2 = 5 

5 = 5 

L.H.S. = R.H.S. 

Q. 66 If 16a4 + 36a2b2 + 81b4 = 91 and 4a2 + 9b2 – 6ab = 13, then what is the value of 3ab? 

A. 3/2 

B. -3 

C. 3/2 

D.

Answer: C. 

Explanation: 

4a2 + 9b2 – 6ab = 13 

(4a2 + 9b2 – 6ab)2 = (13)2 

[(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ac) ]

(4a2)2 + (9b2)2 + (6ab)2 +2(4a2.9b2 – 9b2.6ab – 6ab.4a2) = 169 

16a4 + 36a2b2 + 81b^4 + 2(36a2b2 – 54ab3 – 24a3b) = 169

91 + 2(36a2b2 – 54ab3 – 24a3b) = 169 

36a2b2 – 54ab3 – 24a2b = (169 – 91)/2 

36a2b2 – 54ab3 – 24a3b = 39 

6ab(6ab – 9b2 – 4a2) = 39

6ab(-13) = 39

6ab = -3 

3ab = -3/2 

Q. 67 In ΔABC, C = 90, AC= 5 cm and BC = 12 cm. The bisector of A meets BC at D. What is the length of AD? 

A. 2/3√13 cm

B. 4/3√13 cm 

C. 2√13 cm 

D. (5√13)/3 cm 

Answer: D. 

Explanation: 

By the Pythagoras theorem, 

(AB)2 = (AC)2 + (BC)2 

(AB)2 = (5)2 + (12)2 

(AB)2 = (5)2 + (12)2 

(AB)2 = 25 + 144 

AB = 13 cm 

By angle bisector theorem, 

(AB/BD) = AC/CD

Let CD be x cm. 

13/(12 – x) = 5/x 

13x = 60 – 5x 

x = 60/18 = 10/3 

In ΔACD, 

(AD)2 = (AC)2 + (CD)2 

(AD)2 = (5)2 + (10/3)2 

(AD)2 = 25 +100/9 

(AD)2 = 325/9

AD = 5√13/3 

Q. 68 The value of is: 

A. 3/4 

B. 2/3 

C. 1/2 

D.

Answer: B. 

Explanation: 

Q. 69 Sides AB and DC of cyclic quadrilateral ABCD are produced to meet at E, and sides AD and BC are produced to meet at F. If BAD = 102 and BEC = 38 then the difference between ADC and AFB is: 

A. 21 

B. 31

C. 22 

D. 23 

Answer: C. 

Explanation: 

In ΔADE, 

∠ADE=180  − (∠AED + ∠EAD) 

= 180 − (38 + 102

= 40 

⇒∠ADC = 40 

square ABCD. is a cyclic quadrilateral. 

∴∠DCB + ∠DAB=180 

⇒∠DCB = 180 − ∠DAB 

∠DCB = 180 − 102 

∠DCB = 78

In ΔDFC, 

∠DFC=180 – (∠FDC+∠FCD) 

∠DFC = 180 − (40 + 78

∠DFC = 180 − 118 

∠DFC = 62 

∠AFB = ∠DFC = 62 

Difference between ∠BAD and ∠AFB = 62 – 40 = 22 

Q. 70 If 5sinθ = 4, then the value of (secθ+4cotθ)/(4tanθ – 5cosθ) is: 

A. 3/2 

B.

C. 5/4 

D.

Answer: D. 

Explanation: 

5sinθ = 4 

sinθ = 4/5 

Perpendicular / hypotenuses = 4/5

By triplet 3-4-5, 

Base = 3 

cosθ = base/hypotenuses = 3/5

tanθ = perpendicular/base = 4/3 

(secθ + 4cotθ)/(4tanθ – 5cosθ) 

= (1/cosθ + 4/tanθ)/(4tanθ – 5cosθ) 

= [1/(3/5) + 4/(4/3)]/[4(4/3) – 5(3/5)]

= [(5/3)+5) / {4×(4/3) – 5×(3/5)}] 

= [(14/3) / {(16/3) – 3)}] 

= 14/7 = 2 

Q. 71 The diagonal of a square A is (a + b) units. What is the area (in square units) of the square drawn on the diagonal of square B whose area is twice the area of A? 

A. (a + b)2 

B. 4(a + b)2 

C. 8(a + b)2 

D. 2(a + b)2 

Answer: D. 

Explanation: 

Area of square A = (diagonal)2/2 = (a + b)2/2

Area of square B = 2 × area of square A = 2 × (a + b)2 /2 = (a + b)2

Side of B = a + b 

Diagonal of B = √(2side) = √2(a + b) 

Area (in square units) of the square drawn on the diagonal of square B = (side)2 = {√2(a+b)}2 = 2(a + b)2

Q. 72 The given table represents the exports (in ₹crores) of four items A, B, C and D over a period of six years. Study the table and answer the question that follows. 

The total exports of item D in 2010, 2012 and 2014 is what percentage of the total exports of all the four items in 2011 and 2012? 

A. 44.8% 

B. 44% 

C. 45% 

D. 46.2% 

Answer: B. 

Explanation: 

The total exports of item D. in 2010, 2012 and 2014 = 214 + 247 + 309 = 770 

The total exports of all the four items in 2011 and 2012 = 250 + 134 + 244 + 282 + 225 + 138 + 230 + 247 = 1750 

Required percentage = (770 / 1750) × 100 = 44% 

Q. 73 Pipes A and B can fill a tank in 10 hours and 40 hours, respectively. C is an outlet pipe attached to the tank. If all the three pipes are opened simultaneously, it takes 80 minutes more time than what A and B. together take to fill the tank. A and B are kept open for 7 hours and then closed and C was opened. C will now empty the tank in: 

A. 49 hours 

B. 38.5 hours 

C. 42 hours 

D. 45.5 hours 

Answer: A. 

Explanation: 

Let the total work be 40 units. 

(∵ L.C.M. of 10 and 40 is 40.) 

Efficiency of A = work/time = 40/10 = 4 units/hour 

Efficiency of B = 40/40 = 1 unit/hour 

Time time taken by pipe A and B = 40/(4 + 1) = 8 hours 

Time time taken by pipe C = 8 hours + 80/60 hours = 28/3 hours 

Efficiency of C = 40/(28/3) = 30/7 units/hour 

Work done by pipe A and B in 7 hours = (1 + 4) × 7 = 35 units 

Time taken by pipe C to empty the tank = 35/(30/7) = 8 5/7 

Q. 74 The compound interest on a certain sum at 16⅔% p.a. for 3 years is ₹6,350. What will be the simple interest on the same sum at the same rate for 5⅔ years? 

A. ₹10,200 

B. ₹11,400 

C. ₹7,620 

D. ₹9,600 

Answer: A. 

Explanation: 

Compound interest = 6350 

Rate(r) = 16⅔ %= (50/3)% 

Time(t) = 3 years 

Q. 75 The value of is: 

A. 2 6/7 

B. 2 2/9  

C. 3 4/7  

D. 10/21 

Answer: A. 

Explanation: 

English Comprehension 

Instructions 

For the following questions answer them individually 

Q. 76 In the sentence identify the segment which contains the grammatical error. 

Modern man is completely engross in the mad pursuit of material pleasures and luxuries. 

A. mad pursuit of 

B. material pleasures and luxuries 

C. Modern man is 

D. completely engross 

Answer: D. 

Q. 77 Select the correct passive form of the given sentence. 

They offered me a chair 

A. I offered a chair to them. 

B. A. chair was being offered to me. 

C. A. chair is offered to me by them. 

D. I was offered a chair by them. 

Answer: D. 

Q. 78 Select the most appropriate meaning of the given idiom 

A. bed of roses 

A. A pleasant perfume 

B. An easy and happy situation 

C. A difficult path 

D. A valley full of flowers 

Answer: B. 

Q. 79 Select the correct indirect form of the given sentence. 

“What a good idea!”, Seema remarked. 

A. Seema exclaimed that the idea is good. 

B. Seema exclaimed that it was a very good idea. 

C. Seema said what a good idea it is. 

D. Seema told what an idea! 

Answer: B. 

Q. 80 Select the most appropriate word to fill in the blank. 

I like both tea and coffee but prefer the ______. 

A. last 

B. later 

C. latter 

D. least 

Answer: C. 

Q. 81 Select the most appropriate meaning of the given idiom 

A close-fisted person 

A. A cruel person 

B. A kind person 

C. A strong person 

D. A miserly person 

Answer: D. 

Instructions 

In the following passage some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each blank. 

Comprehension: 

A. (1)______ of trucks carrying soldiers was coming down the mountain road. The trucks (2) ______ slowly as there had been heavy snowfall in that area . Suddenly, with a (3) ______ a huge tree on the hill side fell bringing along with it boulders and mud. (4) ______, the driver of first truck stopped in time. The soldiers got down and started (5) ______ the road. 

Q. 82 Select the most appropriate option for blank no. 1 

A. bevy 

B. crew 

C. convoy 

D. flock 

Answer: C. 

Q. 83 Select the most appropriate option for blank no. 2 

A. are moving 

B. were moving 

C. was moving 

D. has moved 

Answer: B. 

Q. 84 Select the most appropriate option for blank no. 3 

A. crash 

B. buzz 

C. scream 

D. splash 

Answer: A. 

Q. 85 Select the most appropriate option for blank no. 4 

A. Logically 

B. Magically 

C. Fortunately 

D. Similarly 

Answer: C. 

Q. 86 Select the most appropriate option for blank no. 5 

A. altering 

B. clearing 

C. moving 

D. changing 

Answer: B. 

Instructions 

For the following questions answer them individually 

Q. 87 Select one word for the following group of words. 

One who loves his country 

A. Traitor 

B. Conspirator 

C. Patriot 

D. Collaborator 

Answer: C. 

Q. 88 Select synonym of the given word. 

RETAIN 

A. Convey 

B. Maintain 

C. Destory 

D. Gain 

Answer: B. 

Q. 89 Given below are four jumbled sentences. Out of the given options pick the one that gives their correct order. 

A. Aesop was one of them who lived in Greece about 2500 years ago. 

B. He told many interesting stories to the people. 

C. There were many talented people in ancient Greece. 

D. Although he was ugly, he had a very clever brain. 

A. CDBA 

B. BDAC 

C. BADC 

D. CADB 

Answer: D. 

Q. 90 Select the most appropriate segment to substitute the underlined segment of the given sentence. If no substitution is required, select ‘No substitution’. 

Hardly had he sit on the chair than it broke. 

A. No substitution 

B. sat onto a chair then 

C. sit in the chair when 

D. sat on the chair when 

Answer: D. 

Q. 91 Select the most appropriate word to fill in the blank. 

He tried to ______ my ring. 

A. steal 

B. still 

C. stile 

D. steel 

Answer: A. 

Q. 92 Select the most appropriate word to substitute the underlined word of the given sentence. If no substitution is required, select ‘No improvement’. 

The diver dive in the pool from a great height. 

A. dived into the pool 

B. dived at the pool 

C. dives to a pool 

D. No improvement 

Answer: A. 

Q. 93 Select antonym of the given word. 

DEXTERITY 

A. Mastery 

B. Skill 

C. Ignorance 

D. Agility 

Answer: C. 

Q. 94 Select the wrongly spelt word. 

A. Chouffer 

B. Champion 

C. Charisma 

D. Choir 

Answer: A. 

Q. 95 Select the word which means the same as the group of words given. 

Incapable of paying debts 

A. Extravagant 

B. Obsolete 

C. Corrupt 

D. Insolvent 

Answer: D. 

Q. 96 Select antonym of the given word. 

DIVIDE 

A. Unite 

B. Break 

C. Split 

D. Engulf 

Answer: A. 

Q. 97 In the sentence identify the segment which contains the grammatical error. 

My brother, who live in Delhi, has written me a letter. 

A. My brother 

B. me a letter 

C. has written 

D. who live in Delhi 

Answer: D. 

Q. 98 Select synonym of the given word. 

EXPENSIVE 

A. Gentle 

B. Dear 

C. Mild 

D. Sober 

Answer: B. 

Q. 99 Select the wrongly spelt word. 

A. Cremator 

B. Cracker 

C. Creater 

D. Cricketer 

Answer: C. 

Q. 100 Given below are four jumbled sentences. Out of the given options pick the one that gives their correct order. 

A. He is a gifted volleyball player. 

B. But now a days he does not play international matches. 

C. It is because he had an accident last year. 

D. Sanjay is my best friend. 

A. CDBA 

B. DABC 

C. ABCD 

D. DCAB 

Answer: B. 

IBPS PO Main Exam 2019 Previous Year Paper

IBPS PO Main Exam 2019 Previous Year Paper

निर्देश (1 – 4) : निम्नलिखित जानकारी का ध्यानपूर्वक अध्ययन करें तथा तद्नुसार प्रश्नों के उत्तर दें। 

आठ व्यक्ति अर्थात् A, B, C, D, E, F, G और H अलग-अलग पदों अर्थात् टाइपिस्ट, क्लर्क, एसएससी, FA, प्रशासक, प्रबंधक, सीईओ और सीएमडी पद पर काम करते हैं लेकिन आवश्यक नहीं है कि इसी क्रम में हो। ये पदनाम बढ़ते क्रम में हैं चूंकि सीएमडी सबसे वरिष्ठ पद है और टाइपिस्ट सबसे कनिष्ठतम पद है। इनमें से प्रत्येक तीन अलग अलग शहरों अर्थात् दिल्ली, हैदराबाद और मुंबई में काम करते हैं। इन लोगों के बीच कुछ रक्त संबंध है 

और केवल चार महिलाएं हैं। पति और पत्नी एक ही शहर में काम नहीं करते हैं। F, G से वरिष्ठ है। E टाइपिस्ट से वरिष्ठ है और प्रशासक की बहन है लेकिन अपनी बहन के साथ काम नहीं करती है। A, एसएससी से वरिष्ठ है और उस व्यक्ति की पत्नी है, जो मुंबई में काम करता है। प्रबंधक का विवाह प्रशासक से हुआ है और वह सीईओ के साथ काम नहीं करता है। D, एसएससी से कनिष्ठ है। सीएमडी का विवाह B से हुआ है, जो सीईओ के रूप में काम करता है और मुंबई में काम नहीं करता है। वह, जो टाइपिस्ट के रूप में काम करता है, वह हैदराबाद में काम नहीं करता है। C, FA से वरिष्ठ है। H, प्रबंधक से वरिष्ठ है। टाइपिस्ट FA की मां है। सीईओ, FA की बहन है, जो अपने पिता D के साथ दिल्ली में ही काम करती है। 

प्रश्न 1. एसएससी की बहन कौन है? 

(A) टाइपिस्ट 

(B) G 

(C) सीईओ 

(D) A 

(E) इनमें से कोई नहीं 

Ans. D.

 

प्रश्न 2. FA कौन है? 

(A) G का पुत्र 

(B) क्लर्क का भाई 

(C) सीएमडी की बहन 

(D) प्रबंधक का पुत्र 

(E) इनमें से कोई नहीं 

Ans. A

 

प्रश्न 3. में से कौन हैदराबाद में काम करता है? 

(A) B, A 

(B) E, G, F 

(C) H, A 

(D) E, B, A 

(E) इनमें से कोई नहीं 

Ans. A

 

प्रश्न 4. विषम पद का चयन करें। 

(A) प्रशासक 

(B) क्लर्क 

(C) टाइपिस्ट 

(D) एसएससी 

(E) सीईओ 

Ans. B.

 

निर्देश (5 – 7) : निम्नलिखित जानकारी का ध्यानपूर्वक अध्ययन करें तथा तद्नुसार प्रश्नों के उत्तर दें। 

A % B – A, B के या तो 6 या 14 मीटर उत्तर में है 

A $ B – A, B के 12 मीटर दक्षिण में है 

A # B – A, B के 4 मीटर पूर्व में है 

A & B – A, B से या तो 10 मीटर या 15 मीटर पश्चिम में है 

A %# B – का अर्थ है A, B के उत्तर-पूर्व में है 

A $& B – का अर्थ है A, B के दक्षिण-पश्चिम में 

Y %# J, M # K, Y % M, J% K 

 

प्रश्न 5. Y और J के बीच सबसे छोटी दूरी क्या है? 

(A) 11 मी. 

(B) 415 मी. 

(C) 6 मी. 

(D) 815 मी. 

(E) इनमें से कोई नहीं 

Ans. B.

 

प्रश्न 6. यदि N $ M है, तो N और Y के बीच की दूरी क्या है? 

(A) 34 मी. 

(B) 28 मी. 

(C) 23 मी. 

(D) 26 मी. 

(E) इनमें से कोई नहीं 

Ans. D.

 

प्रश्न 7. यदि निम्नलिखित कथन के अनुसार P और R के बीच की सबसे छोटी दूरी 2161 मी. है तो T और P के बीच की दूरी क्या है? T # Q, P & Q, R $ Q 

(A) 15 मी. 

(B) 12 मी. 

(C) 19 मी. 

(D) 14 मी. 

(E) इनमें से कोई नहीं 

Ans. D.

 

निर्देश (8 – 10) : निम्नलिखित जानकारी का ध्यानपूर्वक अध्ययन करें तथा तद्नुसार प्रश्नों के उत्तर दें। एक सोसाइटी में, पश्चिम से पूर्व तक ग्यारह घर हैं और 1 से 11 तक संख्या दी गई है। पश्चिम छोर के घर की संख्या 1 है और पूर्वी छोर में स्थित घर की संख्या 11 है। अलग-अलग आय वाले आठ व्यक्ति इन घरों में रहते हैं (एक घर में एक व्यक्ति) और तीन घर खाली हैं। H, G से 25 वर्ष बड़ा है। E जो D से 3 वर्ष बड़ा है और वह जिसकी आयु 35 वर्ष है, के बीच केवल एक व्यक्ति रहता है। वह, जो A से 7 वर्ष छोटा है, एक खाली घर जो सम संख्या वाला घर है की ठीक दाईं ओर रहता है। वह, जो 64 वर्ष का है और वह, जो 69 वर्ष का है, के बीच कम से कम दो व्यक्ति रहते हैं । खाली घर एक-दूसरे के निकट नहीं हैं। A, जो 46 वर्ष का है, वह संख्या 3 वाले घर के पश्चिम में रहता है, लेकिन अंत में नहीं रहता। खाली घर 64 वर्ष के व्यक्ति के घर के पश्चिम में है। B का घर और वह व्यक्ति जो 64 वर्ष के घर के बीच दो घर हैं। F घर संख्या 11 में रहने वाले व्यक्ति से 4 वर्ष छोटा है। F उस व्यक्ति से 4 वर्ष छोटा है, जो घर संख्यार 11 में रहता है। C उस व्यक्ति से 4 वर्ष छोटा है, जो घर संख्या 5 में रहता है तथा घर संख्या 5 के पश्चिम में रहता है लेकिन अंत में नहीं रहता। A और D जो B से 14 साल बड़ा है, के बीच दो व्यक्ति रहते हैं तथा B के पश्चिम में रहता है। घर संख्या 5 खाली नहीं है। खाली घर तथा जिस घर में 64 वर्ष का व्यक्ति रहता है के बीच केवल एक घर है। B, जो 55 वर्ष का है घर संख्या 6 के पूर्व में एक सम संख्या वाले घर में रहता है। 

प्रश्न 8. कौन 39 वर्ष का है? 

(A) D 

(B) F 

(C) C 

(D) G 

(E) इनमें से कोई नहीं 

Ans. D.

प्रश्न 9. D के पूर्व में कितने व्यक्ति रहते हैं? 

(A) एक 

(B) चार 

(C) दो 

(D) तीन 

(E) इनमें से कोई नहीं 

Ans. (D) 

प्रश्न 10. F के एक निकटतम पड़ोसी की आयु क्या है? 

(A) 60 वर्ष 

(B) 64 वर्ष 

(C) 55 वर्ष 

(D) 39 वर्ष 

(E) इनमें से कोई नहीं 

Ans. (B) 

निर्देश (11 – 15) : दिए गए प्रश्नों का उत्तर देने के लिए निम्नलिखित ग्राफ और तालिका का अध्ययन करें। एक ई-कॉमर्स कंपनी ऑनलाइन उत्पाद बेचती है। सबसे पहले ग्राहक उत्पादों का ऑर्डर करते हैं, फिर उनमे से कछ ग्राहक ऑर्डर रदद कर देते हैं। बाकी ग्राहको का ऑर्डर कंपनी डिलीवर कर देती हैं उसके बाद डिलीवर किए गए ऑर्डरों में से कुछ ग्राहक अपना उत्पाद वापस कर देते हैं। नीचे ग्राफ़ में, दिए गए महीनों के लिए ऑर्डर किए गए उत्पादों में से डिलीवर किए गए उत्पादों का प्रतिशत और डिलीवर किए गए उत्पादों में से वापस किये गए उत्पादों का प्रतिशत दिया गया है। 

नीचे दी गई तालिका में, डिलीवर किए गए उत्पादों की संख्या दी गई है। 

महीना डिलीवर किए गए उत्पादों की संख्या
जनवरी  27000
फरवरी  24000
मार्च 22500 
अप्रैल  21600
मई 24000
जून 32000

प्रश्न 11. जनवरी और मार्च के महीनों में और मार्च और जून के महीनों में रदद किए गए ऑर्डरों की कल संख्या की संख्या का अनुपात क्या है? 

(A) 2 : 3 

(B) 3 : 4 

(C) 4 : 5 

(D) 3 : 5 

(E) 5 : 8 

Ans. (A) 

प्रश्न 12. दिए गए 6 महीनों में किये गए कुल ऑर्डरों की औसत संख्या क्या है? 

(A) 24000 

(B) 27500 

(C) 31500 

(D) 30750 

(E) 31750 

Ans. (E) 

प्रश्न 13. मई के महीने में रद्द किए गए ऑर्डरों की संख्या और वापस आए ऑर्डरों की संख्या में अंतर क्या है? 

(A) 12500 

(B) 16240 

(C) 11280 

(D) 10240 

(E) 11760 

Ans. (D) 

प्रश्न 14. अप्रैल में रद किए गए ऑर्डरों की संख्या फरवरी में रद्द किए गए ऑर्डरों की संख्या से कितने प्रतिशत कम है? 

(A) 75% 

(B) 62.5% 

(C) 85% 

(D) 68% 

(E) 76% 

Ans. C

प्रश्न 15. फरवरी और अप्रैल में ग्राहकों द्वारा स्वीकार किए गए ऑर्डरों की संख्या का योग क्या है? 

(A) 25000 

(B) 24000 

(C) 25600 

(D) 24500 

(E) 22500 

Ans. B.

निर्देश (16 – 20) : दिए गए प्रश्नों के उत्तर के लिए निम्नलिखित जानकारी का अध्ययन करें। तीन बैटरी संचालित रोबोट खिलौने A, B और C हाथ हिलाते हैं और पैर हिलाते हैं। खिलौने A, B और C की बैटरी क्षमता क्रमशः 1500 एमएएच, 1600 एमएएच और 1800 एमएएच है। खिलौनों A, B और C की वर्तमान बैटरी प्रतिशत क्रमशः 80%, 70% और 75% हैं। एक खिलौना के चार बार हाथ हिलाने और तीन बार पैर हिलाने पर 1 एमएएच बैटरी की खपत होती हैं। छः बार हाथ हिलाने और सात बार पैर हिलाने पर 2 एमएएच बैटरी की खपत होती है। 

प्रश्न 16. यदि खिलौना A सुबह 9 बजे शुरु हुआ और 12 बजे दिन में खिलौने की बैटरी ख़त्म हो गयी और इस अवधि के दौरान खिलौना A द्वारा हाथ हिलाने की संख्या, पैर हिलाने की कुल संख्या से 1200 अधिक है, तो औसतन 1 मिनट में खिलौना A द्वारा पैर हिलाने की कुल संख्या कितना हैं? 

(A) 15 

(B) 20 

(C) 25 

(D) 30 

(E) None of these 

Ans. B

प्रश्न 17. यदि खिलौना B का जब तक बैटरी पूरी तरह से खत्म नहीं हो जाती है दवारा हाथ हिलाने की संख्या के दोगुने और पैर हिलाने की संख्या का योग x है, तो निम्नलिखित में से कौन सा x का मान हो सकता है? 

I. 9000 

II. 12600 

III. 9800 

(A) केवल I

(B) केवल II

(C) केवल III

(D) केवल Iऔर III 

(E) तीनों में से कोई नहीं 

Ans. (C) 

प्रश्न 18. खिलौना C, 1500 बार हाथ हिलाता हैं और y बार पैर हिलाता हैं और खिलौना B, y बार हाथ हिलाता हैं और 2000 बार पैर हिलाता है। इसके बाद शेष बैटरी (एमएएच में) दोनों खिलौनों में समान है, तो खिलौना B में कितना प्रतिशत बैटरी शेष है? 

(A) 40% 

(B) 21.5% 

(C) 35% 

(D) 15% 

(E) इनमें से कोई नहीं 

Ans. D.

प्रश्न 19. खिलौना B घूम भी सकता है और 3 बार घूमने में, 1 बार हाथ हिलाने और 7 बार पैर हिलाने में के जितनी बैटरी की आवश्यकता होती है। खिलौना B जब तक बैटरी रहता है, हाथ हिलाने की संख्या, पैर हिलाने की संख्या और घूमने की संख्या का अनुपात 2 : 1 : 2 है, तो खिलौना B द्वारा हाथ हिलाने की संख्या और घूमने की संख्या का योग है 

(A) 1400 

(B) 2800 

(C) 5600 

(D) 3500 

(E) इनमें से कोई नहीं 

Ans. E.

प्रश्न 20. खिलौना D की बैटरी की क्षमता, खिलौने A और B की वर्तमान शेष बैटरी क्षमताओं के औसत के बराबर है और खिलौना D की वर्तमान बैटरी प्रतिशत 75% है। यदि खिलौना D में बैटरी के समाप्त होने तक बराबर संख्या में हाथ और पैर हिलाता हैं, तो खिलौना D कुल कितनी बार हाथ हिलाता हैं? 

(A) 2175 

(B) 1160 

(C) 870 

(D) 2900 

(E) इनमें से कोई नहीं

Ans. D

Direction (21 – 25) : Read the given passage carefully and answer the questions that follow. Certain words are printed in bold to help you locate them while answering some of these. 

Despite agreeing that flexible working can improve work life balance, just 17 percent of British employees are actively encouraged to do so and many don’t have the tech to work effectively. Microsoft UK calls on organisations to help employees reclaim their work-life balance with the workplace culture, tools and know-how to make the most of flexible working. 

British employees are adopting unhealthy ways of working that are having a profound impact on their personal lives, according to new research from Microsoft UK. Asking the views of more than 2,000 British workers, the study found that 30 per cent of Brits regularly sacrifice their personal lives for work, 56 per cent have answered work-related calls out of office and 8 in 10 (80 percent) have struggled to focus at home due to pressure from work. 

These unhealthy ways of working are going unnoticed by many British employees – only 29 per cent of whom admit their workplace has an ‘always on’ culture – but are leaving people struggling to keep their heads above water. 86 per cent of Brits say they have felt anxious due to work pressure in the last year –whilst 87 percent have trouble switching off) and sleeping (86 per cent), as well as feelings of failure (79 per cent). Meanwhile a third (33 percent) don’t have enough time to spend with their family and 41 per cent struggle to make time for health appointments – all due to workload. 

When it comes to addressing the issue, British employees are clear that flexible working can help improve work life balance, spend more time with family and take care of their personal life. However, few feel in a position to take advantage of flexible working policies today. Of the 50 per cent of UK workers whose organisations offer flexible working, just 35 per cent are actively encouraged to do so and more than a third (35 percent) say they need an ‘official reason’ such as an appointment to work outside the office. 

Meanwhile, for those that do make it out of the office to work more flexibly, outdated tech is slowing people down and preventing employees from doing their best work. Just 18 percent per cent of Brits have not faced tech difficulties when working remotely and almost half (48 per cent) of British employees wish their organisation invested in better tech so that they could work more efficiently. 

The findings also show a lack of support systems available for employees in Britain today. Only 23 per cent of organisations regularly implement initiatives to improve employee wellbeing and 53 per cent disagree that their organisation offers training to help employees embrace a healthy, balanced lifestyle. 

Q 21. Which of the following is not an assumption that supports the arguments presented in the third paragraph? 

(A) Unhealthy work culture might cause tensions in personal lives. 

(B) British people have high probability of falling sick. 

(C) A sense of dread and dissatisfaction is common among the British employees. 

(D) Continuous stress has resulted in the Brits losing motivation. 

(E) None of the above. 

Ans. (E) 

Q 22. Which of the following statement(s) is/are NOT TRUE in accordance with the information provided in the passage?

Most of the British employees have been sacrificing their professional life due to faulty equipment. 

British employees are unaware of the flexible work culture. 

III. The work culture in Britain is having an adverse effect on its people. (A) Only I 

(B) Both I & II 

(C) Both II & III 

(D) Only II 

(E) All are incorrect 

Ans. B.

Q 23. Which of the following statements the author is most likely to agree with? 

(A) The present flexible work culture in Britain is not well-defined in order to help the employees. 

(B) Less than a fourth of the employers consider the wellbeing of their employees. 

(C) Proper justifications are not required to work outside the office to prevent employees from slacking off. 

(D) Both A & (B) 

(E) All of the above. 

Ans. (D) 

Q 24. Which of the following is/are correctly inferred from the given passage? 

I. Only proper enforcement of flexible working can solve the issue of stressful work life. 

II. Employers in Britain are supporting a healthy professional life in name only. 

III. Lack of proper means have inhibited the British employees to attain a healthy work culture. 

(A) Only I 

(B) Both I & II 

(C) Both II & III 

(D) Only II 

(E) All are incorrect 

Ans. (C) 

Q 25. Given below is a possible inference that can be drawn from the facts stated in the fourth paragraph. You have to examine the inference in the context of the passage and decide upon its degree of truth or falsity. 

“Employers use all source of loopholes to keep their employees in office.” 

(A) Definitely true 

(B) Probably true 

(C) The data is inadequate 

(D) Probably false 

(E) Definitely false 

Ans. A

Direction: In the following question, multiple sentences have been given. Each sentence has been divided into a few parts which may or may not carry an error. The error, if any, will be in one part of the sentence. The number corresponding to that part and the sentence in which it is, will be your answer. If the given sentences carry no error, mark ‘All are correct’ as your answer. Ignore the errors of punctuation if any. 

Q 26. A) The 48-day strike (1)/ of 35,000 workers of engineering units (2)/ on Jamshedpur has drawn (3)/ strong condemnation from JRD Tata. (4) 

B) That wages had become (1)/ an explosive issue in the engineering industry (2)/ has been amply clear (3)/ for a long time. (4) 

C) This is understandable (1)/ since in JRD’s view the long-drawn-out (2)/ strike has tarnished the Tata image (3)/ as an employer. (4) 

(A) B-2 & A-1 

(B) A-3 & B-3 

(C) B-1 & C-4 

(D) A-4 & C-2 

(E) All are correct 

Ans. (B) 

Direction: In the following question, multiple sentences have been given. Each sentence has been divided into a few parts which may or may not carry an error. The error, if any, will be in one part of the sentence. The number corresponding to that part and the sentence in which it is, will be your answer. If the given sentences carry no error, mark ‘All are correct’ as your answer. Ignore the errors of punctuation if any. 

Q 27. A) The Union Labour Ministry, (1)/ after several infructuous efforts (2)/ to sort out matters, had been compelled (3)/ to pass the deer to the States. (4)

B) Several months had elapsed (1)/ after the settlement in Calcutta and yet employers (2)/ at Jamshedpur had done little (3)/ to seek a negotiated settlement of wages with workers. (4) 

C) The element of inter group rivalries (1)/ between workers also played a part (2)/ in the Jamshedpur strike (3)/ need not be disputed. (4) 

(A) B-2 & A-1 

(B) A-4 & C-2 

(C) B-3 & C-4 

(D) A-3 & C-3 

(E) All are correct 

Ans. (B) 

Direction: In the following question, multiple sentences have been given. Each sentence has been divided into a few parts which may or may not carry an error. The error, if any, will be in one part of the sentence. The number corresponding to that part and the sentence in which it is, will be your answer. If the given sentences carry no error, mark ‘All are correct’ as your answer. Ignore the errors of punctuation if any. 

 

Q 28. A) Through its actions, (1)/ the Donald Trump administration (2)/ has unequivocally announced (3)/ that 2020 will be a year of violence. (4) 

B) The American elite of all hues, liberal or conservative, (1)/ is blinded by its faith in American military supremacy, (2)/ but remains convinced (3)/ that the world is destined to play by its rules. (4) 

C) The overt military action against a foreign leader (1)/ enjoying diplomatic immunity is a travesty (2)/ of professional military ethics, (3)/ a blatant attempt to extent the battlefield dimensions. (4) 

(A) C-2 & A-1 

(B) A-4 & C-3 

(C) A-3 & C-2 

(D) B-3 & C-4 

(E) All are correct 

Ans. D.

Direction: In the following question, multiple sentences have been given. Each sentence has been divided into a few parts which may or may not carry an error. The error, if any, will be in one part of the sentence. The number corresponding to that part and the sentence in which it is, will be your answer. If the given sentences carry no error, mark ‘All are correct’ as your answer. Ignore the errors of punctuation if any. 

Q 29. A) The Trump administration’s actions is (1)/ destroying the rule-based international order (2)/ and pushing it towards barbarism and the medieval ages (3)/ where assassination as a tool of statecraft was legal. (4) 

B) The US-led “Middle-East order,” which Henry Kissinger (1)/ erected in the wake of the oil crisis and the growing demand (2)/ for a New International Economic Order by third world countries (3)/ in the mid-1970s, now lies in tatters. (4) 

C) The US is perturbed (1)/ by the nationalistic surge in Iraq (2)/ and the growing demand for the dethroning (3)/ of US troops from Iraqi soil. (4) 

(A) A-1 & C-3 

(B) B-4 & C-1 

(C) B-3 & C-4 

(D) A-2 & C-2 

(E) All are correct 

Ans. (A) 

Direction (30 – 35) : Read the given passage carefully and answer the questions that follow. 

Many American employees strive to perform their best in the workplace. They work overtime, agree to take on extra projects and rarely take a step away from their desk. This “work hard” mentality isn’t effective – and it’s unhealthy. Employees who believe that they must work 24/7 to achieve a good standing in the workplace have the wrong idea. And unfortunately, employees often gain this idea through employers’ attitudes. 

Chaining yourself to a desk or ________________ (I) in your cubicle isn’t a recipe for success – it’s a recipe for disaster. Without taking adequate breaks from work, employee productivity, mental well-being and overall work performance begin to suffer. Overworked employees often deal with chronic stress that can easily lead to job burnout. Therefore, it’s important that employers to start encouraging employees to take breaks throughout the workday. These breaks are essential in helping employees de-stress and re-charge for the rest of the workday. A recent survey by Tork shows exactly how important lunch breaks are, along with how rare they are in the North American workplace. 

Though taking breaks might sound counterintuitive but when it comes to boosting productivity, it’s one of the best ways to do so. Besides outlining some awesome benefits of regular breaks such as improved mental well-being, creativity boost and more time for healthy habits, the Tork survey also revealed that North American employees who take a lunch break every day have higher scores on a range of engagement metrics, including job satisfaction, likelihood to continue working at the same company and likelihood to recommend their employer to others. 

I recently spoke with Jennifer Deal, the Senior Research Scientist who said “Energy isn’t unlimited, and just as athletes have halftime to rest during a game, employees need to rest so they can do their best work. Taking a break in the middle of the day for lunch is a recovery period, allowing employees to come back refreshed and reinvigorated for the second half”. 

Q 30. What is the central theme of the passage

I. How North American employees are striving to perform better in their jobs by not taking breaks during work. 

II. How important it is for employers to break the myth of working 24*7 and start taking lunch breaks seriously. 

III. How vital it is for the employees to take lunch break during work, reenergize themselves and resume work with enhanced productivity. 

(A) Only I 

(B) Only II

(C) Only III 

(D) Both I and III 

(E) Both II and III 

Ans. C.

प्रश्न 31. वर्ल्ड डे फॉर ऑडियोविजुअल हेरिटेज 2019 का विषय क्या है? 

(A) प्रोटेक्ट एंड शेयर यूअर विजुअल स्टोरी 

(B) एंगेज द पास्ट श्रू साउंड एंड इमेज 

(C) इट्स यूअर स्टोरी – डोंट लूज़ इट 

(D) डिस्कवर, रिमाइंडर एंड शेयर 

(E) अवर लाइफ – डोंट वेस्ट इट 

Ans. (B) 

प्रश्न 32. मेलबर्न क्रिकेट ग्राउंड (MCG) में किस अभिनेता ने पुरुषों और महिलाओं के टूर्नामेंट के लिए आईसीसी विश्व कप 2020 ट्रॉफी का अनावरण किया? 

(A) करीना कपूर 

(B) अनुष्का शर्मा 

(C) दीपिका पादुकोण 

(D) ऐश्वर्या राय 

(E) प्रियंका चोपड़ा 

Ans. A

प्रश्न 33. विक्रम सोलर लिमिटेड एक भारतीय कंपनी है और भारत में दूसरी सबसे बड़ी सौर ऊर्जा कंपनी किस शहर में स्थित है? 

(A) मुम्बई 

(B) बड़ौदा 

(C) जयपुर 

(D) कोलकाता 

(E) रांची 

Ans. (D) 

प्रश्न 34. कितने देशों ने अंतर्राष्ट्रीय सौर गठबंधन (आईएसए) फ्रेमवर्क पर हस्ताक्षर किए हैं? 

(A) 71 

(B) 75 

(C) 78 

(D) 83 

(E) 85 

Ans. D.

प्रश्न 35. किस संगठन ने सामाजिक न्याय के लिए मदर टेरेसा मेमोरियल अवार्ड 2019 प्रस्तुत किया? 

(A) हार्मोनी फाउंडेशन 

(B) भारती फाउंडेशन 

(C) भूमि 

(D) इपास डेवलपमेंट फाउंडेशन 

(E) मैक ए डिफ्रेंस 

Ans. A

प्रश्न 36. विकार्बनन (डीकार्बोनाइजेशन) के उद्देश्य से, किस कंपनी ने पावर प्रोड्यूसर एनटीपीसी और द एनर्जी एंड रिसोर्सेज इंस्टीट्यूट (टीईआरआई) के साथ समझौता ज्ञापन (एमओयू) पर हस्ताक्षर किए हैं? 

(A) सीमेंस लिमिटेड 

(B) जनरल इलेक्ट्रिक लिमिटेड 

(C) रॉबर्ट बोश लिमिटेड 

(D) हिताची 

(E) लार्सन एंड टुब्रो 

Ans. A.

प्रश्न 37. रोबोटिक सर्जरी सुविधा प्रदान करने वाला पहला केंद्र सरकार का स्वास्थ्य केंद्र कौन सा है? 

(A) पीजीआईएमईआर चंडीगढ़ 

(B) क्रिश्चियन मेडिकल कॉलेज वेल्लोर 

(C) सफदरजंग अस्पताल, नई दिल्ली 

(D) राम मनोहर लोहिया अस्पताल, नई दिल्ली 

(E) टाटा मेमोरियल अस्पताल, मुम्बई 

Ans. (C) 

प्रश्न 38. भारत और एशियाई विकास बैंक ने निम्न में से किस राज्य की सड़कों के विकास के लिए 200 मिलियन डॉलर के ऋण समझौते पर हस्ताक्षर किए हैं? 

(A) महाराष्ट्र 

(B) झारखंड 

(C) तमिलनाडु 

(D) केरल 

(E) राजस्थान 

Ans. A

प्रश्न 39. ‘जितने लोग उतने प्रेम’ कविता के लिए किसे व्यास सम्मान से सम्मानित किया गया है? 

(A) सचिन सिन्हा 

(B) सुरेंद्र वर्मा 

(C) लीलाधर जगूड़ी 

(D) सुजीत साहू 

(E) रमाकांत कैलाश 

Ans. C.

प्रश्न 40. बैंक ऑफ बड़ौदा ने फास्टैग जारी किया है जो इलेक्ट्रॉनिक टोल संग्रह पर समग्र समाधान के रूप में कार्य करेगा। फास्टैग किस तकनीक पर काम करता है? 

(A) आरएफआईडी 

(B) ब्लूटूथ 

(C) एनएफसी 

(D) वाईफाई 

(E) जीपीएस 

Ans. A.

IBPS PO Main Exam 2019 Previous Year Paper

IBPS PO Main Exam 2019 Previous Year Paper

Direction (1 – 4) : Study the following data carefully and answer the questions accordingly. 

Eight people A, B, C, D, E, F, G, and H works on different designations i.e. Typist, Clerk, SSC, FA, Administrator, Manager, CEO, and CMD but not necessarily in the same order. These designations are in the increasing order as CMD is the senior-most post and Typist is the junior-most post. Each one of them works in three different cities i.e. Delhi, Hyderabad, and Mumbai. These people have some blood relations among them and there are only four females. The husband and wife do not work in the same city. 

F is senior to G. E is senior to the typist and is the sister of the administrator but does not work with her sister. A is senior to the SSC and is the wife of the one, who works in Mumbai. The manager is married to the administrator and he does not work with the CEO. D is junior to SS(C) CMD is married to B, who works as a CEO and does not work in Mumbai. The one, who works as a typist does not work in Hyderabad. C is senior to F(A) H is a senior to the manager. The typist is the mother of F(A) CEO is the sister of FA, who works in Delhi only with his father (D) 

Q 1. Who is the sister of the SSC? 

(A) The typist 

(B) G 

(C) The CEO 

(D) A 

(E) None of these 

Ans. D.

Q 2. Who is the FA? 

(A) The son of G 

(B) The brother of the clerk 

(C) The sister of the CMD 

(D) The son of the manager 

(E) None of these 

Ans. A

Q 3. Who among the following works in Hyderabad? 

(A) B, A 

(B) E, G, F 

(C) H, A 

(D) E, B, A 

(E) None of these 

Ans. A

Q 4. Find the odd one. 

(A) Administrator 

(B) Clerk 

(C) Typist 

(D) SSC 

(E) CEO 

Ans. B.

Direction (5 – 7) : Study the following data carefully and answer the questions accordingly. 

A % B – A is either 6 or 14m north of B 

A $ B – A is 12m south of B 

A # B – A is 4m east of B 

A & B – A is either 10 or 15m west of B 

A %# B – means A is north-east of B 

A $& B – means A is south-west of B 

Y %# J, M # K, Y % M, J % K 

Q 5. What is the shortest distance between Y and J? 

(A) 11m 

(B) 4√5m 

(C) 6m 

(D) 8√5m 

(E) None of these 

Ans. B.

Q 6. If N $ M, then what is the distance between N and Y? 

(A) 34m 

(B) 28m 

(C) 23m 

(D) 26m 

(E) None of these 

Ans. (D) 

Q 7. If the shortest distance between P and R is 2√61m according to the following statement then what is the distance between T and P? 

T # Q, P & Q, R $ Q 

(A) 15m 

(B) 12m 

(C) 19m 

(D) 14m 

(E) None of these 

Ans. (D) 

Direction (8 – 10) : Study the following data carefully and answer the questions accordingly. 

In a society, there are eleven houses from west to east and numbered 1 to 11. The house in the west end is numbered 1 and the house in the east end is numbered 11. Eight persons with different ages live in these houses (one person in one house) and three houses are vacant. 

H is 25 years older than G. Only one person lives between E, who is 3 years older than D and the one who is 35 years old. The one, who is 7 years younger than A, lives immediately right of a vacant house which is even-numbered house. At least two people live between the one, who is 64 years old and the one, who is 69 years old. Vacant houses are not near to each other. A, who is 46 years old, lives to the west of the house numbered 3 but not at the end. The vacant house is to the west of 64 years old person’s house. There are two houses between B‘s house and the person’s house who is 64 years old. F is 4 years younger than the one, who lives in the house number 11. C is 4 years younger than the one, who lives in the house number 5 and lives to the west of the house number 5 but not at the end. The house at the immediate east of house number 6 is vacant. D does not live in the house number 5 and not near to (B) Two persons live between A and D, who is 14 years older than B and lives to the west of (B) House number 5 is not vacant. Only one house is there between the vacant house and the house in which 64 years old person lives. B, who is 55 years old, lives in an even-numbered house to the east of the house number 6. 

Q 8. Who is 39 years old? 

(A) D 

(B) F 

(C) C 

(D) G 

(E) None of these 

Ans. D.

Q 9. How many people live in the east of D? 

(A) One 

(B) Four 

(C) Two 

(D) Three 

(E) None of these 

Ans. (D) 

Q 10. What is the age of the one who is an immediate neighbor of F? 

(A) 60 years 

(B) 64 years

(C) 55 years 

(D) 39 years 

(E) None of these 

Ans. (B) 

Direction (11 – 15) : Study the following graph and table to answer the given questions: 

An e-commerce company sells products online. First of all, customers order the products, then some of them cancel their orders. Remaining orders are delivered by the company, after which some of the customer return their products. 

In the graph given below the percentage of delivered products from ordered products and percentage of product returned from delivered products for the given months. 

 In the table below, the number of products delivered is given. 

Q 11. What is the ratio of number of sum total of the number of orders canceled in the months of January and March to that of March and June? 

(A) 2 : 3 

(B) 3 : 4 

(C) 4 : 5 

(D) 3 : 5 

(E) 5 : 8 

Ans. (A) 

Q 12. What is the average number of total orders for the given 6 months? 

(A) 24000

(B) 27500 

(C) 31500 

(D) 30750 

(E) 31750 

Ans. (E) 

Q 13. What is the difference of the number of orders canceled and number of orders returned in the month of May? 

(A) 12500 

(B) 16240 

(C) 11280 

(D) 10240 

(E) 11760

Ans. (D) 

Q 14. Number of orders canceled in April is what percent less than the number of orders canceled in February? 

(A) 75% 

(B) 62.5% 

(C) 85% 

(D) 68% 

(E) 76% 

Ans. C

Q 15. What is the sum of the number of the orders finally accepted by customers in February and April? 

(A) 25000 

(B) 24000 

(C) 25600 

(D) 24500 

(E) 22500

Ans. (B) 

Direction (16 – 20) : Study the following information to answer the given questions: 

Three battery operated robot toys A, B and C do hand movement and leg movement. Battery capacities of the toys A, B and C are 1500 mAh, 1600 mAh and 1800 mAh respectively. Present battery percentage of the toys A, B and C are 80%, 70% and 75% respectively. Four hand movements and three leg movements of a toy consume 1 mAh unit of battery. Six hand movements and seven leg movements of a toy consume 2 mAh unit of battery. 

Q 16. If toy A started at 9 AM and the battery of the toy discharged at 12 PM and during this period, total number of hand movements done by toy A is 1200 more than the number of leg movements,then on average how many leg movements done by toy A in 1 minute 

(A) 15 

(B) 20 

(C) 25 

(D) 30 

(E) None of these 

Ans. (B) 

Q 17. If sum of the twice of number of hand movements and number of leg movements done by toy B until the battery runs out fully is x, then which of the following can be the value of x 

  1. 9000 
  2. 12600 

III. 9800 

(A) Only I 

(B) Only II 

(C) Only III 

(D) Only I and III 

(E) None of three 

Ans. (C) 

Q 18. Toy C does 1500 hand movements and y leg movements and toy B does y hand movements and 2000 leg movements. After this the remaining battery (in mAh) is same in both the toys, then what percent of the battery is remaining in the toy B? 

(A) 40% 

(B) 21.5% 

(C) 35% 

(D) 15% 

(E) None of these

Ans. (D) 

 

Q 19. Toy B can rotate too and 3 rotations requires as much battery as much required in 1 hand movement and 7 leg movements. Ratio of the number of hand movements, number of leg movements and number of rotations done by toy B till battery lasts is 2 : 1 : 2, then sum of the number of hand movements and number of rotations done by toy B is 

(A) 1400 

(B) 2800 

(C) 5600 

(D) 3500 

(E) None of these 

Ans. (E) 

Q 20. The battery capacity of toy D is equal to the average of the current remaining battery capacities of Toys A and B and the current battery percentage of toy D is 75%. If toy D moves an equal number of hands and feet until the battery runs out, then how many times does toy D move hands? 

(A) 2175 

(B) 1160 

(C) 870 

(D) 2900 

(E) None of these 

Ans. D

Direction (21 – 25) : Read the given passage carefully and answer the questions that follow. Certain words are printed in bold to help you locate them while answering some of these. 

Despite agreeing that flexible working can improve work life balance, just 17 percent of British employees are actively encouraged to do so and many don’t have the tech to work effectively. Microsoft UK calls on organisations to help employees reclaim their work-life balance with the workplace culture, tools and know-how to make the most of flexible working. 

British employees are adopting unhealthy ways of working that are having a profound impact on their personal lives, according to new research from Microsoft UK. Asking the views of more than 2,000 British workers, the study found that 30 per cent of Brits regularly sacrifice their personal lives for work, 56 per cent have answered work-related calls out of office and 8 in 10 (80 percent) have struggled to focus at home due to pressure from work. 

These unhealthy ways of working are going unnoticed by many British employees – only 29 per cent of whom admit their workplace has an ‘always on’ culture – but are leaving people struggling to keep their heads above water. 86 per cent of Brits say they have felt anxious due to work pressure in the last year –whilst 87 percent have trouble switching off) and sleeping (86 per cent), as well as feelings of failure (79 per cent). Meanwhile a third (33 percent) don’t have enough time to spend with their family and 41 per cent struggle to make time for health appointments – all due to workload. 

When it comes to addressing the issue, British employees are clear that flexible working can help improve work life balance, spend more time with family and take care of their personal life. However, few feel in a position to take advantage of flexible working policies today. Of the 50 per cent of UK workers whose organisations offer flexible working, just 35 per cent are actively encouraged to do so and more than a third (35 percent) say they need an ‘official reason’ such as an appointment to work outside the office. 

Meanwhile, for those that do make it out of the office to work more flexibly, outdated tech is slowing people down and preventing employees from doing their best work. Just 18 percent per cent of Brits have not faced tech difficulties when working remotely and almost half (48 per cent) of British employees wish their organisation invested in better tech so that they could work more efficiently. 

The findings also show a lack of support systems available for employees in Britain today. Only 23 per cent of organisations regularly implement initiatives to improve employee wellbeing and 53 per cent disagree that their organisation offers training to help employees embrace a healthy, balanced lifestyle. 

Q 21. Which of the following is not an assumption that supports the arguments presented in the third paragraph? 

(A) Unhealthy work culture might cause tensions in personal lives. 

(B) British people have high probability of falling sick. 

(C) A sense of dread and dissatisfaction is common among the British employees. 

(D) Continuous stress has resulted in the Brits losing motivation. 

(E) None of the above. 

Ans. (E) 

Q 22. Which of the following statement(s) is/are NOT TRUE in accordance with the information provided in the passage?

I. Most of the British employees have been sacrificing their professional life due to faulty equipment. 

II. British employees are unaware of the flexible work culture. 

III. The work culture in Britain is having an adverse effect on its people. (A) Only I 

(B) Both I & II 

(C) Both II & III 

(D) Only II 

(E) All are incorrect 

Ans. B.

Q 23. Which of the following statements the author is most likely to agree with? 

(A) The present flexible work culture in Britain is not well-defined in order to help the employees. 

(B) Less than a fourth of the employers consider the wellbeing of their employees. 

(C) Proper justifications are not required to work outside the office to prevent employees from slacking off. 

(D) Both A & (B) 

(E) All of the above. 

Ans. (D) 

Q 24. Which of the following is/are correctly inferred from the given passage? 

I. Only proper enforcement of flexible working can solve the issue of stressful work life. 

II. Employers in Britain are supporting a healthy professional life in name only. 

III. Lack of proper means have inhibited the British employees to attain a healthy work culture. 

(A) Only I 

(B) Both I & II 

(C) Both II & III 

(D) Only II 

(E) All are incorrect 

Ans. (C) 

Q 25. Given below is a possible inference that can be drawn from the facts stated in the fourth paragraph. You have to examine the inference in the context of the passage and decide upon its degree of truth or falsity. 

“Employers use all source of loopholes to keep their employees in office.” 

(A) Definitely true 

(B) Probably true 

(C) The data is inadequate 

(D) Probably false 

(E) Definitely false 

Ans. A

Direction: In the following question, multiple sentences have been given. Each sentence has been divided into a few parts which may or may not carry an error. The error, if any, will be in one part of the sentence. The number corresponding to that part and the sentence in which it is, will be your answer. If the given sentences carry no error, mark ‘All are correct’ as your answer. Ignore the errors of punctuation if any. 

Q 26. A) The 48-day strike (1)/ of 35,000 workers of engineering units (2)/ on Jamshedpur has drawn (3)/ strong condemnation from JRD Tata. (4) 

B) That wages had become (1)/ an explosive issue in the engineering industry (2)/ has been amply clear (3)/ for a long time. (4) 

C) This is understandable (1)/ since in JRD’s view the long-drawn-out (2)/ strike has tarnished the Tata image (3)/ as an employer. (4) 

(A) B-2 & A-1 

(B) A-3 & B-3 

(C) B-1 & C-4 

(D) A-4 & C-2 

(E) All are correct 

Ans. (B) 

Direction: In the following question, multiple sentences have been given. Each sentence has been divided into a few parts which may or may not carry an error. The error, if any, will be in one part of the sentence. The number corresponding to that part and the sentence in which it is, will be your answer. If the given sentences carry no error, mark ‘All are correct’ as your answer. Ignore the errors of punctuation if any. 

Q 27. A) The Union Labour Ministry, (1)/ after several infructuous efforts (2)/ to sort out matters, had been compelled (3)/ to pass the deer to the States. (4)

B) Several months had elapsed (1)/ after the settlement in Calcutta and yet employers (2)/ at Jamshedpur had done little (3)/ to seek a negotiated settlement of wages with workers. (4) 

C) The element of inter group rivalries (1)/ between workers also played a part (2)/ in the Jamshedpur strike (3)/ need not be disputed. (4) 

(A) B-2 & A-1 

(B) A-4 & C-2 

(C) B-3 & C-4 

(D) A-3 & C-3 

(E) All are correct 

Ans. (B) 

Direction: In the following question, multiple sentences have been given. Each sentence has been divided into a few parts which may or may not carry an error. The error, if any, will be in one part of the sentence. The number corresponding to that part and the sentence in which it is, will be your answer. If the given sentences carry no error, mark ‘All are correct’ as your answer. Ignore the errors of punctuation if any. 

Q 28.  A) Through its actions, (1)/ the Donald Trump administration (2)/ has unequivocally announced (3)/ that 2020 will be a year of violence. (4) 

B) The American elite of all hues, liberal or conservative, (1)/ is blinded by its faith in American military supremacy, (2)/ but remains convinced (3)/ that the world is destined to play by its rules. (4) 

C) The overt military action against a foreign leader (1)/ enjoying diplomatic immunity is a travesty (2)/ of professional military ethics, (3)/ a blatant attempt to extent the battlefield dimensions. (4) 

(A) C-2 & A-1 

(B) A-4 & C-3 

(C) A-3 & C-2 

(D) B-3 & C-4 

(E) All are correct 

Ans. D.

Direction: In the following question, multiple sentences have been given. Each sentence has been divided into a few parts which may or may not carry an error. The error, if any, will be in one part of the sentence. The number corresponding to that part and the sentence in which it is, will be your answer. If the given sentences carry no error, mark ‘All are correct’ as your answer. Ignore the errors of punctuation if any. 

Q 29. A) The Trump administration’s actions is (1)/ destroying the rule-based international order (2)/ and pushing it towards barbarism and the medieval ages (3)/ where assassination as a tool of statecraft was legal. (4) 

B) The US-led “Middle-East order,” which Henry Kissinger (1)/ erected in the wake of the oil crisis and the growing demand (2)/ for a New International Economic Order by third world countries (3)/ in the mid-1970s, now lies in tatters. (4) 

C) The US is perturbed (1)/ by the nationalistic surge in Iraq (2)/ and the growing demand for the dethroning (3)/ of US troops from Iraqi soil. (4) 

(A) A-1 & C-3 

(B) B-4 & C-1 

(C) B-3 & C-4 

(D) A-2 & C-2 

(E) All are correct 

Ans. (A) 

Direction (30 – 35) : Read the given passage carefully and answer the questions that follow. 

Many American employees strive to perform their best in the workplace. They work overtime, agree to take on extra projects and rarely take a step away from their desk. This “work hard” mentality isn’t effective – and it’s unhealthy. Employees who believe that they must work 24/7 to achieve a good standing in the workplace have the wrong idea. And unfortunately, employees often gain this idea through employers’ attitudes. 

Chaining yourself to a desk or ________________ (I) in your cubicle isn’t a recipe for success – it’s a recipe for disaster. Without taking adequate breaks from work, employee productivity, mental well-being and overall work performance begin to suffer. Overworked employees often deal with chronic stress that can easily lead to job burnout. Therefore, it’s important that employers to start encouraging employees to take breaks throughout the workday. These breaks are essential in helping employees de-stress and re-charge for the rest of the workday. A recent survey by Tork shows exactly how important lunch breaks are, along with how rare they are in the North American workplace. 

Though taking breaks might sound counterintuitive but when it comes to boosting productivity, it’s one of the best ways to do so. Besides outlining some awesome benefits of regular breaks such as improved mental well-being, creativity boost and more time for healthy habits, the Tork survey also revealed that North American employees who take a lunch break every day have higher scores on a range of engagement metrics, including job satisfaction, likelihood to continue working at the same company and likelihood to recommend their employer to others. 

I recently spoke with Jennifer Deal, the Senior Research Scientist who said “Energy isn’t unlimited, and just as athletes have halftime to rest during a game, employees need to rest so they can do their best work. Taking a break in the middle of the day for lunch is a recovery period, allowing employees to come back refreshed and reinvigorated for the second half”. 

Q 30. What is the central theme of the passage? 

I. How North American employees are striving to perform better in their jobs by not taking breaks during work. 

II. How important it is for employers to break the myth of working 24*7 and start taking lunch breaks seriously. 

III. How vital it is for the employees to take lunch break during work, reenergize themselves and resume work with enhanced productivity. 

(A) Only I 

(B) Only II 

(C) Only III 

(D) Both I and III 

(E) Both II and III 

Ans. C.

Q 31. What is the theme of the World Day for Audiovisual Heritage 2019? 

(A) Protect and Share Your Visual Story 

(B) Engage the Past Through Sound and Image 

(C) It’s Your Story – Don’t lose it 

(D) Discover, Remember and Share 

(E) Our Life- Don’t waste it 

Ans. (B) 

Q 32. Which actor unveiled the ICC World Cup 2020 trophies for the men’s and women’s tournament at the Melbourne Cricket Ground (MCG)? 

(A) Kareena Kapoor 

(B) Anushka Sharma 

(C) Deepika Padukone 

(D) Aishwarya Rai 

(E) Priyanka Chopra 

Ans. A

Q 33. Vikram Solar Limited is an Indian company and the second-largest solar energy company in India is located in which city? 

(A) Mumbai 

(B) Baroda 

(C) Jaipur 

(D) Kolkata 

(E) Ranchi 

Ans. (D) 

Q 34. How many countries have signed the International Solar Alliance (ISA) framework? 

(A) 71 

(B) 75 

(C) 78 

(D) 83 

(E) 85 

Ans. D.

Q 35. Which organization presented the Mother Teresa Memorial Award 2019 for social justice? 

(A) Harmony Foundation 

(B) Bharti Foundation 

(C) Bhumi 

(D) Ipas Development Foundation 

(E) Make A Difference

Ans. A

 

Q 36.For the purpose of decarbonization, which company has signed Memorandum of Understanding (MoU) with power producer NTPC and The Energy and Resources Institute (TERI)? 

(A) Siemens Limited

(B) General Electric Limited 

(C) Robert Bosch Limited 

(D) Hitachi 

(E) Larsen & Toubro

Ans. A.

 

Q 37. Which is the first central government healthcare center to have a robotic surgery facility? 

(A) PGIMER Chandigarh 

(B) Christian Medical College Vellore 

(C) Safdarjung Hospital, New Delhi 

(D) Ram Manohar Lohia Hospital, New Delhi 

(E) Tata Memorial Hospital, Mumbai 

Ans. (C) 

Q 38. India and Asian Development Bank has signed $200 million loan agreement for the development of the roads of which of the following state? 

(A) Maharashtra 

(B) Jharkhand 

(C) Tamil Nadu 

(D) Kerala 

(E) Rajasthan 

Ans. A

Q 39. Who has been awarded the Vyas Samman for ‘Jitane Log Utane Prem’ poem? 

(A) Sachin Sinha 

(B) Surendra Verma 

(C) Liladhar Jagudi 

(D) Sujeet sahu 

(E) Ramakanth Kailash 

Ans. C.

Q 40. Bank of Baroda has issued FASTag that will act as the composite solution on Electronic Toll Collection. FAStag works on which technology? 

(A) RFID 

(B) Bluetooth 

(C) NFC 

(D) WiFi 

(E) GPS

Ans. A.

Jee Mains 25 February 2021 Shift-II Previous Year Paper

PHYSICS

SECTION A

Q. 1: An electron with kinetic energy K1 enters between parallel plates of a capacitor at an angle ‘α’ with the plates. It leaves the plates at angle ‘β’ with kinetic energy K2. Then the ratio of kinetic energies K1 : K2 will be:

(A) sin2β/cos2α

(B) cos2β/cos2α

(C) cosβ/sinα

(D) cosβ/cosα

Answer: (B)
Physics JEE Main 2021 Paper Solutions For Shift 2 Feb 25
∵v1cosα = v2cosβ [electric field inside a parallel plate capacitor is perpendicular to the plates, hence, there will be no change in parallel component of velocity]
v1/v2 = cosβ/cosα
Then the ratio of kinetic energies
k1/k2 = ½ mv12/ ½ mv22 = (v1/v2)2 = (cosβ/cosα)2
k1/k2 = cos2β/cos2α

 

Q. 2: Two identical springs of spring constant ‘2K’ are attached to a block of mass m and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. Then, time period of oscillations of this system is:

Shift 2 Physics JEE Main 2021 Paper Solutions For Feb 25

(A) π√(m/k)

(B) π√(m/2k)

(C) 2π√(m/k)

(D) 2π√(m/2k)

Answer: (A)
Shift 2 Physics Solved Paper JEE Main 2021 For Feb 25
Springs are in parallel combination.
Hence, Keff = 2k + 2k = 4k
∵ T = 2π √(m/keff)
 = 2π√(m/4k)
T  = π √(m/k)

 

Q. 3: The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n = 2 to n = 1 state is:

(A) 194.8 nm

(B) 490.7 nm

(C) 913.3 nm

(D) 121.8 nm

Answer: (D)
∆E = 10.2 eV is the energy difference between the state n = 2 & n = 1
∆E = –3.4 – (–13.6) = 10.2 eV
hc/λ = 10.2 ev
λ = hc/(10.2)e (in meters) where ‘e’ = 1.6 × 10–19 J/V
= 12400/10.2 Å (because hc = 12400 eV nm)
= 121.56 nm
≃ 121.8 nm

 

Q. 4: In a ferromagnetic material below the Curie temperature, a domain is defined as:

(A) a macroscopic region with consecutive magnetic dipoles oriented in opposite directions.

(B) a macroscopic region with zero magnetization.

(C) a macroscopic region with saturation magnetization.

(D) a macroscopic region with randomly oriented magnetic dipoles.

Answer: (C)
In a ferromagnetic material below the Curie temperature, the domain is defined as a macroscopic region with saturation magnetization.

 

Q. 5: The point A moves with a uniform speed along the circumference of a circle of radius 0.36m and covers 30o in 0.1s. The perpendicular projection ‘P’ form ‘A’ on the diameter MN represents the simple harmonic motion of ‘P’. The restoring force per unit mass when P touches M will be:

Shift 2 JEE Main 2021 Feb 25 Paper With Solutions Physics

(A) 100 N

(B) 50 N

(C) 9.87 N

(D) 0.49 N

Answer: (C)
Shift 2 Physics JEE Main 2021 Paper With Solutions Feb 25
The point covers 30o in 0.1 sec.
Means
π/6 → 0.1sec.
1 → 0.1/(π/6)
2π = → 0.1×6×2π/π
T = 1.2 sec.
We know that ω = 2π/T
ω = 2π/1.2
Restoring force (F) = mω2A
Then, Restoring force per unit mass (F/m) = ω2A
F/m = (2π/1.2)2×0.36
≃ 9.87 N

 

Q. 6: Match List I with List II.

List I List II
(a) Rectifier (i) Used either for stepping up or stepping down the A.C.voltage
(b) Stabilizer (ii) Used to convert A.C. voltage into D.C. voltage
(c) Transformer (iii) Used to remove any ripple in the rectified output voltage
(d) Filter (iv) Used for constant output voltage even when the input voltage or load current change

Choose the correct answer form the options given below:

(A) (a)-(ii), (b)- (i), (c)-(iv), (d)-(iii)

(B) (a)-(ii), (b)- (iv), (c)-(i), (d)-(iii)

(C) (a)-(ii), (b)- (i), (c)-(iii), (d)-(iv)

(D) (a)-(iii), (b)- (iv), (c)-(i), (d)-(ii)

Answer: (B)
(a) Rectifier:- used to convert A.C voltage into D.C. Voltage.
(b) Stabilizer:- used for constant output voltage even when the input voltage or load current change
(c) Transformer:- used either for stepping up or stepping down the A.C. voltage.
(d) Filter:- used to remove any ripple in the rectified output voltage.

 

Q. 7: Y = A sin(ωt + ϕ) is the time – displacement equation of an SHM, At t = 0, the displacement of the particle is Y = A/2 and it is moving along negative x-direction. Then, the initial phase angle ϕ will be.

(A) π/6

(B) π/3

(C) 2π/3

(D) 5π/6

Answer: (D)
Shift 2 Physics JEE Main 2021 Paper With Solutions For Feb 25
y = A sin (ωt + ϕ)
t = 0, x = A/2
1/2 = sin ϕ
ϕ = π/6, 5π/6
v = dy/dt = A ωcos(ωt + ϕ)
t = 0, v = A ωcosϕ
ϕ = π/6, for v (positive)
ϕ = 5π/6, for v (negative)
∴ϕ = 5π/6

 

Q. 8: A sphere of radius ‘a’ and mass ‘m’ rolls along horizontal plane with constant speed v0. It encounters an inclined plane at angle θ and climbs upwar(D) Assuming that it rolls without slipping how far up the sphere will travel (along the incline)?

Shift 2 JEE Main Feb 25 2021 Physics Paper With Solution

(A) (⅖) v02/g sin θ

(B) 10v02/7gsin θ

(C) v02/5gsin θ

(D) 7v02/10gsin θ

Answer: (D)
Shift 2 Feb 25 JEE Main 2021 Physics Papers With Solutions
From energy conservation
mgh = ½ mv2 + ½ Iω2
mgh = ½ mv2 + ½×(⅖)ma2× v02/a2
gh = ½ v02+ ⅕ v02
gh = (7/10)v02
h = (7/10)v02/g
From triangle, sinθ = h/l
Then, h = lsinθ
l sinθ = (7/10) (v02/g)
l = (7/10) (v02/g sin θ)

 

Q. 9: Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter 0.1 μm. If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that:

(A) its size decreases, but intensity increases

(B) its size increases, but intensity decreases

(C) its size increases, and intensity increases

(D) its size decreases, and intensity decreases

Answer: (A)
For diffraction through a single slit, for first minimum.
sin θ = 1.22λ/D
If D is increased, then sinθ will decrease i.e θ will decrease
∴ size of circular fringe will decrease but intensity increases.

 

Q. 10: An electron of mass me and a proton of mass mp = 1836 me are moving with the same speed. The ratio of their de Broglie wavelength λelectronProton will be:

(A) 918

(B) 1836

(C) 1/1836

(D) 1

Answer: (B)
Given mass of electron = me
Mass of proton = mp
∴ given mp = 1836 me
From de-Broglie wavelength
λ = h/p = h/mv
λep = mp/me [v is same]
= 1836me/me
λep= 1836

 

Q. 11: The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength 491 nm is 0.710 V. When the incident wavelength is changed to a new value, the stopping potential is 1.43 V. The new wavelength is:

(A) 400 nm

(B) 382 nm

(C) 309 nm

(D) 329 nm

Answer: (B)
From the photoelectric effect equation
hc/λ = ϕ + evs
where Vs is the stopping potential and ϕ is work function of the metal.
So, evs1 = hc/λ1 – ϕ ……(i)
evs2 = hc/λ2 – ϕ …..(ii)
Subtract equation (i) from equation (ii)
evs1 – evs2 = hc/λ1– hc/λ2
vs1 – vs2 = (hc/e) (1/λ1 – 1/λ2)
(0.710 – 1.43) = 1240 (1/491 – 1/λ2)
(because hc = 1240 eV nm)
-0.72/1240 = 1/491 – 1/λ2
1/λ2 = 1/491 + 0.72/1240
1/λ2 = 0.00203 + 0.00058
1/λ2 = 0.00261
λ2 = 383.14
λ2 ≃ 382 nm

 

Q. 12: The truth table for the following logic circuit is:

Physics Feb 25 Solved Paper JEE Main 2021 For Shift 2

Answer: (D)
Physics Solved Feb 25 Paper Shift 2 JEE Main 2021
If A = B = 0 then output y = 1
If A = B = 1 then output y = 1

 

Q. 13: If e is the electronic charged, c is the speed of light in free space and h is planck’s constant, the quantity (1/4πε0) |e|2/hc has dimensions of:

(A) [ LC-1]

(B) [M0 L0 T0]

(C) [ M L T0]

(D) [M L T-1]

Answer: (B)
Given
e = electronic charge
c = speed of light in free space
h = planck’s constant
(1/4πε0) e2/hc = (ke2/hc)× λ22 [multiply and divide by lambda = wavelength]
= F×λ/E [ke22 has dimensions of force and hc/λ = E]
= E/E [F× λ has dimension of E]
= dimensionless
= [ M0 L0 T0]

 

Q. 14: A charge ‘q’ is placed at one corner of a cube as shown in figure. The flux of electrostatic field E through the shaded area is:

Feb 25 Shift 2 JEE Main 2021 Physics Paper With Solutions

(A) q/48ε0

(B) q/8ε0

(C) q/24ε0

(D) q/4ε0

Answer: (C)
Total flux through the cube = (q/ε0)× ⅛ = q/8ε0
Total flux through one “outer” face of the cube = (q/8ε0)×1/3 = q/24ε0
[Because there is flux only through 3 faces]
Hence, total flux through shaded area
ϕT = (q/24ε0 + q/24ε0)×1/2 [half of each face is shaded]
ϕT = q/24ε0

 

Q. 15: Thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If V2 = 2V1 then the ratio of temperature T2/T1 is:

Feb 25 Shift 2 JEE Main 2021 Solved Paper For Physics

(A) 1/√2

(B) 1/2

(C) 2

(D) √2

Answer: (D)
Shift 2 JEE Main 2021 Solved Paper Physics Feb 25
From P-V diagram,
Given PV1/2 = constant …..(i)
We know that
PV = nRT
P ∝ (T/V) [for 1 mole]
Put in equation (i)
(T/V) (V)1/2 = constant
T ∝V1/2
T2/T1 = √(V2/V1)
T2/T1 = √(2V1/V1)
T2/T1 = √2

 

Q. 16: Given below are two statements:

Statement I: In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell’s distribution.

Statement II: In a diatomic molecule, the rotational energy at a given temperature equals the transnational kinetic energy for each molecule.

In the light of the above statements, choose the correct answer from the options given below:

(A) Both statement I and statement II are false.

(B) Both statement I and statement II are true.

(C) Statement I is false but statement II is true.

(D) Statement I is true but statement II is false.

Answer: (D)
The translational kinetic energy & rotational kinetic energy both obey Maxwell’s distribution independent of each other.
T.K.E. of diatomic molecules = (3/2) kT [3 translational D.O.F.]
R.K.E. of diatomic molecules = (2/2) kT = [2 rotational D.O.F.]
So statement I is true but statement II is false.

 

Q. 17: An LCR circuit contains resistance of 110 Ω and a supply of 220 V at 300 rad/s angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by 450. If on the other hand, only inductor is removed the current leads by 450 with the applied voltage. The rms current flowing in the circuit will be:

(A) 2.5 A

(B) 2 A

(C) 1 A

(D) 1.5 A

Answer: (B)
When L and C are connected with R in series the circuit will come in resonance So, current in the circuit will be:
Irms = Vrms/R
= 220/110
= 2 A

 

Q. 18: For extrinsic semiconductors: when doping level is increased;

(A) Fermi–level of p and n-type semiconductors will not be affected.

(B) Fermi–level of p-type semiconductors will go downward and Fermi–level of n-type semiconductor will go upward.

(C) Fermi–level of both p–type and n–type semiconductors will go upward for T >TFK and downward for T<TFK, where TF is Fermi temperature.

(D) Fermi–level of p-type semiconductor will go upward and Fermi–level of n–type semiconductors will go downward.

Answer: (B)
In n-type semiconductor, pentavalent impurity is added Each pentavalent impurity donates a free electron. So the Fermi-level of n-type semiconductor will go upward and in p-type semiconductor, trivalent impurity is added. Each trivalent impurity creates a hole in the valence band So the Fermi-level of p-type semiconductor will go downward.

 

Q. 19: A stone is dropped from the top of a building. When it crosses a point 5m below the top, another stone starts to fall from a point 25m below the top, both stones reach the bottom of the building simultaneously. The height of the building is: [Take g = 10 m/s2]

(A) 45 m

(B) 35 m

(C) 25 m

(D) 50 m

Answer: (A)
Physics JEE Main Feb 25 2021 Paper With Solutions For Shift 2
Velocity of particle (1) at 5m below top u1 = √2gh = √(2×10×5) =10 m/s
For particle (1), using 2nd equation of motion
20+h = 10t + ½ gt2 …..(i)
For particle (2), using 2nd equation of motion
h = ½ gt2 …..(ii)
Put equation (ii) in equation (i)
20 + ½ gt2 = 10t + ½ gt2
t = 2 sec.
Put in equation (ii)
h = ½ gt2
= ½ ×10 × 22
h = 20m
The height of the building = 25 + 20 = 45m

 

Q. 20: If a message signal of frequency ‘fm’ is amplitude modulated with a carrier signal of frequency ‘fc’ and radiated through an antenna, the wavelength of the corresponding signal in air is:

[Given, C is the speed of electromagnetic waves in vacuum/air]

(A) c/(fc+fm)

(B) c/(fc-fm)

(C) c/fm

(D) c/fc

Answer: (A)
Equation of amplitude modulated wave y = (Ac + Am sin ωmt) sin ωct
Here angular frequency of modulated signal = ωc
Thus frequency of modulated signal = fc
Thus wavelength = c/fc

Section B

Q. 1: The initial velocity v1 required to project a body vertically upward from the surface of the earth to just reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity ve such that vi = √(x/y) ve. The value of x will be_______.

Answer: 20
Physics Feb 25 JEE Main 2021 Paper Solution For Shift 2
Here R = radius of the earth
From energy conservation
-Gmem/R + ½ mvi2 = -Gmem/11R + 0
½ mvi2 = (10/11)Gmem/R
vi = √(20Gme/11R)
vi = √(20/11) ve {∵escape  velocity  ve = √(Gme/R)}
Then the value of x = 20

 

Q. 2: The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4% will be ___%.

Answer: 2
Speed of transverse wave is
V = √(T/μ)
Taking log on both sides
ln v = ½ lnT – ½ ln μ
Δv/v = ½ ΔT/T ⇒ (Δv/v)×100 = 1/2 ( ΔT/T)×100
= ½ ×4 [ μ is constant for a string]
(Δv/v)×100 = 2%

 

Q. 3: The peak electric field produced by the radiation coming from the 8 W bulb at a distance of 10 m is (x/10) √(µ0c/π) V/m. The efficiency of the bulb is 10% and it is a point source. The value of x is ___.

Answer: 2
Intensity I = ½ c∈0E02
Intensity = Power / Area = 8 /(4π × 102)
(8/4π×102) ×½ =¼ × c ×(1/µ0c2) ×E02 [Multiply by ½ and ∈0 =1/μ0c2]
E0 = (2/10)√(µ0c/π)
⇒ x = 2

 

Q. 4: Two identical conducting spheres with negligible volume have 2.1nC and -0.1nC charges, respectively. They are brought into contact and then separated by a distance of 0.5 m. The electrostatic force acting between the spheres is _______× 10-9 N. [Given : 4πε0 = 1/9×109 SI unit]

Answer: 36
Physics Solved Feb 25 Paper Shift 2 JEE Main 2021
When they are brought into contact & then separated by a distance = 0.5 m. Then charge distribution will be
Physics JEE Main Shift 2 Feb 25 2021 Paper Solution
The electrostatic force acting b/w the sphere is
Fe = kq1q2/r2
= 9×109×1×10-9×1×10-9/(0.5)2
= (900/25) × 10-9
Fe = 36 ×10-9 N

 

Q. 5: A current of 6A enters one corner P of an equilateral triangle PQR having 3 wires of resistance 21Ω each and leaves by the corner R. The currents i1 in ampere is______.

25 Feb 2021 JEE Main Physics Solved Paper Shift 2

Answer: 2
25 Feb JEE Main Shift 2 2021 Physics Solved Paper
The current i1 = (R2/(R1 + R2))i
= (2/(4+2))×6
i1 = 2A

 

Q. 6: The wavelength of an X-ray beam is 10 Å. The mass of a fictitious particle having the same energy as that of the X-ray photons is (x/3) h kg. The value of x is _______.

Answer: 10
Given wavelength of an X-ray beam = 10 Å
∵E = hc/λ = mc2
m = hc/λ will be the mass of a particle having the same energy
The mass of a fictitious particle having the same energy as that of the X-ray photons = (x/3)h kg
(x/3) h = h/cλ
x = 3/cλ
= 3/3×108×10×10-10
x = 10

 

Q. 7: A reversible heat engine converts one- fourth of the heat input into work. When the temperature of the sink is reduced by 52 K, its efficiency is doubled The temperature in Kelvin of the source will be_______.

Answer: 208
∵ n = W/Qin = 1/4
¼ = 1 – T2/T1 [for reversible heat engine]
T2/T1 = 3/4
When the temperature of the sink is reduced by 52k then its efficiency is doubled.
1/2 = 1 -(T2 – 52)/T1
(T2– 52)/T1 = 1/2
T2/T1 – 52/T1 = 1/2
¾ – 52/T1 = 1/2
52/T1 = 1/4
T1 = 208 K is the source temperature.

 

Q. 8: If P× Q= Q× P , the angle between P and Q is θ(0o<θ< 360o). The value of ‘θ’ will be ____.

Answer: 180
25 Feb Shift 2 JEE Main 2021 Solved Paper Physics

 

Q. 9: Two particles having masses 4g and 16g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n:2. The value of n will be_____.

Answer: 1
Relation b/w kinetic energy & momentum is
p = √(2mKE) (∵KE = same)
p1/p2 = √(m1/m2)
n/2 = √(4/16)
n = 1

 

Q. 10 : Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.20 m. Then charge on each of the sphere is (a/21)×10-8C. The value of ‘a’ will be________. [Take g = 10 m/s2]

Answer: 20
Physics JEE Feb 25 Main 2021 Solved Paper Shift 2
From FBD, T sinθ = kq2/d2 and T cosθ = mg
Dividing them,
mg tanθ = kq2/d2
q = √(mg tanθ)/25k
= √(10×10-6×10×1/√24(25)9×109)
= √(10-4×4/√24×25×4×9×109)
= (⅔)√(10-4/√24×1011)
Thus (a/21)×10-8 = ⅔ √(10-15/√24)
= ⅔ √(10-16/0.49)
a = 2×21/3×0.7
= 20

CHEMISTRY

SECTION A

Q. 1. What is ‘X’ in the given reaction?

JEE Main 25th Feb Shift 2 Chemistry Paper Question 6

Answer: (A)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 6 solution

Q. 2. The major product of the following reaction:

Answer: (D)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 8 solution

Q. 3. Given below are two statements:

Statement I: The identification of Ni2+ is carried out by dimethylglyoxime in the presence of NH4OH

Statement II: The dimethylglyoxime is a bidentate neutral ligand.

In the light of the above statements, choose the correct answer from the options given below:

(A) Both statement I and statement II are true

(B) Both statement I and statement II are false

(C) Statement I is false but statement II is true

(D) Statement I is true but statement II is false

Answer: (D)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 1 solution
Dimethylglyoxime is a negative bidentate legend.

 

Q. 4. Carbylamine test is used to detect the presence of a primary amino group in an organic compound Which of the following compounds is formed when this test is performed with aniline?

Answer: (B)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 2 solution

 

Q. 5. The correct order of bond dissociation enthalpy of halogen is:

(A) F2>Cl2>Br2>I2

(B) Cl2>F2>Br2>I2

(C) Cl2>Br2>F2>I2

(D) I2>Br2>Cl2>F2

Answer: (C)
Fact based
F2 has F — F, F2 involves repulsion of non-bonding electrons & more over its size is small and hence due to high repulsion its bond dissociation energy is very low.

Q. 6. Which one of the following statements is FALSE for hydrophilic sols?

(A) These sols are reversible in nature

(B) The sols cannot be easily coagulated

(C) They do not require electrolytes for stability

(D) Their viscosity is of the order of that of H2O

Answer: (D)
Fact based

Q. 7. Water does not produce CO on reacting with

(A) C3H8

(B) C

(C) CH4

(D) CO2

Answer: (D)
H2O + CO2 H2CO3

 

Q. 8: The correct sequence of reagents used in the preparation of 4-bromo-2-nitroethyl benzene from benzene is:

(A) CH3COCl/AlCl3, Br2/AlBr3, HNO3/H2SO4, Zn/HCl

(B) CH3COCl/AlCl3, Zn-Hg/HCl, Br2/AlBr3, HNO3/H2SO4

(C) Br2/AlBr3, CH3COCl/AlCl3, HNO3/H2SO4, Zn/HCl

(D) HNO3/H2SO4, Br2/AlCl3, CH3COCl/AlCl3, Zn-Hg/HCl

Answer: (B)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 9 solution

 

Q. 9. Given below are two statements:

Statement I: α and β forms of sulphur can change reversibly between themselves with slow heating or slow cooling.

Statement II: At room temperature the stable crystalline form of sulphur is monoclinic sulphur.

In the light of the above statements, choose the correct answer from the options given below.

(A) Both statement I and statement II are false

(B) Statement I is true but statement II is false

(C) Both statement I and statement II are true

(D) Statement I is false but statement II is true

Answer: (B)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 16 solution

 

Q. 10. Correct statement about the given chemical reaction is:

JEE Main 25th Feb Shift 2 Chemistry Paper Question 17

(A) Reaction is possible and compound (A) will be a major product.

(B) The reaction will form a sulphonated product instead of nitration.

(C) NH2 group is ortho and para directive, so product (B) is not possible.

(D) Reaction is possible and compound (B) will be the major product.

Answer: (A)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 17 solution

Q. 11. Which of the following compounds is added to the sodium extract before addition of silver nitrate for testing of halogens?

(A) Nitric acid

(B) Sodium hydroxide

(C) Hydrochloric acid

(D) Ammonia

Answer: (A)
NaCN + HNO3 → NaNO3 + HCN ↑
Na2S + HNO3 → NaNO3 + H2S ↑
Nitric acid decomposes NaCN & Na2S, else they precipitate in test & misguide the resolve.

 

Q. 12: Given below are two statements:

Statement I: The pH of rain water is normally ~5.6.

Statement II: If the pH of rain water drops below 5.6, it is called acid rain.

In the light of the above statements, choose the correct answer from the option given below.

(A) Statement I is false but Statement II is true

(B) Both statement I and statement II are true

(C) Both statement I and statement II are false

(D) Statement I is true but statement II is false

Answer: (B)
Both statements are correct

 

Q. 13. The solubility of Ca(OH)2 in water is:

[Given: The solubility product of Ca(OH)2 in water = 5.5×10-6]

(A) 1.11 ×10-6

(B) 1.77 ×10-6

(C) 1.77×10-2

(D) 1.11×10-2

Answer: (D)
Ca(OH)2 ⇌ Ca+2 + 2OH
s (2s + 10-7)
s(2s+10-7)2 = 55×10-7
4s3 = 55×10-7
s3 = 5500 / 4 × 10-9

s = (2250/2) 1/3× 10-3

s = (1125)⅓ × 10-3
s = 1.11 × 10-2

 

Q. 14. The major components of German Silver are:

(A) Cu, Zn and Mg

(B) Ge, Cu and Ag

(C) Zn, Ni and Ag

(D) Cu, Zn and Ni

Answer: (D)
Fact
German silver is alloy which does not have silver.
Cu-50%; Ni-30%; Zn-20%

 

Q. 15. The method used for the purification of Indium is:

(A) Van Arkel method

(B) Vapour phase refining

(C) Zone refining

(D) Liquation

Answer: (C)
Fact
Ga, In, Si, Ge are refined by zone refining or vacuum refining.

 

Q. 16. Which of the following is correct structure of α-anomer of maltose

Answer: (D)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 12

Q. 17. The major product of the following reaction is:

JEE Main 25th Feb Shift 2 Chemistry Paper Question 13

(A) CH3CH2CH2CHO

(B) CH3CH2CH=CH–CHO

(C) CH3CH2CH2CH2CHO

(D) JEE Main 25th Feb Shift 2 Chemistry Paper Question 13

Answer: (C)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 13 solution

 

Q. 18. The correct order of acid character of the following compounds is:

JEE Main 25th Feb Shift 2 Chemistry Paper Question 14

(A) II>III>IV>I

(B) III>II>I>IV

(C) IV>III>II>I

(D) I>II>III>IV

Answer: (A)
Acidity of carboxylic acid α-R>-H>-I
1 / α + R > + H > + I
JEE Main 25th Feb Shift 2 Chemistry Paper Question 14 solution

Q. 19. Which among the following species has unequal bond lengths?

(A) XeF4

(B) SiF4

(C) BF4-

(D) SF4

Answer: (D)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 15 solution

 

Q. 20. If which of the following orders the given complex ions are arranged correctly with respect to their decreasing spin only magnetic moment?

(i) [FeF6]3-

(ii) [Co(NH3)6]3+

(iii) [NiCl4]2-

(iv) [Cu(NH3)4]2+

(A) (ii)>(i)>(iii)>(iv)

(B) (iii)>(iv)>(ii)>(i)

(C) (ii)>(iii)>(i)>(iv)

(D) (i)>(iii)>(iv)>(ii)

Answer: (D)
[FeF6]3-: Fe3+ 3d5 → 5-unpaired electrons as F- is weak field legend
[Co(NH3)6]3+: Co3+ 3d6→ No-unpaired electron as NH3 is strong field light and causes pairing
[NiCl4]2-: Ni2+ 3d8 → 2-unpaired electrons
[Cu(NH3)4]2+: Cu2+ 3d9 → 1-unpaired electrons

 

SECTION B

Q. 1. Consider titration of NaOH solution versus 1.25 M oxalic acid solution. At the end point following burette readings were obtained.

(i) 4.5 mL (ii) 4.5 mL (iii) 4.4 mL (iv) 4.4 mL (v) 4.4 mL

If the volume of oxalic acid taken was 10.0 ml. then the molarity of the NaOH solution is ____M. (Rounded-off to the nearest integer)

Answer: 6
Eq. of NaOH = Eq. of oxalic acid
[NaOH] × 1 × 4.4 = 5/4 × 2 ×10
[NaOH] = 100 / 4 × 4.4 = 25 / 4.4 = 5.68
Nearest integer = 6 M

 

Q. 2. Electromagnetic radiation of wavelength 663 nm is just sufficient to ionize the atom of metal A. The ionization energy of metal A in kJ mol—1 is____. (Rounded off to the nearest integer)

[h=6.63×10-34Js, c = 3.00×108ms-1, NA=6.02×1023 mol-1]

Answer: 180
Energy required to ionize an atom of metal ‘A’ = hc / λ = hc / 663 nm for 1 mole atoms of ‘A’
Total energy required = NA × hc / λ

[6.023 × 1023  × 6.63 × 10-34  × 3  × 108]/[663 × 10-9]

= 6.023 × 3 × 1023-34+8+7
= 18.04 × 104 J/mol
= 180.4 kJ/mol
Nearest Integer = 180 kJ/Mol.

 

Q. 3. Copper reduces into NO and NO2 depending upon the concentration of HNO3 in solution. (Assuming fixed [Cu2+] and PNO=PNO2), the HNO3 concentration at which the thermodynamic tendency for reduction of into NO and NO2 by copper is same is 10x M.

The value of 2x is ______. (Rounded-off to the nearest integer)

[Given: 

E0(Cu2+ /Cu) = 0.34V, E0 (No3 / NO) = 0.96V, E0(No3 / NO2 = 0.79V and at 298 K, 

RT/F(2.303)= 0.059

Answer: 4
Anode
Cu(s) → Cu+2 + 2e
Cathode (1)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 7 solution
JEE Main 25th Feb Shift 2 Chemistry Paper Question 7 solution
JEE Main 25th Feb Shift 2 Chemistry Paper Question 7 solution
log (HNO3) = 2.16
[HNO3] = 102.16 = 10x
x = 2.16 ⇒ 2x = 4.32 ≈ 4

 

Q. 4. Five moles of an ideal gas at 293 K is expanded isothermally from an initial pressure of 2.1 MPa to 1.3 MPa against a constant external 4.3 MP(A) The heat transferred in this process is ____kJ mol-1. (Rounded-off of the nearest integer)

[Use R = 8.314 J mol-1 K-1]

Answer: 15
Moles (n) = 5
T = 293 K
Process = Iso T. → Irreversible
Pini = 2.1 M Pa
Pt = 1.3 M Pa
Pext = 4.3 mPa
Work = – Pext Δv

=−4.3×(5×293R / 1.3 − 5×293/2.1)

=−5×293×8.314×43(1/13 −1/21)

=(5×293×8.314×43×8)/(21×13)

= -15347.7049 J
= – 15.34 kJ
Isothermal process, so ΔU = 0
w = – Q
Q = 15.34 kJ / mol
So, answer is 15.

 

Q. 5. Among the following, the number of metal/s which can be used as electrodes in the photoelectric cell is _____(Integer answer).

Answer: (A)
Cs is used in photoelectric cells due to its very low ionization potential.

 

Q. 6. The rate constant of a reaction increases by five times on increasing temperature from 270 C to 520C. The value of activation energy in kJ mol-1 is ______.

(Rounded off to the nearest integer)

[R=8.314 J K-1 mol-1]

Answer: 52
JEE Main 25th Feb Shift 2 Chemistry Paper Question 7
Ea = 51524.96 J/mol
Ea = 51.524 kJ/mol
52 Ans.

 

Q. 7. If a compound AB dissociates to the extent of 75% in an aqueous solution, the molality of the solution which shows a 2.5 K rise in the boiling point of the solution is ______molal.

Answer: 3
AB → A+ + B
1 – α α α
α = 3 / 4
N = 2
i = [1+(2-1)α]
2.5 = [1+(2-1)3/4] × 0.52 × m

m = 2.5/0.52 × 7/4 = 10/3.64 = 2.747
m= 2.747≈ 3 mol/kg

 

Q. 8. The spin only magnetic moment of a divalent ion in aqueous solution (atomic number 29) is ____BM.

Answer: 2
29Cu+2 → [Ar]183d9
JEE Main 25th Feb Shift 2 Chemistry Paper Question 2
No. of unpaired e = 1
Magnetic moment = μ = √n(n + 2)
μ = √(1)(1 + 2) = √3B.M.
= 1.73 B.M

 

Q. 9. The number of compound/s given below which contain/s —COOH group is ______

(A) Sulphanilic acid

(B) Picric acid

(C) Aspirin

(D) Ascorbic acid

Answer: (A)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 3 solution

 

Q. 10. The unit cell of copper corresponds to a face centered cube of edge length 3.596 Å with one copper atom at each lattice point. The calculated density of copper in kg/m3 is ______.

Answer: 9077
a = 3.596 Å

d = Z × GMM / NA × a3

d = (Z4 × 63.54 × 10-3)/ 6.022 × 1023 ×  (3.956 × 10-10)3

d = 0.9076 × 104 = 9076.2 kg/m3

MATHS 

SECTION A

Q. 1: If the curve x2 + 2y2 = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is:

(A) 𝜋/2 + tan–1(1/4)

(B) 𝜋/2 – 𝑡𝑎𝑛–1(1/4)

(C) 𝜋/2 + 𝑡𝑎𝑛–1(1/3)

(D) 𝜋/2 – 𝑡𝑎𝑛–1(1/3)

Answer: (A)
JEE Main Feb 2021 Solved Maths Paper
Using homogenization
x2 + 2y2 = 2(1) 2
⇒x2 + 2y2 = 2(x + y) 2
⇒x2 + 2y2 = 2x2 + 2y2 + 4xy
⇒x2 + 4xy = 0
for ax2 + 2hxy + by2 = 0, obtuse angle between lines θ is
tan θ = ±(2√(h2–ab))/(a+b)
⇒tan θ = ±4
⇒tan θ = –4
cot θ = -1/4
θ = cot–1(–1/4)
θ = π – cot–1 (1/4)
θ = π – (π/2– tan–1(1/4) )
θ = π/2 + tan-1(1/4)

 

Q. 2:

JEE Main Feb 2021 Maths Solved Question 8

(A) loge|x2 + 5x – 7| + c

(B) (1/4) loge |x2 + 5x – 7| + c

(C) 4 loge|x2 + 5x – 7| + c

(D) loge √(x2 + 5x – 7) + c

Answer: (C)
JEE Main Feb 2021 Maths Question 8 Solution

 

Q. 3: A hyperbola passes through the foci of the ellipse x2/25 + y2/16 = 1 and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is:

(A) x2/9 – y2/4 = 1

(B) x2/9 – y2/16 = 1

(C) x2 – y2 = 9

(D) x2/9 – y2/25 = 1

Answer: (B)
For ellipse, e1 = √(1–16/25)=3/5
Foci = (±3,0)
Let equation of hyperbola be x2/A2 – y2/B2 = 1, passes through (±3, 0)
A2 =9, A=3, e2=5/3
e22 = 1 + B2/A2
25/9 = 1 + B2/9 ⇒B2 = 16
x2/9 – y2/16 = 1

 

Q. 4: limn→∞[1/n + n/(n+1)2 + n/(n+2)2 + …….. + n/(2n-1)2] is equal to:

(A) 1

(B) 1/3

(C) 1/2

(D) 1/4

Answer: (C)
JEE Main Feb 2021 Maths Solved Question 10

 

Q. 5: In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarians and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are 35%, 20% and 10% respectively. A person is chosen from the group at random and is found to be suffering from chest disorder. The probability that the selected person is a smoker and non-vegetarian is:

(A) 7/45

(B) 8/45

(C) 14/45

(D) 28/45

Answer: (D)
Based on Bayes’ theorem
Probability = ((160/400×35/100))/((160/400×35/100)+(100/400×20/100)+(140/400×10/100) )
= 5600/9000
= 28/45

 

Q. 6: The following system of linear equations

2x + 3y + 2z = 9

3x + 2y + 2z = 9

x – y + 4z = 8

(A) does not have any solution

(B) has a unique solution

(C) has a solution (α, β, γ) satisfying α + β2 + γ3 = 12

(D) has infinitely many solutions

Answer: (B)
Determinant of given system = -20 ≠ 0
It has a unique solution.

 

Q. 7: The minimum value of f(x) = a^ax + a^(1-ax) where a, x ∈ R and a > 0, is equal to:

(A) a + 1/a

(B) a + 1

(C) 2a

(D) 2√a

Answer: (D)
Using AM ≥ GM inequality, we get

 

Q. 8: A function f(x) is given by f(x) = 5x/(5x+5), then the sum of the series f(1/20) + f(2/20) + f(3/20) + …… + f(39/20) is equal to:

(A) 19/2

(B) 49/2

(C) 39/2

(D) 29/2

Answer: (C)
f(x) = 5x/(5x + 5)….(i)
⇒ f(2–x) = 52–x/(52–x +5)
⇒f(2–x) = 5/(5x+5)……(ii)
Adding equation(i)and(ii)
f(x)+f(2–x)=1
f(1/20)+f(39/20)=1
f(2/20)+f(38/20)=1
……
…..
f(19/20) + f(21/20)=1
and f(20/20) = f(1) = 1/2
Therefore, f(1/20) + f(2/20) + f(3/20) + …… + f(39/20) = 19 + 1/2 = 39/2

 

Q. 9: A plane passes through the points A(1,2,3), B(2,3,1) and C(2,4,2). If O is the origin and P is (2,–1,1), then the projection of vector(OP) on this plane is of length:

(A) √(2/5)

(B) √(2/3)

(C) √(2/11)

(D) √(2/7)

Answer: (C)
A(1,2,3),B(2,3,1),C(2,4,2),O(0,0,0)
Equation of plane passing through A, B, C will be
JEE Main 2021 Feb Shift 2 Maths Solutions
(x – 1)(–1 + 4) – (y – 2)(–1 + 2) + (z – 3)(2 – 1) = 0
(x – 1)(3) – (y – 2)(1) + (z – 3)(1) = 0
3x – 3 – y + 2 + z – 3 = 0
3x – y + z – 4 = 0, is the required plane equation
Now, given O(0,0,0) & P(2,–1,1)
Plane is 3x – y + z – 4 = 0
Let O’ & P’ be the foot of perpendiculars.
JEE Main 2021 Feb Shift 2 Maths Solution
JEE Main 2021 Feb Shift 2 Maths Solved Paper

 

Q. 10: The contra positive of the statement “If you will work, you will earn money” is:

(A) If you will not earn money, you will not work

(B) You will earn money, if you will not work

(C) If you will earn money, you will work

(D) To earn money, you need to work

Answer: (A)
Contrapositive of p → q is ~q →~p
p: you will work
q: you will earn money
~q: you will not earn money
~p: you will not work
~q →~p: if you will not earn money, you will not work

 

Q. 11: The shortest distance between the line x – y = 1 and the curve x2 = 2y is:

(A) 1/2

(B) 0

(C) 1/(2√2)

(D) 1/√2

Answer: (C)
Shortest distance must be along common normal
JEE Main Feb 2021 Maths Solved Question 17
m1 (slope of line x–y = 1) = 1 ⇒slope of perpendicular line =–1
m2 = 2x/2 = x ⇒ m2 = h ⇒slope of normal = –1/h
–1/h=–1 ⇒h=1
So, the point is (1,1/2)
Therefore, Shortest distance (D) =|(1–1/2–1)/√(1+1)|=1/(2√2)

 

Q. 12: Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen element of A leaves remainder 2 when divided by 5 is:

(A) 1/5

(B) 2/9

(C) 97/297

(D) 122/297

Answer: (C)
Total cases
= 4C1 × 9 × 9 × 9 – 3C1 × 9 × 9
(as 4 digit number having 0 at thousands place have to be excluded)
For a number to have a remainder 2 when divided by 5 it’s unit digit should be 2 or 7
Case 1: when unit digit is 2
Number of four-digit number = 3C1×9×9 – 2C1×9
Case 2: when unit digit is 7
Number of four digits number = 8 × 9 × 9
So total number favorable cases = 3×92 – 2×9 + 8×92
Required Probability = ((3×9×9)–(2×9)+(8×9×9))/((4×93) – (3×92))
= 97/297

 

Q. 13: cosec[2 cot–1( 5) + cos–1(4/5) ] is equal to:

(A) 75/56

(B) 65/56

(C) 56/33

(D) 65/33

Answer: (B)
cosec[2 cot–1( 5) + cos–1(4/5) ]
JEE Main Feb 2021 Maths Solved Question 19

 

Q. 14: If 0 < x, y < π and cos x + cos y – cos (x + y) = 3/2, then sin x + cos y is equal to:

(A) (1+√3)/2

(B) (1–√3)/2

(C) √3/2

(D) 1/2

Answer: (A)
JEE Main Feb 2021 Maths Solved Question 20

 

Q. 15: If α, β∈ R are such that 1 – 2i (here i2 = –1) is a root of z2 + αz + β = 0, then (α – β) is equal to:

(A) 7

(B) -3

(C) 3

(D) -7

Answer: (D)
1-2i is a root of z2 + αz + β = 0.
(1-2i) 2 + α(1-2i)+β=0
⇒1-4-4i+α-2iα+β=0
⇒(α+β-3)-i(4+2α)=0
⇒α+β-3=0 & 4+2α=0
So, α=-2, β=5
Therefore, α-β=-7

 

Q. 16: If , then

(A) 1/(I2 + I4 ) , 1/(I3 + I5 ), 1/(I4 + I6) are in G.P.

(B) 1/(I2 + I4 ) , 1/(I3 + I5 ), 1/(I4 + I6) are in A.P.

(C) I2 + I4 , I3 + I5 , I4 + I6) are in A.P.

(D) I2 + I4 , I3 + I5 , I4 + I6) are in G.P.

Answer: (B)

In+2 + In = 1/(n+1)
I2 + I4 =1/3, I3 + I5 =1/4 and I4 + I6 =1/5
So, 1/(I2 + I4 ) , 1/(I3 + I5 ) and 1/(I4 + I6) are in A.P.

Q. 17: If for the matrix, A= AAT = I2, then the value of α4 + β4 is:

(A) 1

(B) 3

(C) 2

(D) 4

Answer: (A)
JEE Main Feb 2021 Shift 2 Maths Solutions

 

Q. 18: Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions from the set A to the set A × B. Then:

(A) y = 273x

(B) 2y = 91x

(C) y = 91x

(D) 2y = 273x

Answer: (B)
Number of elements in A = 3
Number of elements in B = 5
Number of elements in A × B = 15
Number of one-one function is x = 5 × 4 × 3
⇒x = 60
Number of one-one function is y = 15 × 14 × 13
⇒y = 15 × 4 × 14/4 × 13
⇒y = 60 × 7/2 × 13
⇒2y = (13)(7x)
⇒2y = 91x

 

Q. 19: Let α and β be the roots of x2 – 6x – 2 = 0. If an = αn – βn for n ≥ 1, then the value of (a10–2a8)/(3a9 ) is:

(A) 4

(B) 1

(C) 2

(D) 3

Answer: (C)
α and β be the roots of x2–6x–2=0.
So,
α2–6α–2=0⇒α2–2=6α
β2–6β–2=0⇒β2–2=6β
Now,
JEE Main Feb 2021 Maths Solved Question 15

 

Q. 20: Let A be a 3 × 3 matrix with det(A) = 4. Let Ri denote the ith row of A. If a matrix B is obtained by performing the operation R2→ 2R2 + 5R3 on 2A, then det(B) is equal to:

(A) 64

(B) 16

(C) 80

(D) 128

Answer: (A)
JEE Main Feb 2021 Maths Question 16 Solution

Section B

Q. 1: Let . If the area of the parallelogram whose adjacent sides are represented by the vectors a and a is 8√3 square units, then 

a.bis equal to ______.

Answer: 2
Area of parallelogram = 

|a × b|


(64)(3) = 16α2 + 64 + 16α2
⇒ α2 = 4
Now, 

a.b = 3 – α2 + 3
= 6 – α2
= 6 – 4
= 2

 

Q. 2: If the curve y = y(x) represented by the solution of the differential equation (2xy2 – y)dx + xdy = 0, passes through the intersection of the lines, 2x – 3y = 1 and 3x + 2y = 8, then |y(1)| is equal to ______.

Answer:1
Given,
(2xy2 – y)dx + xdy = 0
⇒ dy/dx + 2y2 – y/x = 0
⇒ (–1/y2) . dy/dx + (1/y) (1/x) = 2
Let, 1/y = z
(–1/y2) dy/dx = dz/dx
⇒dz/dx + z(1/x) = 2
Feb 2021 Maths JEE Main Paper Solutions
As it passes through P(2, 1)
[Point of intersection of 2x – 3y = 1 and 3x + 2y = 8]
Therefore, 2/1 = 4 + c
⇒c = –2
⇒x/y = x2 – 2
Put x = 1
1/y = 1 – 2 = –1
⇒y(1) = –1
⇒|y(1)| = 1

 

Q. 3: If limx→0 ax−(e4x−1) / ax(e4x−1) exists and is equal to b, then the value of a – 2b is ______.

Answer: 5

limx→0 ax−(e4x−1) / ax(e4x−1)

Applying L’Hospital Rule

limx→0 a−4e4x / a(e4x−1)+ax(4e4x) So for limit to exist,a=4
Applying L’Hospital Rule

limx→0 −16e4x / a(4e4x) + a(4e4x) + ax(16e4x)

(-16)/(4a+4a)=(–16)/32=–1/2=b
a-2b = 4–2((–1)/2) = 4+1 = 5

 

Q. 4: A line L passing through origin is perpendicular to the lines

Solved JEE Main Feb 2021 Maths Paper Questions

If the co-ordinates of the point in the first octant on L2 at the distance of √17 from the point of intersection of L and L1 are (a, b, c), then 18(a+b+c) is equal to ______.

Answer: 44
Solved JEE Main Maths Feb 2021 Paper Question
D.R. of L is parallel to (L1 × L2) ⇒ (-2, 3, -2)
Equation of l : x/2 = y/(–3) = z/2
Solving L & L1
(2λ, –3λ, 2λ) = (µ + 3, 2µ – 1, 2µ + 4)
µ = – 1 , λ = 1
So, intersection point P(2, –3, 2)
Let, Q(2ν + 3, 2ν + 3, ν + 2) be required point on L2
Solved JEE Main Maths Feb 2021 Exam Questions

 

Q. 5: A function f is defined on [–3,3] as

JEE Main Maths Feb 2021 Paper Question

where [x] denotes the greatest integer ≤ x. The number of points, where f is not differentiable in (–3,3) is ______.

Answer: (5)
Feb 2021 JEE Main Maths Paper Question
Points of non-differentiable in (–3, 3) are at x = –2, –1, 0, 1, 2.
i.e. 5 points.

 

Q. 6: A line is a common tangent to the circle (x – 3)2 + y2 = 9 and the parabola y2 = 4x. If the two points of contact (a, b) and (c, d) are distinct and lie in the first quadrant, then 2(a+c) is equal to ______.

Answer: 9
Sol. Circle: (x – 3)2+ y2= 9
Parabola: y2 = 4x
Let common tangent equation be y = mx + a/m
⇒y = mx + 1/m
⇒m2x – my + 1 = 0
The above line is also tangent to circle
(x – 3)2 + y2= 9
Therefore, the perpendicular from (3, 0) to line = 3
⇒|(3m2 – 0 + 1)/√(m2+m4 )| = 3
⇒(3m2 + 1)2 = 9(m2 + m4)
⇒m = ±1/√3
Tangent is
y = 1/√3x + √3 (it will be used)
=> m = 1/√3
or y = –1/√3x – √3 (rejected)
JEE Main Feb 2021 Maths Solved Question Problems
For Parabola, point of contact is (a/m2 , 2a/m)= (3, 2√3) = (c, d)
Solving Circle (x – 3)2 + y2 = 9 & line equation y = (1/√3) x + √3
(x – 3)2 + ((1/√3) x + √3)2 = 9
⇒x2 + 9 – 6x + (1/3)x2 + 3 + 2x = 9
⇒(4/3)x2 – 4x + 3 = 0
⇒x = 3/2=a
∴ 2(a + c) = 2(3/2+3)= 9

 

Q. 7: The value of is ______.

Answer: 19

x2-x-2=(x–2)(x+1)

Solved JEE Main Feb 2021 Maths Paper Question

 

Q. 8: If the remainder when x is divided by 4 is 3, then the remainder when (2020+x)2022 is divided by 8 is ______.

Answer: 1
Let x = 4k + 3
(2020 + x)2022
= (2020 + 4k + 3)2022
= (2024 + 4k – 1)2022
= (4A – 1)2022
=2022C0(4A)2022(–1)0 + 2022C1(4A)2021(–1)1 + ……+2022C2021(4A)1(–1)2021+ 2022C2022(4A)0(–1)2022
Which will be of the form 8λ+1
So, Remainder is 1.

 

Q. 9: If the curves x = y4 and xy = k cut at right angles, then (4k)6 is equal to ______.

Answer: 4
Feb 2021 JEE Main Maths Exam Question

 

Q. 10: The total number of two digit numbers ‘n’, such that 3n+7n is a multiple of 10, is ______.

Answer: 45
Feb 2021 JEE Main Maths Paper Solutions
Let n = 2t; t ∈ N
3n = 32t = (10 – 1)t
=10p + (–1)t
= 10p ± 1
If n = even then 7n + 3n will not be multiple of 10
So, if n is odd then only 7n + 3n will be a multiple of 10
Therefore, n = 11,13,15,………..,99
Therefore, the answer is 45

Jee Mains 25 February 2021 Shift-I Previous Year Paper

PHYSICS

SECTION A

Q. 1: Match List-I with List-II:

List-I List-II
(A)h (Planck’s constant) (i) [MLT–1]
(B)E (Kinetic energy) (ii) [ML2T–1]
(C)V (Electric potential) (iii) [ML2T–2]
(D)P (Linear momentum) (iv) [ML2I–1T–3]

Choose the correct answer from the options given below:

(A) (A) → (ii), (B) →(iii), (C) → (iv), (D) → (i)

(B) (A) →(i), (B) → (ii), (C) →(iv), (D) → (iii)

(C) (A) → (iii), (B) → (ii), (C) →(iv), (D) →(i)

(D) (A) → (iii), (B) → (iv), (C) →(ii), (D) →(i)

Answer: (A)
K.E. = [ML2T–2]
P (Linear momentum) = [MLT–1]
h (Planck’s constant) = [ML2T–1]
V (Electric potential) = [ML2T–3I–1]

 

Q. 2: The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lines 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while the 72nd division on circular scale coincides with the reference line. The radius of the wire is:

(A) 1.64 mm

(B) 1.80 mm

(C) 0.82 mm

(D) 0.90 mm

Answer: (C)
Least count. = pitch/no. of div.
= 1 mm/100
= 0.01 mm
+ve zero error = 8 × L.C. = +0.08 mm
Measured reading = 1mm + 72 × L.C.
= 1mm + 0.72 mm
= 1.72 mm
True reading = 1.72 – 0.08
= 1.64 mm
Radius = 1.64/2 = 0.82 mm

 

Q. 3: If the time period of a two meter long simple pendulum is 2 s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is:

(A) 2π2 ms–2

(B) 16 m/s2

(C) 9.8 ms–2

(D) π2 ms–2

Answer: (A)
T = 2π√(l/g)
T2 = 4π2l/g
g = 4π2l/T2
= 4π2×2/(2)2 = 2π2 ms–2

 

Q. 4: An α particle and a proton are accelerated from rest by a potential difference of 200 V. After this, their de Broglie wavelengths are λα and λp respectively. The ratio λp/λα is:

(A) 8

(B) 2.8

(C) 3.8

(D) 7.8

Answer: (B)
λ = h/p
= h/√(2mqV)
λp/λα = √(mαqα/mpqp)
= √(4×2/1×1)
= 2√2 = 2.8

 

Q. 5: Given below are two statements: one is labelled as Assertion A and the other is labelled as reason R.

Assertion A: The escape velocities of planet A and B are same. But A and B are of unequal masses.

Reason R: The product of their masses and radii must be same. M1R1 = M2R2

In the light of the above statements, choose the most appropriate answer from the options given below:

(A) Both A and R are correct but R is NOT the correct explanation of A

(B) A is correct but R is not correct

(C) Both A and R are correct and R is the correct explanation of A

(D) A is not correct but R is correct

Answer: (B)
Ve = escape velocity
ve = √(2GM/R)
So, for same ve, M1/R1 = M2/R2
A is true but R is false

 

Q. 6: A diatomic gas, having Cp = (7/2)R and Cv = (5/2)R, is heated at constant pressure. The ratio dU : dQ : dW

(A) 3 : 7 : 2

(B) 5 : 7 : 2

(C) 5 : 7 : 3

(D) 3 : 5 : 2

Answer: (B)
Since the gas is diatomic in nature and the process is isobaric, we have
Cp = (7/2)R
Cv = (5/2)R
dU = nCvdT
dQ = nCpdT
dW = nRdT
dU : dQ : dW
Cv : Cp : R
(5/2) R : (7/2) R : R
5 : 7 : 2

 

Q. 7: Statement I: A speech signal of 2 kHz is used to modulate a carrier signal of 1 MHz. The bandwidth requirement for the signal is 4 kHz.

Statement II: The side band frequencies are 1002 kHz and 998 kHz.

In the light of the above statements, choose the correct answer from the options given below:

(A) Both statement I and statement II are false

(B) Statement I is false but statement II is true

(C) Statement I is true but statement II is false

(D) Both statement I and statement II are true

Answer: (D)
Side band = (fc – fm) to (fc + fm)
= (1000 – 2) kHz to (1000 + 2) kHz
= 998 kHz to 1002 kHz
Band width = 2fm
= 2 ×2kHz
= 4 kHz
Both statements are true.

 

Q. 8: The current (i) at time t = 0 and t = ∞ respectively for the given circuit is:

Shift 1 Physics Solved Paper JEE Main 2021 For Feb 25

(A) 18E/55,5E/18

(B) 5E/18,18E/55

(C) 5E/18,10E/33

(D) 10E/33,5E/18

Answer: (C)
Shift 1 JEE Main 2021 Feb 25 Paper With Solutions Physics
At t = 0, inductor is open
Initial-state equivalent of the circuit shown in figure -1 is
Shift 1 Physics JEE Main 2021 Paper With Solutions Feb 25
Req = 6×9/(6+9) = 54/15
I (t = 0) = E×15/54 = 5E/18
At t = ∞, For steady state inductor is replaced by plane wire
Steady state equivalent of the circuit shown in figure-1 is
Shift 1 JEE Main Feb 25 2021 Physics Paper With Solution
Equivalent circuit diagram is given by
Shift 1 Feb 25 JEE Main 2021 Physics Papers With Solutions
Req =1×4/(1+4) + 5×5/(5+5)
= 4/5 + 5/2
= (8 + 25)/10
= 33/10
I = E/Req = 10E/33

 

Q. 9: Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively.

If TA and TB are the time periods of A and B respectively then the value of TB – TA:

Shift 1 JEE Main 2021 Solved Paper Physics Feb 25

[Given: Radius of earth = 6400 km, mass of earth = 6×1024 kg]

(A) 4.24× 102 s

(B) 3.33 × 102 s

(C) 1.33 × 103 s

(D) 4.24 × 103 s

Answer: (C)
Feb 25 Shift 1 JEE Main 2021 Solved Paper For Physics
V = √(GMe/r)

T = 2​𝜋r/ (√(GMe/r)) = 2​𝜋r/ (√(r/GMe))

T =√(4𝜋2r3/GMe) = √(4𝜋2r3/GMe)
T2 – T1 = √(4𝜋2(8000×103)3/G×6×1024 ) – √(4𝜋2(7000×103)3/G×6×1024 )
≅ 1.33 ×103 s

 

Q. 10: An engine of a train, moving with uniform acceleration, passes the signal post with velocity u and the last compartment with velocity v. The velocity with which middle point of the train passes the signal post is:

(A) √(v2 – u2)/2

(B) (v – u)/2

(C) √(v2 + u2)/2

(D) (u + v)/2

Answer: (C)
Feb 25 Shift 1 JEE Main 2021 Solved Paper For Physics
a = uniform acceleration
u = velocity of first compartment
v = velocity of last compartment
l = length of train
v2 = u2 + 2as (3rd equation of motion)
v2 = u2 + 2al …..(1)
v2 middle = u2 + 2al/2
∴ v 2middle = u2 + al ….(2)
From equation (1) and (2)
v2middle = u2 + (v2 – u2)/2
= (v2 + u2)/2
∴ vmiddle = √(v2 + u2)/2

 

Q. 11: A 5V battery is connected across the points X and Y. Assume D1 and D2 to be normal silicon diodes. Find the current supplied by the battery if the +ve terminal of the battery is connected to point X.

Shift 1 Physics JEE Main 2021 Paper With Solutions For Feb 25

(A) ~0.86 A

(B) ~0.5 A

(C) ~0.43 A

(D) ~1.5 A

Answer: (C)
Since silicon diode is used so 0.7 Volt is drop across it, only D1 will conduct so current through cell.
I = (5 – 0.7)/10 = 0.43 A

 

Q. 12: A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force F1. Now a spherical cavity of radius R/2 is made in the sphere (as shown in figure) and the force becomes F2. The value of F1: F2 is:

Shift 1 Physics JEE Main 2021 Paper Solutions For Feb 25

(A) 41 : 50

(B) 36 : 25

(C) 50 : 41

(D) 25 : 36

Answer: (A)
Gravitational field intensity g1 = GM/(3R)2 = GM/9R2 …(1)
Gravitational field intensity g2 = GM/9R2 – G(M/8)/(5R/2)2
= GM/9R2 – GM/R250
= (41/9×50) GM/R2….(2)
Implies , g1/g2 = 41/50
⇒ F1/F2 = mg1/mg2 = 41/50

 

Q. 13: A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336 m/s. The zero of the metre scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is:

(A) 13 cm

(B) 14.8 cm

(C) 16.6 cm

(D) 18.4 cm

Answer: (B)
λ = v/f
= 336/504 = 66.66cm
λ/4 = l + e = l + 0.3d
= l + 1.8
16.66 = l + 1.8 cm
l = 14.86 cm

 

Q. 14: A proton, a deuteron and an α particle are moving with the same momentum in a uniform magnetic fiel(D) The ratio of magnetic forces acting on them is _______ and their speeds are in the ratio______.

(A) 2 : 1 : 1 and 4 : 2 : 1

(B) 1 : 2 : 4 and 2 : 1 :1

(C) 1 : 2 : 4 and 1 : 1 : 2

(D) 4 : 2 : 1 and 2 : 1 : 1

Answer: (A)
As v = p/m & F = qvB
∴ F = qpB/m
F1 = qpB/m, v1 = p/m
F2 = qpB/2m, v2 = p/2m
F3 = 2qpB/4m, v3 = p/4m
F1 : F2 : F3 & V1 : V2 : V3
1 : ½ : ½  & 1 : ½ :¼
2 : 1 : 1 & 4 : 2 : 1

 

Q. 15: Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: When a rod lying freely is heated, no thermal stress is developed in it.

Reason R: On heating, the length of the rod increases

In the light of the above statements, choose the correct answer from the options given below:

(A) A is true but R is false

(B) Both A and R are true and R is the correct explanation of A

(C) Both A and R are true but R is NOT the correct explanation of A

(D) A is false but R is true

Answer: (C)
If a rod is free and it is heated then there is no thermal stress produced in it.
The rod will expand due to increase in temperature.
So, both A & R are true.

 

Q. 16: In an octagon ABCDEFGH of equal side, what is the sum of

Physics JEE Main 2021 Paper With Solutions For Shift 1 Feb 25

Answer: (A)

Physics Feb 25 Solved Paper JEE Main 2021 For Shift 1
Physics Solution Feb 25 Paper Shift 1 JEE Main 2021

 

Q. 17: Two radioactive substances X and Y originally have N1 and N2 nuclei respectively. Half-life of X is half of the half-life of Y. After three half-lives of Y, numbers of nuclei of both are equal. The ratio N1/N2 will be equal to:

(A) 8/1

(B) 1/8

(C) 3/1

(D) 1/3

Answer: (A)
After n half-life no of nuclei undecayed = No/2n
Given, t(1/2)x= t(1/2y)/2
So 3 half-life of y = 6 half-life of x
Given, Nx = Ny after 3t(½)y
N1/26 = N2/23
N1/N2 = 26/23 = 23= 8/1

 

Q. 18: The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

Physics Feb 25 Shift 1 JEE Main 2021 Solved Paper

(A) 0.8 H and 250 μF

(B) 0.8 H and 150 μF

(C) 1.33 H and 250 μF

(D) 1.33 H and 150 μF

Answer: (A)
Physics JEE Main 2021 Feb 25 Solved Papers Shift 1
Since key is open, circuit is series L-C-R circuit
15 = irms (60)
∴irms = ¼ A
Now, 20 = ¼ XL = ¼ (ωL)
∴ L = 4/5 = 0.8 H
& 10 = ¼ 1/(100C)
C = (1/4000) F
= 250 μF

 

Q. 19: Two coherent light sources having intensities in the ratio 2x produce an interference pattern. The ratio (Imax – Imin)/(Imax + Imin) will be:

(A) 2√(2x)/(x + 1)

(B) √(2x)/(2x + 1)

(C) 2√(2x)/(2x + 1)

(D) √(2x)/(x + 1)

Answer: (C)
Let I1 = 2x
I2 = 1
Imax = (√I1 + √I2)2
Imin = (√I1 – √I2)2

(Imax-Imin)/ (Imax+ Imin) = [(√2x + 1)2 -(√2x – 1)2] / [(√2x + 1)2 +​(√2x – 1)2]

= 4√(2x)/(2 + 4x)
= 2√(2x)/(2x + 1)

 

Q. 20: Magnetic fields at two points on the axis of a circular coil at a distance of 0.05 m and 0.2 m from the centre are in the ratio 8 : 1. The radius of coil is ______

(A) 0.15 m

(B) 0.2 m

(C) 0.1 m

(D) 1.0 m

Answer: (C)
Physics JEE Main Feb 25 2021 Paper Solution For Shift 1
B = μ0NiR2/2(R2 + x2)3/2
at x1 = 0.05m, B1 = μ0NiR2/2(R2 + (0.05)2)3/2
at x2 = 0.2m, B2 = μ0NiR2/2(R2 + (0.2)2)3/2
B1/B2 = (R2 + 0.04)3/2/(R2 + 0.0025)3/2
(8/1)2/3 = (R2 + 0.04)/(R2 + 0.0025)
4 (R2 + 0.0025) = R2 + 0.04
3R2 = 0.04 – 0.01
R2 = 0.03/3 = 0.01
R = √0.01 = 0.1 m

Section – B

Q. 1: The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as U= α/r10– β/r5 – 3. Where, a and b are positive constants. The equilibrium distance between two atoms will (2α/β)a/(B) Where a =_______

Answer: 1
F = -dU/dr
F = -[-10α/r11 + 5β/r6]
for equilibrium, F = 0
10α/r11 = 5β/r6
2α/β = r5
r = (2α/β)1/5
a = 1

 

Q. 2: A small bob tied at one end of a thin string of length 1m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position is ______ m/s. (take g = 10 m/s2)

Answer: 5
Shift 1 Physics 2021 JEE Main Solution Paper For Feb 25
By conservation of energy,
v2min = V2 – 4gl ….(1)
Tmax = mg + mv2/l ….(2)
Tmin = mv2min/l – mg ….(3)
from equation (1) and (3)
Tmin = (m/l) (v2 – 4gl) – mg
Tmax/Tmin = (v2/l + g)/(v2/l – 5g)
5/1 = (v2/1 + 10)/ (v2/1 – 50)
5v2 – 250 = v2 + 10
v2 = 65 ….(4)
from equation (4) and (1)
v2min = 65 – 40 = 25
vmin = 5 m/s

 

Q. 3: In a certain thermodynamic process, the pressure of a gas depends on its volume as kV3. The work done when the temperature changes from 1000 C to 3000 C will be ____ nR, where n denotes the number of moles of a gas.

Answer: 50
P = kv3
pv–3 = k
x = –3
w = nR(T1 – T2)/(x – 1)
= nR(100-300)/(-3 -1)
= nR(-200)/-4
= 50nR

 

Q. 4: In the given circuit of potentiometer, the potential difference E across AB (10 m length) is larger than E1 and E2 as well. For key K1 (closed), the jockey is adjusted to touch the wire at point J1 so that there is no deflection in the galvanometer. Now the first battery (E1) is replaced by the second battery (E2) for working by making K1 open and E2 close(D) The galvanometer gives then null deflection at J2. The value of E1/E2 is the smallest fraction of a/b, Then the value of a is ____.

Shift 1 Physics Solved Papers JEE Main 2021 Feb 25

Answer: 1
E1/E2 = l1/l2
= 3×100 cm + (100 – 20)cm)/(7×100 cm + 60 cm)
= 380/760
= ½
= a/b
a = 1

 

Q. 5: The same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of a convex lens is ______ cm.

Answer: 15
1/v – 1/u = 1/f …(1)
m = v/u ….(2)
from (1) and (2) we get
m = f/(f + u)
Given conditions
m1 = -m2
f/(f – 10) = -f/(f – 20)
f – 20 = –f + 10
2f = 30
f = 15 cm

 

Q. 6: A transmitting station releases waves of wavelength 960 m. A capacitor of 256 μF is used in the resonant circuit. The self inductance of coil necessary for resonance is _____ × 10–8H.

Answer: 10
At resonance
ωr = 1/√(Lc)
∴ 2πf = 1/√(Lc)
∴ 4π2c22 = 1/Lc
∴4π2×3×108×3×108/960×960 = 1/L×2.56×10-6
L = 375×960/10-6×4×π2×9×1016 = 103/1010
= 10–7 H
= 10 × 10–8 H

 

Q. 7: The electric field in a region is given by . The ratio of flux of reported field through the rectangular surface of area 0.2 m2 (parallel to y-z plane) to that of the surface of area 0.3 m2(parallel to x-z plane) is a : 2, where a = ________

[Here i, j and k are unit vectors along x, y and z-axes respectively]

Answer: 1

Shift 1 Physics JEE Main 2021 Solution Paper For Feb 25
Therefore, a = 1

 

Q. 8: 512 identical drops of mercury are charged to a potential of 2 V each. The drops are joined to form a single drop. The potential of this drop is ____ V.

Answer: 128
Let charge on each drop = q
Radius = r
V = kq/r
2 = kq/r
Radius of bigger
4πR3/3 = 512 × (4/3) πr3
R = 8r
V = k(512)q/R = (512/8) (kq/r)
= (512/8) × 2
= 128 V

 

Q. 9: A monatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with a velocity 30 m/s. If the container is suddenly stopped then the change in temperature of the gas (R=gas constant) is x/3R. Value of x is ______.

Answer: 3600
ΔKE = ΔU
ΔU = nCVΔT
½ mv2 = (3/2) nRΔT
mv2/3nR = ΔT
4×(30)2/3×1×R = ΔT
ΔT = 4×(30)2/3×1×R
x/3R = 1200/R
x = 3600

 

Q. 10: A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V = 3t volt. (where t is in second). If the voltage is applied when t = 0, then the energy stored in the coil after 4 s is _______ J.

Answer: 144
L di/dt = ε
= 3t
L ∫di = 3 ∫t dt
Li = 3t2/2
i = 3t2/2L
Energy stored in the coil, E = ½ Li2
= ½ L (3t2/2L)2
= ½ × 9t4/4L
= 9/8 × (4)4/2
= 144 J

Chemistry

SECTION A

Q. 1. The hybridization and magnetic nature of [Mn(CN)6]4– and [Fe(CN)6]3–, respectively are:

(A) d2sp3 and paramagnetic

(B) sp3d2 and paramagnetic

(C) d2sp3 and diamagnetic

(D) sp3d2 and diamagnetic

Answer: (A)
JEE Main 25th Feb Shift 1 Chemistry Paper Question 17 solution

 

Q. 2. Identify A and B in the chemical reaction.

JEE Main 25th Feb Shift 1 Chemistry Paper Question 18

Answer: (D)
JEE Main 25th Feb Shift 1 Chemistry Paper Question 18 solution

 

Q. 3. Compound(s) which will liberate carbon dioxide with sodium bicarbonate solution is/are:

JEE Main 25th Feb Shift 1 Chemistry Paper Question 19

(A) 2 and 3 only

(B) 1 only

(C) 2 only

(D) 3 only

Answer: (A)
Compounds that are more acidic than H2CO3, gives CO2 gas in reaction with NaHCO3. Compound B i.e. Benzoic acid and compound C i.e. picric acid both are more acidic than H2CO3.

 

Q. 4. Ellingham diagram is a graphical representation of:

(A) ΔG vs T

(B) (ΔG – TΔS) vs T

(C) ΔH vs T

(D) ΔG vs P

Answer: (A)
Ellingham diagram tells us about the spontaneity of a reaction with temperature.

 

Q. 5. Which of the following equations depicts the oxidizing nature of H2O2?

(A) Cl2 + H2O2 → 2HCl + O2

(B) KlO4 + H2O2 → KlO3 + H2O + O2

(C) 2l + H2O2 + 2H+ → I2 + 2H2O

(D) I2 + H2O2 + 2OH → 2I + 2H2O + O2

Answer: (C)
2l + H2O2 + 2H+ → I2 + 2H2O
Oxygen reduces from –1 to –2
So, its reduction will take place. Hence it will behave as oxidising agent or it shows
oxidising nature.

 

Q. 6. In Freundlich adsorption isotherm at moderate pressure, the extent of adsorption (x/m) is directly proportional to Px. The value of x is:

(A) ∞

(B) 1

(C) zero

(D) 1/n

Answer: (D)
x / m = px
The formula is x / m = px
Hence, x= 1 / n. The value of ‘n’ is any natural number.

 

Q. 7. According to molecular orbital theory, the species among the following that does not exist is:

(A) He2

(B) He2+

(C) O22-

(D) Be2

Answer: (D)
B.O. of Be2 is zero, so it does not exist.

 

Q. 8. In which of the following pairs, the outermost electronic configuration will be the same?

(A) Fe2+ and Co+

(B) Cr+ and Mn2+

(C) Ni2+ and Cu+

(D) V2+ and Cr+

Answer: (B)
Cr+ → [Ar]3d5
Mn2+ → [Ar]3d5

 

Q. 9. Given below are two statements:

Statement-I: An allotrope of oxygen is an important intermediate in the formation of reducing smog.

Statement-II: Gases such as oxides of nitrogen and Sulphur present in the troposphere contribute to the formation of photochemical smog.

(A) Statement I and Statement II are true

(B) Statement I is true about Statement II is false

(C) Both Statement I and Statement II are false

(D) Statement I is false but Statement II is true

Answer: (C)
Reducing smog acts as a reducing agent and the reducing character is due to presence of sulphur dioxide and carbon particles.

 

Q. 10. The plots of radial distribution functions for various orbitals of hydrogen atom against ‘r’ are given below:

JEE Main 25th Feb Shift 1 Chemistry Paper Question 13
JEE Main 25th Feb Shift 1 Chemistry Paper Question 13

(A) (4)

(B) (2)

(C) (1)

(D) (3)

Answer: (A)
3s orbital
Number of radial nodes = n – λ – 1
For 3s orbital n = 3, λ = 0
Number of radial nodes = 3 – 0 – 1 = 2
It is correctly represented in graph of option 4

 

Q. 11. Identify A in the given chemical reaction.

Answer: (D)


JEE Main 25th Feb Shift 1 Chemistry Paper Question 5 solution
Aromatization reaction or hydroforming reaction.

 

Q. 12. Given below are two statements:

Statement-I: CeO2 can be used for oxidation of aldehydes and ketones.

Statement-II: Aqueous solution of EuSO4 is a strong reducing agent.

(A) Statement I is true, statement II is false

(B) Statement I is false, statement II is true

(C) Both Statement I and Statement II are false

(D) Both Statement I and Statement II are true

Answer: (D)
CeO2 can be used as an oxidizing agent like seO2. Similarly, EuSO4 is used as a reducing agent.

 

Q. 13. The major product of the following chemical reaction is:

JEE Main 25th Feb Shift 1 Chemistry Paper Question 7

(A) (CH3CH2CO)2O

(B) CH3CH2CHO

(C) CH3CH2CH3

(D) CH3CH2CH2OH

Answer: (B)
JEE Main 25th Feb Shift 1 Chemistry Paper Question 7 solution

Q. 14. Complete combustion of 1.80 g of an oxygen-containing compound (CxHyOz) gave 2.64 g of CO2 and 1.08 g of H2O. The percentage of oxygen in the organic compound is:

(A) 63.53

(B) 51.63

(C) 53.33

(D) 50.33

Answer: (C)
n(CO2) = 2.64 / 44 = 0.06
nc = 0.06
weight of carbon = 0.06 × 12 = 0.72 gm
n(H2O) = 1.08 / 1.8 = 0.06
nH = 0.06 × 2 = 0.12
weight of H = 0.12 gm
∴ Weight of oxygen in CxHyOz
= 1.8 – (0.72 + 0.12)
= 0.96 gram
% weight of oxygen = 0.96/18 × 100 = 53.3%

 

Q. 15.The correct statement about B2H6 is:

(A) All B–H–B angles are 120°.

(B) Its fragment, BH3, behaves as a Lewis base.

(C) Terminal B–H bonds have less p-character when compared to bridging bonds.

(D) The two B–H–B bonds are not of the same length.

Answer: (C)
The terminal bond angle is greater than that of bridge bond angle
Bond angle ∝ S-character

α  1/ pcharacter

 

Q. 16. Which of the glycosidic linkage galactose and glucose is present in lactose?

(A) C-1 of glucose and C-6 of galactose

(B) C-1 of galactose and C-4 of glucose

(C) C-1 of glucose and C-4 of galactose

(D) C-1 of galactose and C-6 of glucose

Answer: (B)
JEE Main 25th Feb Shift 1 Chemistry Paper Question 14

 

Q. 17. Which one of the following reactions will not form acetaldehyde?

Answer: (A)
JEE Main 25th Feb Shift 1 Chemistry Paper Question 14 solution

 

Q. 18. Which of the following reactions will not give p-amino azobenzene?

JEE Main 25th Feb Shift 1 Chemistry Paper Question 16

(A) 2 only

(B) 1 and 2

(C) 3 only

(D) 1 only

Answer: (A)
JEE Main 25th Feb Shift 1 Chemistry Paper Question 16 solution

 

Q. 19. The solubility of AgCN in a buffer solution of pH = 3 is x. The value of x is: [Assume: No cyano complex is formed; Ksp(AgCN) = 2.2 × 10–16 and Ka (HCN) = 6.2 × 10–10]

(A) 0.625 × 10-6

(B) 1.6 × 10-6

(C) 2.2 × 10-16

(D) 1.9 × 10-5

Answer: (D)
Let solubility is x
AgCN ⇌ Ag+ + CNKsp = 2.2 × 10–16
x x
H+ + CN ⇌ HCN

K = 1/ Ka

K= 1/ 6.2 × 10–10

Ksp × 1/ka = [Ag+] [CN] × [HCN] / [H+][CN]
2.2 × 10-16 × 1 / 6.2 × 10-10 = [S][S] / 10-3
S2 = 2.2 / 6.2 × 10-9
S2 = 3.55 × 10–10
S = √3.55 × 10–10
S = 1.88 × 10–5 ⇒ 1.9 × 10–5

 

Q. 20. Which statement is correct?

(A) Buna-S is a synthetic and linear thermosetting polymer

(B) Neoprene is an addition copolymer used in plastic bucket manufacturing

(C) Synthesis of Buna-S needs nascent oxygen

(D) Buna-N is a natural polymer

Answer: (C)
Synthesis of Buna-S needs nascent oxygen.

SECTION B

Q. 1. A car tire is filled with nitrogen gas at 35 psi at 27°C. It will burst if pressure exceeds 40 psi. The temperature in °C at which the car tyre will burst is ______. (Rounded-off to the nearest integer)

Answer: 69.85°C ≃ 70°C
P1 / T1 = P2 / T2
35 / 300 = 40 / T2
T2 = 40 × 300 / 35
= 342.86 K
= 69.85°C ≃ 70°C

 

Q. 2. The reaction of cyanamide, NH2CN(s) with oxygen was run in a bomb calorimeter and ΔU was found to be –742.24 kJ mol–1. The magnitude of ΔH298 for the reaction NH2CN (s) + 3/2 O2 (g) → N2 (g) + O2 (g) + H2O(l) is______kJ. (Rounded off to the nearest integer). [Assume ideal gases and R = 8.314 J mol–1 K–1]

Answer: 741 kJ/mol
NH2CN(s) + 3/2 O2(g) → N2(g) + CO2(g) + H2O(λ)
Δng = (1 + 1) – 3/2 = ½
ΔH = ΔU + Δng RT
= -742.24 + ½ × 8.314 × 298 / 1000
= -742.24 + 1.24
= 741 kJ/mol

 

Q. 3. The ionization enthalpy of Na+ formation from Na(g) is 495.8 kJ mol–1, while the electron gain enthalpy of Br is –325.0 kJ mol–1. Given the lattice enthalpy of NaBr is –728.4 kJ mol–1. The energy for the formation of NaBr ionic solid is (–)_____ × 10–1 kJ mol–1.

Answer: 5576 kJ
Na(s) → Na+(g) ΔH = 495.8
½ Br2(λ) + e → Br(g) ΔH = 325
Na+(g) + Br(g) → NaBr(s) ΔH = –728.4
Na(s) + ½ Βr2(λ) → NaBr(s). ΔH =?
ΔH = 495.8 – 325 – 728.4
–557.6 kJ = –5576 × 10–1 kJ

 

Q. 4. Consider the following chemical reaction.

Answer: 7
JEE Main 25th Feb Shift 1 Chemistry Paper Question 6 solution
All carbon atoms in benzaldehyde are sp2 hybridized.

 

Q. 5. Among the following, the number of halide(s) which is/are inert to hydrolysis is ______.

(A) BF3

(B) SiCl4

(C) PCl5

(D) SF6

Answer: 1
Due to crowding, SF6 is not hydrolyzed.

 

Q. 6. In basic medium CrO42– oxidizes S2O32– to form SO24 and itself changes into Cr(OH)4–. The volume of 0.154 M CrO42– required to react with 40 mL of 0.25 M S2O32– is ______ mL. (Rounded-off to the nearest integer)

Answer: 173 mL
17H2O + 8CrO4 + 3S2O3 → 6SO4 + 8Cr(OH)4– + 2OH
Applying mole-mole analysis
0.154 × v / 8 = 40 × 0.25 / 3
V = 173 mL

 

Q. 7. 1 molal aqueous solution of an electrolyte A2B3 is 60% ionise(D) The boiling point of the solution at 1 atm is _____ K. (Rounded-off to the nearest integer). [Given Kb for (H2O) = 0.52 K kg mol–1]

Answer: 375 K
A2B3 → 2A+3 + 3B–2
No. of ions = 2 + 3 = 5
wi = 1 + (n – 1) ∝
= 1 + (5 – 1) × 0.6
= 1 + 4 × 0.6 = 1 + 2.4 = 3.4
ΔTb = Kb × m × i
= 0.52 × 1 × 3.4 = 1.768°C
ΔTb = (Tb)solution – [(TbH2O)]solution
1.768 = (Tb)solution – 100
(Tb)solution = 101.768 °C
= 375 K

 

Q. 8. Using the provided information in the following paper chromatogram:

JEE Main 25th Feb Shift 1 Chemistry Paper Question 10

The calculated Rf value of A ______ × 10–1.

Answer: 4

Rr = Distance Travelled By Solvent / Distance Travelled By Compound

On chromatogram distance travelled by compound is → 2 cm
Distance travelled by solvent = 5 cm
So Rf = 2 / 5 = 4 × 10–1 = 0.4

 

Q. 9. For the reaction, aA + bB → cC + dD, the plot of log k vs 1/T is given below:

JEE Main 25th Feb Shift 1 Chemistry Paper Question 3

The temperature at which the rate constant of the reaction is 10–4s–1 is ________ K. [Rounded off to the nearest integer)

[Given: The rate constant of the reaction is 10–5 s–1 at 500 K]

Answer: 526 K

log10 K = log10 A – E0/2.303RT

Slope = E0/2.203 = -10000

log10 K1/K2 = ​E0/2.203 × (1/T1 – 1/T2)

log10 10-4/10-5 = 1000 × (1/500 -1/T)

1 = 1000 × (1/500 -1/T)

1/10000 = 1/500 = 1/T

1/T = 1/500 = 1/10000

1/T = 20-1 / 10000 = 19/10000

T = 10000 / 19
T= 526 K

 

Q. 10. A 0.4g mixture of NaOH, Na2CO3 and some inert impurities was first titrated with N / 10HCl using phenolphthalein as an indicator, 17.5 mL of HCl was required at the end point. After this methyl orange was added and titrate(D) 1.5 mL of the same HCl was required for the next end point. The weight percentage of Na2CO3 in the mixture is ______. (Rounded-off to the nearest integer)

Answer: 3%
1st end point reaction
NaOH + HCl → NaCl + H2O
nf = 1
NaCO3 + HCl → NaHCO3
nf = 1
Eq of HCl used = n(NaOH) × 1 + n(Na2CO3) × 1
17.5 × 1/10 × 10-3 = n(NaOH) + n(Na2CO3)

2nd end point
NaHCO3 + HCl → H2CO3
1.5 × 1/10 × 10-3 = n(NaHCO3) × 1 = n(NaHCO3)
0.15 mmol = n(Na2CO3)
0.15 = n(Na2CO3)

W(Na2CO3) = 0.15×106×10-3 × 100 × 10
= 3 × 106 × 10–2
= 3 × 1.06 = 3.18%

Maths

SECTION A

Q. 1: A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A, with uniform spee(D) At that point, the angle of depression of the boat with the man’s eye is 30° (Ignore man’s height). After sailing for 20 seconds towards the base of the tower (which is at the level of water), the boat has reached point B, where the angle of depression is 45°. Then the time taken (in seconds) by the boat from B to reach the base of the tower is :

(A) 10(√3-1)

(B) 10√3

(C) 10

(D) 10(√3+1)

Answer: (D)
JEE MAIN 2021 Feb 25 Shift 1 Solution 4
x + y = √3h ….…….(1)
Also,
h/y = tan 45o
h = y …….(2)
put in (1)
x + y = √3y
x = (√3 – 1)y
x/20=v (speed)
Therefore, time taken to reach
Foot from B
= y/V
= x/(√3-1)x . 20
= 10 (√3 + 1)

 

Q. 2:

JEE MAIN 2021 Feb 25 Shift 1 Solution 5

(A) xyz = 4

(B) xy – z = (x + y)z

(C) xy + yz + zx = z

(D) xy + z = (x+y)z

Answer: (D)
JEE MAIN 2021 Feb 25 Shift 1 Solved Question 5

 

Q. 3: The equation of the line through the point (0,1,2) and perpendicular to the line (x-1)/2 = (y+1)/3 = (z-1)/-2 is :

(A) ​x/-3 = (y-1)/ 4 = (z-2)/3

(B) x/3 = (y-1)/ 4 = (z-2)/3

(C) x/3 = (y-1)/ -4 = (z-2)/3

(D) x/3 = (y-1)/ 4 = (z-2)/-3

Answer: (A)

(x-1)/2 = (y+1)/3 = (z-1)/-2 =λ
Any point on this line (2λ + 1, 3λ – 1, -2λ + 1)
Direction ratio of given line d1 ≡ (2, 3, -2)
Direction ratio of the line to be found  d2 ≡(2λ+1,3λ−2,−2λ−1)

 ∴ d1 d2 = 0

λ = 2 / 17
Direction ratio of line (21, -28, -21) (3, -4, -3) ≡ (-3, 4, 3)

 

Q. 4: The coefficients a,b and c of the quadratic equation, ax2 + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is :

(A) 1/54

(B) 1/72

(C) 1/36

(D) 5/216

Answer: (D)
ax2 + bx + c = 0
a,b,c ∈ {1,2,3,4,5,6}
n(s) = 6 × 6 × 6 = 216
D=0 ⇒ b2 = 4ac
ac = b2/4, If b = 2, ac = 1 ⇒ a = 1,c = 1
If b = 4, ac = 4 ⇒ a = 1, c = 4
a = 4, c = 1
a = 2, c = 2
If b = 6, ac = 9 ⇒ a = 3, c = 3
Therefore, probability = 5/216

 

Q. 5: Let α be the angle between the lines whose direction cosines satisfy the equations l +m – n = 0 and l2 + m2 – n2 = 0. Then the value of sin4 α + cos4 α is :

(A) 3/4

(B) 1/2

(C) 5/8

(D) 3/8

Answer: (C)
Given that l+m=n ….(1)
l2 + m2 – n2 = 0 ….(2)
Squaring equation (1)
l2 + m2 + 2lm = n2 ….(3)
From equations (2) and (3)
lm=0 ⇒ l = 0 or m = 0
Case (1) : l = 0
⇒ m=n
⇒ l2 + m2 + n2 = 0
⇒ m=n = ±1/(√2 )
∴(l,m,n) = (0, 1/√2, 1/√2) or (0, -1/√2, -1/√2)
Case (2): m = 0
⇒ l = n
⇒ l2 + m2 + n2 = 0
JEE MAIN 2021 Feb 25 Shift 1 Solution 2

 

Q. 6: The value of the integralJEE MAIN 2021 Feb 25 Shift 1 Solution 3

(where c is a constant of integration)

(A) 1/18[9 – 2 sin6θ – 3 sin4θ – 6 sin2θ ](3/2) + c

(B) 1/18[11 – 18 sin2θ + 9 sin4θ – 2 sin6θ ](3/2) + c

(C) 1/18[11 – 18 cos2θ + 9 cos4θ – 2 cos6θ ](3/2) + c

(D) 1/18[9 – 2 cos6θ – 3 cos4θ – 6 cos2θ ](3/2) + c

Answer: (C)
Using trig identities, sin2A = 2sinAcosA and 1-cos2A = 2sin2A
JEE MAIN 2021 Feb 25 Shift 1 Solved Question 3

 

Q. 7: The statement A→ (B → A) is equivalent to:

(A) A → (A ᐱ B)

(B) A → (A ᐯ B)

(C) A → (A → B) 

(D) A → (A ↔ B)

Answer: (B)
A → (B → A)
⇒ A → (∼ B ᐯ A)
⇒ ∼ A ᐯ (∼ B ᐯ A)
⇒ ∼ B ᐯ (∼ A ᐯ A)
⇒ ∼ B ᐯ t
= t (tautology)
From options:
(B) A → (A ᐯ B)
⇒ ∼ A ᐯ (A ᐯ B)
⇒ (∼ A ᐯ A) ᐯ B
⇒ t ᐯ B
⇒ t

 

Q. 8: The integer k, for which the inequality x2 – 2(3k – 1)x + 8k2 – 7 >0 is valid for every x in R is :

(A) 3

(B) 2

(C) 4

(D) 0

Answer: (A)
D < 0
(2(3k-1))2 – 4(8k2 – 7) < 0
4(9k2 – 6k + 1) – 4(8k2 – 7) < 0
k2 – 6 k + 8 < 0
(k–4)(k–2)<0
2< k < 4
then k = 3

 

Q. 9: All possible values of θ ∈ [0, 2π] for which sin2θ + tan2θ > 0 lie in

a.(0,π/2)∪(π,3π/2)

(B) (0,π/4)∪(π/2,3π/4)∪(π,5π/4)∪(3π/2,7π/4)

(C) (0,π/2)∪(π/2,3π/4)∪(π,7π/4)

(D) (0,π/4)∪(π/2,3π/4)∪(3π/2,11π/6)

Answer: (B)
JEE MAIN 2021 Feb 25 Shift 1 Solved Problem 12

 

Q. 10: The image of the point (3,5) in the line x – y + 1 = 0, lies on :

(A) (x – 2)2 + (y – 4) 2 =4

(B) (x – 4) 2 + (y + 2)2 =16

(C) (x – 4)2 + (y – 4)2 = 8

(D) (x – 2)2 + (y – 2)2 =12

Answer: (A)
Image of P(3, 5) on the line x – y + 1 = 0 is

(x-3)/1 = (y-5)/-1 = (-2(3-5+1))/ 2 = 1

x = 4, y = 4
Image is (4, 4)
Which lies on (x – 2)2 + (y – 4)2 = 4

 

Q. 11: If Rolle’s theorem holds for the function f(x) = x3 – ax2 + bx – 4, x ∈ [1, 2] with f'(4/3) = 0, then ordered pair (a, b) is equal to :

(A) (–5, 8)

(B) (5, 8)

(C) (5, –8)

(D) (–5, –8)

Answer: (B)
f(1) = f(2)
⇒ 1 – a + b –4 = 8 – 4a + 2b –4
3a – b = 7 …(1)
f’(x) = 3x2 – 2ax + b
⇒f’(4/3) = 0 ⇒ 3 x 16/9 – 8a/3 + b =0
⇒–8a + 3b = –16 …(2)
a = 5, b = 8

 

Q. 12: If a curve passes through the origin and the slope of the tangent to it at any point (x, y) is (x2-4x+y+8)/(x-2), then this curve also passes through the point :

(A) (4, 5)

(B) (5, 4)

(C) (4, 4)

(D) (5, 5)

Answer: (D)

dy/dx = [(x-2)2 +y+4]/(x-2) = (x-2) + (y+4)/(x-2)

Let x – 2 = t ⇒ dx = dt
and y + 4 = u ⇒dy = du
dy/dx = du/dt
du/dt = t + u/t ⇒ du/dt – u/t = t
Here, IF = 1/t
u. (1/t) = ∫ t.(1\t) dt
⇒ u/t = t + c
⇒ (y+4)/(y-2) = (x – 2) + c
Passing through (0, 0)
c = 0
⇒ (y + 4) = (x – 2)2

 

Q. 13: The value of  ∫1-1 x2 ex^3 dx where [t] denotes the greatest integer ≤ t,is :

(A) (e+1)/3

(B) (e-1)/3e

(C) (e+1)/3e

(D) 1/3e

Answer: (C)
JEE MAIN 2021 Feb 25 Shift 1 Solution 19

 

Q. 14: When a missile is fired from a ship, the probability that it is intercepted is 1/3 and the probability that the missile hits the target, given that it is not intercepted, is 3/4. If three missiles are fired independently from the ship, then the probability that all three hit the target, is:

(A) 1/8

(B) 1/27

(C) 3/4

(D) 3/8

Answer:(A)
Probability of not getting intercepted = 2/3
Probability of missile hitting target = 3/4
Probability that all 3 hit the target = (2/3 x3/4)3 = ⅛

 

Q. 15: If the curves, x2/a + y2/b  and x2/c + y2/d intersect each other at an angle of 90°, then which of the following relations is true ?

(A) a + b = c + d

(B) a- b = c – d

(C) ab = (c+d)/(a+b)

(D) a-c = b+d

Answer: (B)

x2/a + y2/b ………(1)

diff : 

2x/a +2y/b dx/dy =0

y/b . dx/dy = -x/a

dx/dy = -bx/ay……(2)

x2/c + y2/d………(3)

Diff : 

dy/dx = -dx/cy ………(4)

m1m2 = –1 

⇒ -bx/ay × -dx/cy​ =−1

⇒ bdx2 = – acy2…….(5)
(1)–(3) ⇒ (1/a – 1/c)x2 + (1/b – 1/d) y2 = 0
Solve above equation using 5
⇒ (c – a) – (d – b) = 0
⇒ c – a = d – b
⇒ c – d = a – b

 

Q. 16: A tangent is drawn to the parabola y2 = 6x which is perpendicular to the line 2x + y =1. Which of the following points does NOT lie on it?

(A) (0,3)

(B) (-6,0)

(C) (4,5)

(D) (5,4)

Answer: (D)
Equation of tangent : y = mx + 3/(2m)
mT = (1/2) (Because perpendicular to line 2x + y = 1)
Therefore, tangent is: y = x/2 + 3 ⇒ x – 2y + 6 = 0

 

Q. 17: Let f, g: N→N such that f(n + 1)= f(n)+ f(1) for all n ∈ N and g be any arbitrary function. Which of the following statements is NOT true ?

(A) f is one-one

(B) If fog is one-one, then g is one-one

(C) If g is onto, then fog is one-one

(D) If f is onto, then f(n) = n for all n ∈ N

Answer: (C)
f(n + 1) = f(n) +f(1)
⇒ f(n + 1)- f(n)= f(1) → A.P. with common difference = f(1)
General term = Tn = f(1) + (n-1)f(1) = nf(1)
⇒f(n) = nf(1)
Clearly f(n) is one-one.
For fog to be one-one, g must be one-one.
For f to be onto, f(n) should take all the values of natural numbers.
As f(x) is increasing, f(1)=1
⇒f(n)=n
If g is many one, then fog is many one. So “if g is onto, then fog is one-one” is incorrect.

 

Q. 18: Let the lines (2 – i)z = (2 + i)zˉ and (2 + i)z + (i – 2)zˉ– 4i = 0, (here i2 = –1) be normal to a circle C. If the line iz + zˉ+ 1 + i = 0 is tangent to this circle C, then its radius is :

(A) 3/√2

(B) 3√2

(C) 3/(2√2)

(D) 1/(2√2)

Answer: (C)
(2–i)z = (2+i)zˉ

⇒(2–i)(x+ iy)=(2+i)(x–iy)
⇒2x–ix + 2iy + y=2x+ ix–2iy+y
⇒2ix –4iy=0
L1 ∶ x–2y=0
⇒(2+i)z+(i –2)zˉ–4i=0.
⇒(2+i) (x + iy)+(i –2)(x–iy)– 4i = 0.
⇒2x +ix + 2iy – y + ix – 2x + y +2iy – 4i =0
⇒2ix + 4iy – 4i =0
L2 ∶ x+2y–2 = 0
Solve L1 and L2
4y=2 or y=1/2
∴ x = 1
Centre(1, 1/2)
L3∶ iz + zˉ+ 1 + i = 0
⇒i(x+iy)+x–iy+1+i=0
⇒ix–y+x–iy+1+i=0
⇒(x–y+1)+i(x–y+1)=0
Radius = distance from (1, 1/2) to x – y + 1 = 0
r = (1-1/2+1)/ √2
r = 3/2√2

 

Q. 19:

JEE MAIN 2021 Feb 25 Shift 1 Solution 16

(A) 1/2

(B) 1/e

(C) 1

(D) 0

Answer: (C)
JEE MAIN 2021 Feb 25 Shift 1 Solved Problem 16

 

Q. 20: The total number of positive integral solutions (x, y, z) such that xyz = 24 is

(A) 36

(B) 45

(C) 24

(D) 30

Answer: (D)
x.y.z = 24
x.y.z= 23 × 31
x=2(a1) ⋅3(b1)
y = 2(a2) ⋅3(b2)
z = 2(a3)⋅3(b3)
a1, a2, a3 ∈ {0,1,2,3}
b1, b2, b3 ∈ {0,1}
Case 1: a1 + a2 + a3 =3
Non negative solution = (3+3-1) C(3-1) = 5C2 = 10
Case 2: b1 + b2 + b3 = 1
Non negative solution = (1+3-1) C(3-1) = 3C2 = 3
∴ Total solutions =10×3=30

Section B

Q. 1: Let A is a matrix where x, y and z are real numbers such that x + y + z > 0 and xyz = 2. If A2 = l3, then the value of x3 + y3 + z3 is ______.

Answer: 7
Maths JEE MAIN 2021 Shift 1 Feb 25 Solutions

 

Q. 2: Let A1, A2, A3,…. be squares such that for each n ≥ 1, the length of the side of An equals the length of diagonal of An+1. If the length of A1 is 12 cm, then the smallest value of n for which area of An is less than one is ____________.

Answer: (9)
JEE MAIN 2021 Feb 25 Shift 1 Solutions

 

Q. 3: The locus of the point of intersection of the lines (√3)kx + ky – 4√3 = 0 and √3x – y – 4√3 k = 0 is a conic, whose eccentricity is _________.

Answer: (2)
(√3)kx + ky – 4√3 = 0 …(1)
√3kx -ky= 4√3 k2 …(2)
Adding equation (1) & (2)
2√3 kx = 4√3(k^2 + 1)
x = 2 (k + 1/k) ….(3)
Subtracting equation (1) & (2)
y = 2√3(1/k – k) ………(4)
x2/4 – y2/12 = 4
x2/16 – y2/48 = 1 – Hyperbola
e2 = 1 + 48/16
or e = 2

 

Q. 4:

JEE MAIN 2021 Feb 25 Shift 1 Maths Problems Solution

Answer: 13
Maths JEE MAIN 2021 Feb 25 Shift 1 Solutions
|I2 + A|=|I2 – A|
From equation (1)
∴a2 + b2 = 1
⇒13(a2 + b2) = 13

 

Q. 5: The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area A. Then A4 is equal to ___________

Answer: (64)
JEE MAIN 2021 Feb 25 Shift 1 Maths Solutions

 

Q. 6: The number of points, at which the function f(x) = |2x + 1| – 3|x+2|+|x2 + x–2|, x ∈ R is not differentiable, is ________.

Answer: 2
Maths JEE MAIN 2021 Feb 25 Shift 1 Problem Solution
Check at 1, –2 and -1/2
Non-Differentiable at x = 1 and -1/2

 

Q. 7: If the system of equations

kx + y + 2z = 1

3x – y – 2z = 2

–2x – 2y – 4z = 3

has infinitely many solutions, then k is equal to __________.

Answer: 21
D = D1 = D2 = D3 = 0
Choose D2 = 0
k(–8+6)–1(–12–4)+2(9+4)=0
–2k + 16 + 26 = 0
2k = 42
k = 21

 

Q. 8: The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3, 4,5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5 is ________.

Answer: 32
Maths JEE MAIN 2021 Shift 1 Feb 25 Paper Solutions

 

Q. 9: Let f(x) be a polynomial of degree 6 in x, in which the coefficient of x6 is unity and it has extrema at x = –1 and x = 1. If limx→0 f(x)/x3 =1, then 5.f(2) is equal to _________.

Answer: (144)
f(x) = x6 + ax5 + bx4 + x3
f’(x) = 6x5 + 5ax4 + 4bx3 + 3x2
Roots 1 & – 1
Therefore, 6 + 5a + 4b + 3 = 0 & – 6 + 5a – 4b + 3 = 0 solving
a = -3/5 and b = -3/2
f(x) = x6 – (3/5)x5 – (3/2)x4 + x3
5.f(2) = 5 [64 – 96/5 – 24 + 8] = 144

 

Q. 10: Let  and be three given vectors. If r is a vector such that and r.b =0, then 

r.a =0 is equal to _______

Answer: 12
Maths 2021 JEE MAIN Feb 25 Shift 1 Solutions

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