**SSC CGL 4th March 2020 Shift-II **

**General Intelligence and Reasoning **

**Instructions **

For the following questions answer them individually

**Q. 1 Select the figure that can replace the question mark (?) in the following series. **

**Answer: **B.

**Q. 2 Three different positions of the same dice are shown. Select the symbol that will be on the face opposite to the one showing ‘@’. **

**A. **#

**B. **!

**C. **&

**D. **<

**Answer: **A.

**Q. 3 Select the option in which the words share the same relationship as that shared by the given pair of words. Turmeric : Spices **

**A. **Fig : Cashew Nuts

**B. **Nutmeg : Chilli Flakes

**C. **Dates : Dry Fruits

**D. **Apricot : Pear

**Answer: **C.

**Explanation: **

Turmeric is the spices.

Similarly,

Dates are the dry fruits.

∴ The correct answer is option C.

**Q. 4 In the given Venn diagram, ‘Group A’ represents those who can speak ‘English’, ‘Group B’ represents those who can speak ‘Hindi’, and ‘Group C’ represents those who can speak ‘Marathi’. The numbers given in the diagram represent the number of persons in that particular category. **

**How many persons can speak exactly two languages? **

**A. **12

**B. **3

**C. **21

**D. **18

**Answer: **D.

**Q. 5 Select the letter-cluster that can replace the question mark (?) in the following series. **

**AOS, CQU, ? , GUY, IWA. **

**A. **ESW

**B. **GSW

**C. **FSX

**D. **DRV

**Answer: **A.

**Explanation: **

The series follows as pattern,

(A + 2)(O + 2)(S + 2) = CQU

**(C + 2)(Q + 2)(U + 2) = ESW **

(E + 2)(S + 2)(W + 2) = GUY

(G + 2)(U + 2)(Y + 2) = IWA.

∴ The correct answer is option A.

**Q. 6 Select the number that can replace the question mark (?) in the following series. 4, 25, 121, ? , 529, 961 **

**A. **361

**B. **289

**C. **256

**D. **324

**Answer: **B.

**Explanation: **

The series follows as pattern,

(2)^{2} = 4

(5)^{2}= 25

(11)^{2}= 121

(17)^{2} **= **289

(23)^{2} = 529

(29)^{2} = 961

∴The correct answer is option B.

**Q. 7 In a certain code language, ‘GUM is coded as ‘49441169’. How will ‘WAX’ be coded as in that language? **

**A. **5291576

**B. **8412525

**C. **3611121

**D. **2891400

**Answer: **A.

**Explanation: **

G(7) =7^{2} = 49

U(21) =(21)^{2}= 441

M(13) =(13)^{2}= 169

Similarly,

W(23) =(23)^{2}= 529

A(1) =(1)^{2}= 1

X(24) =(24)^{2}= 576

‘WAX’ is coded as ‘5291576’.

∴ The correct answer is option A.

**Q. 8 Study the given pattern carefully and select the number that can replace the question mark (?) in it.**

**A. **27

**B. **28

**C. **29

**D. **25

**Answer: **B.

**Q. 9 Select the letter that can replace the question mark (?) in the following series. W, Q, ?, H, E, C. **

**A. **N

**B. **L

**C. **K

**D. **M

**Answer: **B.

**Explanation: **

W – 6 = Q

Q – 5 = L

L – 4 = H

H – 3 = E

E – 2 = C.

∴ The correct answer is option B.

**Q. 10 Study the given pattern carefully and select the number that can replace the question mark (?) in it **

**A. **446

**B. **444

**C. **4126

**D. **464

**Answer: **D.

**Q. 11 Product A is costlier than product B by ₹2. If the price of product A is increased by two times the price of product B, the new price of product A becomes ₹17. What is the price of product B? **

**A. **₹5

**B. **₹7

**C. **₹3

**D. **₹6

**Answer: **A.

**Explanation: **

Let the price of product A be x, so the price of product B = x – 2.

According to the question,

x + 2(x-2) = 17, solving this we get,

x + 2x – 4 = 17,

3x = 17 + 4

3x = 21, x = 7

Price of Product A. = Rs. 7, so Price of Product B. = 7 – 2 = Rs 5.

**Q. 12 Select the correct mirror image of the given figure when a mirror is placed on the right of the figure.**

**Answer: **D.

**Q. 13 How many triangles are there in the given figure? **

**A. **12

**B. **10

**C. **11

**D. **9

**Answer: **C.

**Q. 14 Arrange the following words in a logical and meaningful order. **

**1. Micron **

**2. Metre **

**3. Mile **

**4. Millimetre **

**5. Kilometre **

**6. Centimetre **

**A. **1-4-6-2-3-5

**B. **1-4-6-2-5-3

**C. **4-6-2-5-1-3

**D. **4-6-2-5-3-1

**Answer: **B.

**Explanation: **

Arrangement of the words in a logical and meaningful order

Micron, Millimetre, Centimetre, Metre, Kilometre, Mile

∴ The correct answer is option B.

**Q. 15 ‘Grapes’ is related to ‘Fruit’ in the same way as ‘Pepper’ is related to ‘…………….’ **

**A. **Cereals

**B. **Spices

**C. **Pulses

**D. **Dry Fruits

**Answer: **B.

**Explanation: **

‘Grapes’ is related to ‘Fruit’ in the same way as ‘Pepper’ is related to ‘spices’

∴ The correct answer is option B.

**Q. 16 In a certain code language, PYTHON’ is written as ‘LMFRWN’. How will ‘RHYTHM’ be written asin that language? **

**A. **MFRWFX

**B. **NFRWFS

**C. **KFRWFP

**D. **MFRWFT

**Answer: **C.

**Explanation: **

Similarly,

∴ The correct answer is option C.

**Q. 17 Select the option whois related to the third number in the same way as the second number is related to the first number. 6 : 252 :: 5 : ? **

**A. **175

**B. **150

**C. **125

**D. **225

**Answer: **B.

**Explanation: **

(6)^{3 }+ (6)^{2} = 216 + 36 = 252

(5)^{3 }+ (5)^{2} = 125 + 25 = 150

∴The correct answer is option B.

**Q. 18 Select the option in which the given figure is embedded (rotation is not allowed). **

**Answer: **A.

**Q. 19 Fourletter-clusters have been given, out of which three are alike in some manner and one is different. Select the odd letter-cluster. **

**A. **HFE

**B. **HVG

**C. **GMF

**D. **DVR

**Answer: **A.

**Explanation: **

Except option A, remaining all have only consonant letters.

∴ The correct answer is option A.

**Q. 20 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(s) from the statements. Statements: **

**1. All cars are trucks. **

**2. Some buses are cars. **

**Conclusions: **

**I. All cars are buses. **

**II. Some buses are trucks. **

**III. All trucks are buses. **

**A. **Only conclusions II and III follow.

**B. **Only conclusions I and III follow.

**C. **Only conclusion I follows.

**D. **Only conclusion II follows.

**Answer: **D.

**Explanation: **

From Venn diagram,

Only conclusion II follows.

∴ The correct answer is option D.

**Q. 21 ***A *+ *B ***means ‘B. is the sister of A’: **

*A *− *B ***means ‘A. is the father of B’: **

*A *× *B ***means ‘B. is the son of A’; **

*A *÷ *B ***means ‘B. is the husband of A’. *** *

**If ***E *÷ *F *− *H *+ *J *× *G *+ *D***, then how is D. related to H? **

**A. **Father

**B. **Niece

**C. **Uncle

**D. **Aunt

**Answer: **B.

**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,

D. is the niece of the H

**Q. 22** **Select the option that depicts how the given transparent sheet of paper would appear if it is folded at the dotted line.**

**Answer: **D.

**Q. 23 Four words have been given, out of which three are alike in some manner and one is different. Select the odd word. **

**A. **Rajkot

**B. **Ahmedabad

**C. **Surat

**D. **Jhalrapatan

**Answer: **D.

**Explanation: **

Except the option D, remaining all are cities of Gujarat state.

∴ The correct answer is option D.

**Q. 24 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 the rest. **

**A. **6-174

**B. **8-138

**C. **5-155

**D. **11-143

**Answer: **B.

**Explanation: **

174 is divisible by 6.

155 is divisible by 5.

143 is divisible by 11.

But,

138 is not divisible by 8.

∴ The correct answer is option B.

**Q. 25 Which two digits should be interchanged to make the given equation correct? **

32 ÷ 6 + 26 − 13 × 6 = 54

**A. **3 and 1

**B. **3 and 6

**C. **6 and 2

**D. **2 and 3

**Answer: **C.

**Explanation: **

32 ÷ 6 + 26 − 13 × 6 = 54

From the option C,

On interchanging,

36 ÷ 2 + 62 − 13 × 2 = 54

18 + 62 − 26 = 54

54 = 54

∴ The correct answer is option C.

**General Awareness **

**Instructions **

For the following questions answer them individually

**Q. 26 Which of the following is NOT a twin city of India? **

**A. **Hubli and Dharwad

**B. **Cuttack and Bhubaneswar

**C. **Ahmedabad and Gandhinagar

**D. **Thrissur and Thiruvalla

**Answer: **D.

**Q. 27 Who is the first Indian to bag two International hat-tricks in cricket? **

**A. **Virat Kohli

**B. **Kedar Jadhav

**C. **Rohit Sharma

**D. **Kuldeep Yadav

**Answer: **D.

**Q. 28 Who chaired the sixth meeting of the Island Development Agency in New Delhi in January 2020? **

**A. **Narendra Modi

**B. **Nirmala Sitharaman

**C. **Nitin Gadkari

**D. **Amit Shah

**Answer: **D.

**Q. 29 In which state did the second phase of Intensified Mission Indradhanush (IMI) 2.0 begin in January 2020? **

**A. **Kerala

**B. **Uttar Pradesh

**C. **Punjab

**D. **Bihar

**Answer: **B

**Q. 30 Who was chosen as foreign secretary of India in January 2020? **

**A. **Harsh Vardhan Shringla

**B. **Nirupama Rao

**C. **Ranjan Mathai

**D. **Vijay Keshav Gokhale

**Answer: **A.

**Q. 31 Which city of India is known as ‘The Athens of the East’? **

**A. **Patna

**B. **Allahabad

**C. **Kochi

**D. **Madurai

**Answer: **D.

**Q. 32 In which city was the Jhanda Satyagraha or Flag Satyagraha of 1923 held? **

**A. **Bombay

**B. **Nagpur

**C. **Calcutta

**D. **Ahmedabad

**Answer: **B.

**Q. 33 Which part of the body is responsible for the manufacture of red blood cells? **

**A. **Heart

**B. **Brain

**C. **Lungs

**D. **Bone marrow

**Answer: **D.

**Q. 34 Which pillar inscriptions have recorded the achievements of Samudra Gupta, who was known as the ‘Napoleon of India’ for his conquests? **

**A. **Allahabad Pillar

**B. **Iron Pillar

**C. **Vijaya Stambha

**D. **Sun Pillar

**Answer: **A.

**Q. 35 Who was appointed as Managing Director of the International Monetary Fund in October, 2019? **

**A. **Rodrigo Rato

**B. **Christine Lagarde

**C. **Kristalina Georgieva

**D. **Dominique Strauss-Kahn

**Answer: **C.

**Q. 36 Which of the following is NOT a nationalised bank? **

**A. **United Bank of India

**B. **State Bank of India

**C. **Punjab National Bank

**D. **Punjab and Sind Bank

**Answer: **B.

**Q. 37 Jellyfish are an example of which type of phylum? **

**A. **Phylum -Porifera

**B. **Phylum -Protozoa

**C. **Phylum -Ctenophora

**D. **Phylum – Cnidaria

**Answer: **D.

**Q. 38 In which period was the legendary Victoria Terminus station (currently Chhatrapati Shivaji Maharaj Terminus), Mumbai built? **

**A. **1933 to 1943

**B. **1911 to 1921

**C. **1843 to 1853

**D. **1878 to 1888

**Answer: **D.

**Q. 39 Which Tennis star will have a Swiss coin minted in his/her honour? **

**A. **Rafael Nadal

**B. **Novak Djokovic

**C. **Serena Williams

**D. **Roger Federer

**Answer: **D.

**Q. 40 In the sequence of planets in the solar system, which planet comes in between Mars and Saturn? **

**A. **Uranus

**B. **Venus

**C. **Jupiter

**D. **Mercury

**Answer: **C.

**Q. 41 In which state has the Jawara Dance, a dance form to celebrate wealth, originated? **

**A. **Rajasthan

**B. **Madhya Pradesh

**C. **Gujarat

**D. **Kerala

**Answer: **B.

**Q. 42 Which Union Minister of Home Affairs released a book titled Karmayodha Granth in New Delhi? **

**A. **P Chidambaram

**B. **Amit Shah

**C. **Sushilkumar Shinde

**D. **Rajnath Singh

**Answer: **B.

**Q. 43 Which city in India is world renowned for one of the most traditional embroidery styles, Chikankari? **

**A. **Ahmedabad

**B. **Hyderabad

**C. **Udaipur

**D. **Lucknow

**Answer: **D.

**Q. 44 John Maynard Keynes, best known for his economic theories (Keynesian economics), hailed from which country? **

**A. **England

**B. **Australia

**C. **Denmark

**D. **Sweden

**Answer: **A.

**Q. 45 Georg Simon Ohm in whose honour we have the famous Ohm’s Law, hailed from which country? **

**A. **Russia

**B. **Spain

**C. **Poland

**D. **Germany

**Answer: **D.

**Q. 46 Who was the first Governor of Madhya Pradesh? **

**A. **BD. Sharma

**B. **GP Singh

**C. **NN Wanchu

**D. **Dr. Sitaramayya

**Answer: **D.

**Q. 47 Freedom fighter Sucheta Kripalani, became the first woman chief minister of which state? **

**A. **Andhra Pradesh

**B. **Uttar Pradesh

**C. **Gujarat

**D. **Rajasthan

**Answer: **B.

**Q. 48 Methane is a colourless, odourless, non-toxic but flammable gas. What is its common name? **

**A. **Laughing gas

**B. **Heating gas

**C. **Blue vitriol

**D. **Marsh gas

**Answer: **D.

**Q. 49 The development of a fruit without fertilization is called ______. **

**A. **Parthenocarpy

**B. **Gametogamy

**C. **Hybridogenesis

**D. **Apomixis

**Answer: **A.

**Q. 50 Which US based Indian topped the Forbes India’s ‘20 people to watch in the 2020s’ list? **

**A. **Prashant Kishor

**B. **Hasan Minhaj

**C. **Mahua Moitra

**D. **Dushyant Chautala

**Answer: **B.

**Quantitative Aptitude **

**Instructions **

For the following questions answer them individually

**Q. 51 The time taken by a boat to travel 13 km downstream is the same as time taken by it to travel 7 km upstream. If the speed of the stream is 3 km/h, then how much time (in hours) will it take to travel a distance of 44.8 km in still water? **

**A. **4^{12}/_{25}

**B. **5^{3}/_{5}

**C. **5^{2}/_{5}

**D. **4^{13}/_{25}

**Answer: **A.

**Explanation: **

Speed of the stream = 3 km/h

Let the speed of the boat be v.

Speed in downstream = 3 + v

Speed in upstream = v – 3

Time = distance/speed

According to the question,

The time taken by a boat to travel 13 km downstream = time taken by boat to travel 7 km upstream

13/(3 + v) = 7/(v – 3)

13v – 39 = 21 + 7v

6v = 60

v = 10 km/h

Speed of boat = 10 km/h

The time taken by a boat to travel a distance of 44.8 km in still water = 44.8/10 = 112/25 = 4^{12}/_{25}hr

**Q. 52 The given table represents the revenue (in ₹ crores) of a company from the sale of four products A. B. C. and D. in 6 years. Study the table carefully and answer the question that follows. **

**The number of years in which the revenue of the company from the sale of product D. is more than the average revenue from the sale of product A. over six years, is: **

**A. **4

**B. **1

**C. **3

**D. **2

**Answer: **D.

**Explanation: **

The number of years in which the revenue of the company from the sale of product D. is more than the average revenue from the sale of product A. over six years = 2

(In the year 2013 and 2014)

**Q. 53 In **△*PQR*, ∠*Q *= 85^{∘ }**and **∠*R *= 65^{∘}**. Points S and T are on the sides PQ and PR, respectively such that **∠*STR *= 95^{∘}**, and the ratio of the QR and ST is 9 : 5. If PQ = 21.6 cm, then the length of PT is: **

**A. **10.5 cm

**B. **9.6 cm

**C. **12 cm

**D. **9 cm

**Answer: **C.

**Explanation: **

∠*PTS *+ ∠*STR *= 180^{∘}

∠*PTS *= 180^{∘ }− 95^{∘ }= 85^{∘}

△PTS is similar to △PQR So,

( ∠P is common and ∠*PTS *= ∠*SQR * )

*ST / QR *= *PT/PQ *

(QR : ST = 9 : 5 and PQ = 21.6 cm)

*5 / 9 *= *PT/21.6 *

21.6 × 5 = *PT *× 9

PT = 108/9 = 12 cm

∴ The length of PT is 12 cm.

**Q. 54 If **30*x*^{2 }− 15*x *+ 1 = 0**, then what is the value of **25*x*^{2 }+ (36*x*^{2})^{ −1}**? **

**A. **9/2

**B. **6 ¼** **

**C. **65/12

**D. **55/12

**Answer: **D.

**Explanation: **

30*x*^{2 }− 15*x *+ 1 = 0

Dividing by x,

30*x *− 15 + ^{1}/*x *= 0

5*x *− 15/6 + ^{1}/6*x *=

5*x *+ ^{1}/6*x *= 5/2

taking square both side,

(5*x *+ ^{1}/6*x*)^{2 } = (5/2)^{2 }

25*x*^{2 }+ ^{1}/36*x*^{2} + 2 × 5*x *× ^{1}/6*x *= 25/4

25*x*^{2 }+ ^{1}/36*x*^{2 }= 25/4 – 5/3

25*x*^{2 }+ ^{1}/36*x*^{2 }= 55/12

**Q. 55 The income of A is 60% less than that of B, and the expenditure of A is equal to 60%of B’s expenditure. If A’s income is equal to 70% of B’s expenditure, then what is the ratio of the savings of A and B? **

**A. **3 : 8

**B. **5 : 9

**C. **4 : 7

**D. **2 : 15

**Answer: **D.

**Explanation: **

Let the income of B be 100.

Income of A = 100×40/100 = 40

A’s income is equal to 70% of B’s expenditure so,

40 = 70% of B’s expenditure

Expenditure of B = 40/70×100 = 400/7

Saving of B = 100 – 400/7 = 300/7

The expenditure of A is equal to 60%of B’s expenditure so,

Expenditure of A = 60% of B’s expenditure

Expenditure of A = 60× 400/(7×100) = 240/7

Saving of A. = 40 – 240/7 = 40/7

The ratio of the savings of A and B = 40/7 : 300/7 = 2 : 15

**Q. 56 The value of is:**

**A. **1 ⅘

**B. **1 ^{9}/_{10}

**C. **3 ⅘** **

**D. **9 ½

**Answer: **B.

**Explanation:**

**Q. 57 A cylindrical vessel of radius 30 cm and height 42 cm is full of water. Its contents are emptied into a rectangular tub of length 75 cm and breadth 44 cm. The height (in cm) to which the water rises in the tub is: (Take ***π *= 22/7**) **

**A. **36

**B. **30

**C. **40

**D. **45

**Answer: **A.

**Explanation: **

Volume of the cylindrical vessel = *πr*^{2}*h *= ^{22}/_{7} × 30^{2 }× 42 = 118800

If we replace the water from the cylindrical vessel to rectangular tub then volume should be equal of the cylindrical vessel rectangular tub.

Volume of the cylindrical vessel = Volume of rectangular tub

118800 = length ×*breadth *× *height*

118800 = 75 × 44 × *height *

Height = 118800/3300 = 36 cm

**Q. 58 The given table represents the revenue (in ₹ crores) of a company from the sale of four products A B C and D in 6 years. Study the table carefully and answer the question that follows. **

**The total revenue of the company from the sale of products B, C and D in 2014 is what percentage of the total revenue from the sale of products C and D in 6 years? **

**A. **18

**B. **25

**C. **28

**D. **20

**Answer: **B.

**Explanation: **

Total revenue of the company from the sale of products B, C and D in 2014 = 92 + 96 + 92 = 280

Total revenue from the sale of products C. and D. in 6 years = 82 + 76 + 98 + 102 + 96 + 92 + 88 +93 + 93 + 97 + 103 + 102 = 1120

Required percentage =^{280}/1120 ×100 = 25%

**Q. 59 If **7 sin^{2 } *θ *− cos^{2 }*θ *+ 2 sin *θ *= 2, 0^{∘ }< *θ *< 90^{∘}**, then the value of **(sec 2*θ*+cot 2*θ*)/(cosec 2*θ*+tan 2*θ*) **is: **

**A. (**2√3+1)/ 3

**B. **1

**C. **⅕ (1+2√3)

**D. ⅖ **(1+√3)

**Answer: **C.

**Explanation: **

7 sin^{2 }*θ *− cos^{2 }*θ *+ 2 sin *θ *= 2

⇒ 7 sin^{2} *θ *− ^{ }cos^{2 }*θ *+ 2 sin *θ *− 2 = 0

⇒ 7 sin^{2} *θ *− (1 − sin^{2} *θ*) +2 sin *θ *− 2 = 0

⇒ 8 sin^{2 } *θ *+ 2 sin *θ *− 3 = 0

⇒ 8 sin^{2} *θ *+ 6 sin *θ *− 4 sin *θ *− 3 = 0

⇒ 2 sin *θ*(4 sin *θ *+ 3) − 1(4 sin *θ *+ 3) = 0

⇒ (2 sin *θ *− 1)(4 sin *θ *+ 3) = 0

0^{∘ }< *θ *< 90^{∘}

For ,

2 sin *θ *− 1=0

*θ *= sin^{-1}(1/2)

*θ *= 30°

(sec 2×30°+cot 2×30°)/(cosec 2×30°+tan 2×30°)

**Q. 60 ****The ratio of boys and girls in a group is 7 : 6. If 4 more boys join the group and 3 girls leave the group, then the ratio of boys to girls becomes 4 : 3. What is the total number of boys and girls initially in the group? **

**A. **117

**B. **78

**C. **91

**D. **104

**Answer: **D.

**Explanation: **

The ratio of boys and girls in a group is 7 : 6.

Let the boys be 7x and girls be 6x.

When 4 more boys join the group and 3 girls leave the group, then the ratio of boys to girls = 4 : 3

(7*x*+4)/(6*x*−3) = 4/3

21x + 12 = 24x -12

3x = 24

x = 8

Initially boys and girls = 7x + 6x = 13x = 13×8 = 104

**Q. 61 The difference in compound interest on a certain sum at 10% p.a. for one year, when the interest is compounded half yearly and yearly, is ₹88.80. What is the simple interest on the same sum for 1⅔ years at the same rate? **

**A. **₹5,916

**B. **₹5,986

**C. **₹5,980

**D. **₹5,920

**Answer: **D.

**Explanation: **

Principal = p

Rate(r) = 10%

Time(t) = 1 year

compound interest = *p*(1 + *r*/100)* ^{t }*−

When interest is calculated yearly = *p*(1 + 10/100) − *p *= *p *× (110/100) − *p*

When interest is calculated half yearly,

Rate(r) = 10/2 = 5%

Time(t) = 1×2 = 2

Interest = p(1 + 5/100)^{2} – p = p(105/100)^{2} – p

Difference of interest = 88.80

*p *× (105/100) × (105/100) − *p *− *p *× (110/100) + *p *= 88.80

*p *× 1.05 × 105 − *p *× 110 = 8880

110.25p – 110p = 8880

p = 8880/.25 = 35520

Simple interest for 1⅔ years,

t =1⅔ = 5/3 years

Interest =prt/100 = (35520 ×10 ×5/3)/100

= Rs.5920

**Q. 62 The expression **3 sec^{2 }*θ *tan^{2 }*θ *+ tan^{6 }*θ *− sec^{6} *θ ***is equal to: **

**A. **-2

**B. **1

**C. **2

**D. **-1

**Answer: **D.

**Explanation: **

3 sec^{2 }*θ *tan^{2 }*θ *+ tan^{6 }*θ *− sec^{6} *θ*

= −3 sec^{2 }*θ *tan^{2 }*θ*(tan^{2 }*θ *− sec^{2 }*θ*) + tan^{6 }*θ *− sec^{6} *θ*

(∵ tan^{2 }*θ *− sec^{2 }*θ *= −1)

= (tan^{2 }*θ *− sec^{2} *θ* )^{3}

( ∵ (*a *− *b*)^{3 }= *a*^{3 }− *b*^{3 }− 3*ab*(*a *− *b*) )

=(−1)^{3} = -1

**Q. 63 One-third of goods are sold at a 15% profit. 25% of the goods are sold at a 20% profit and the rest at a 20% loss. If the total profit of ₹138.50 is earned on the whole transaction, then the value(in ₹) of the goods is: **

**A. **₹8,587

**B. **₹8,030

**C. **₹7,756

**D. **₹8,310

**Answer: **D.

**Explanation: **

Let the total goods be 300

One third, means 100 goods are sold at 15℅ profit

25℅ means 75 goods are sold at 20℅ profit

The rest, means 125 goods are 20℅ loss

Let the price of each good be Re. 1

So, now calculating the profit and loss amounts:

For 100 goods, profit is 15℅ = Rs. 115

For 75 goods, profit is 20℅ = Rs. 90

For 125 goods, loss is 20℅ = Rs. 100

So, total amount of the selling price= Rs. 305

Total cost price = Rs.300

So, the profit = Selling price- cost price = Rs. 305-300 = Rs.5

Now equating it to the real values:

Rs. 5 is the profit when the total amount of goods is Rs 300.

Rs. 138.50 is the profit when total amount of goods is= (300/5)*138.5 = Rs. 8310

∴ The value of the goods is Rs. 8310.

**Q. 64 The given table represents the revenue (in ₹ crores) of a company from the sale of four products A B C and D in 6 years. Study the table carefully and answer the question that follows. **

**What is the ratio of the total revenue of the company in 2014 from the sale of all the four products to the total revenue from the sale of product C in 2014 to 2017? **

**A. **14 : 23

**B. **18 : 19

**C. **7 : 10

**D. **7 : 9

**Answer: **B.

**Explanation: **

Total revenue of the company in 2014 from the sale = 80 + 92 + 96 + 92 = 360

The total revenue from the sale of product C. in 2014 to 2017 = 96 + 88 + 93 + 103 = 380

The ratio of the total revenue of the company in 2014 from the sale of all the four products to the total revenue from the sale of product C. in 2014 to 2017 = 360 : 380

= 18 : 19

**Q. 65 If the 6-digit numbers ***x*35624** and **1257*y*4** are divisible by 11 and 12, respectively, then what is the value of (5x – 2y ) ? **

**A. **26

**B. **12

**C. **10

**D. **13

**Answer: **A.

**Explanation: **

Divisibility rule of 11,

The sum of of alternative digit are equal so,

x + 5 + 2 = 3 + 6 + 4

x = 6

Divisibility rule of 12,

The number should be divisible by 3 and 4.

For the divisible by 4,

last 2 digits of the number should by divisible by 4 so possible value of y =

Value of (5x – 2y ) = 5 × 6 − 2 × 2 = 30 – 4 = 26

**Q. 66 If a + b + c = 7 and ab + bc + ca = -6, then the value of ***a*^{3 }**+ ***b*^{3}** + ***c*^{3}**-3***abc ***is: **

**A. **469

**B. **472

**C. **463

**D. **479

**Answer: **A.

**Explanation: **

We know that,

*a*^{3 }+ *b*^{3 }+ *c*^{3 }− 3*abc *= (*a *+ *b *+ *c*)(*a*^{2 }+ *b*^{2 }+ *c*^{2 }− (*ab *+ *bc *+ *ac*))

a + b + c = 7

Squaring both sides,

(*a *+ *b *+ *c*)^{2 }= 49

*a*^{2 }+ *b*^{2 }+ *c*^{2 }+ 2(*ab *+ *bc *+ *ac*) = 49

*a*^{2 }+ *b*^{2 }+ *c*^{2 }= 49 + 12 = 61

*a*^{3 }+ *b*^{3 }+ *c*^{3 }− 3*abc *= (*a *+ *b *+ *c*)(*a*^{2 }+ *b*^{2 }+ *c*^{2 }− (*ab *+ *bc *+ *ac*))

= 7(61 – (-6)) = 7× 67 = 469

**Q. 67 The given table represents the revenue (in ₹ crores) of a company from the sale of four products A, B, C and D in 6 years. Study the table carefully and answer the question that follows. **

**By what percentage is the total revenue of the company from the sale of products A, B and D in 2012 and 2013 more than the total revenue from the sale of product B in 2013 to 2016? (Correct to one decimal place) **

**A. **44.5

**B. **31.2

**C. **43.6

**D. **45.4

**Answer: **D.

**Explanation: **

Total revenue of the company from the sale of products A, B. and D. in 2012 and 2013 = 98 + 74 + 74 + 94 + 96 + 102 = 538 Total revenue from the sale of product B. in 2013 to 2016 = 96 + 92 + 84 + 98 = 370

Required percentage =(538−370)/370 × 100 = 45.4%

**Q. 68 A and B, working together, can complete a work in d days. Working alone, A takes (8 + d) days and B. takes (18 + d) days to complete the same work. A work for 4 days. The remaining work will be completed by B alone, in: **

**A. **24 days

**B. **16 days

**C. **18 days

**D. **20 days

**Answer: **A.

**Explanation: **

To find the time when A and B,

working together = √(*moredaystakenbyA *× *moredaystakenbyB *)

d = 12

Time taken by A to complete the work = (8 + d) = 8 + 12 = 20

Time taken by B to complete the work = (18 + d) = 18 + 12 = 30 Let the total work be 60.

(LCM of 20 and 30 is 60.)

Efficiency of A = 60/20 = 3

Efficiency of B = 60/30 = 2

Work done by A in 4 days = efficiency 3× 4 = 12days

Remaining work = 60 – 12 = 48

Time taken by B to complete the remaining work = 48/2 = 24 days

The remaining work will be completed by B alone, in 24 days.

**Q. 69 Two chords AB and CD of a circle are produced to intersect each other at a point P outside the circle. If AB = 7 cm, BP = 4.2 cm and PD = 2.8 cm, then the length of CD is: **

**A. **12 cm

**B. **14.6 cm

**C. **15.8 cm

**D. **14 cm

**Answer: **D.

**Explanation: **

AB = 7 cm, BP = 4.2 cm and PD = 2.8 cm

By the property,

PA×PB = PC× PD

(PA = AB + BP = 7 + 4.2 = 11.2 cm)

11.2 × 4.2 = PC × 2.8

PC = 16.8 cm

CD = PC – PD = 16.8 – 2.8 = 14 cm

**Q. 70 The value of{tan**^{2}*θ*** – sin**^{2}*θ***}{2 + tan**^{2}*θ*** + cot**^{2}*θ***} is: **

**A. **cosec^{6}*θ*

**B. **cos^{4}*θ*

**C. **sin^{6}*θ*

**D. **sec^{4}*θ*

**Answer: **C.

**Explanation: **

{tan^{2}*θ* – sin^{2}*θ*}{2 + tan^{2}*θ* + cot^{2}*θ*}

={tan^{2}*θ* – sin^{2}*θ*}{1 + tan^{2}*θ* + 1 + cot^{2}*θ*}

={tan^{2}*θ* – sin^{2}*θ*}{sec^{2}*θ* + cosec^{2}*θ*}

={tan^{2}*θ* – sin^{2}*θ*}{1/cos^{2}*θ* +1/sin^{2}*θ*}

={(tan^{2}*θ* – sin^{2}*θ*)(sin^{2}*θ *cos^{2}*θ*)}{cos^{2}*θ* + sin^{2}*θ*}

= (tan^{2}*θ* – sin^{2}*θ*)(sin^{2}*θ*cos^{2}*θ*)

= sin^{4}*θ* – sin^{4}*θ *cos^{2}*θ*

= sin^{4}*θ*(1 – cos^{2}*θ*) = sin^{4}*θ *sin^{2}*θ* = sin^{6}*θ*

**Q. 71 In ΔABC, D and E are the points on sides AC and BC, respectively, such that DE is parallel to AB. F is a point on CE such that DF ****⊥**** CE. If CE = 6 cm, and CF = 2.5 cm, then BC is equal to: **

**A. **14.4 cm

**B. **15.6 cm

**C. **14 cm

**D. **12 cm

**Answer: **A.

**Q. 72 The marked price of an article is ₹740. After two successive discounts of 15% and x %,it is sold for ₹566.10. What is the value of x ? **

**A. **12

**B. **5

**C. **10

**D. **20

**Answer: **C.

**Explanation: **

**Q. 73 The average weight of some students in a class was 58.4 kg. When 5 students having the average weight 62.8 kg joined the class, the average weight of all students in the class increased by 0.55 kg. The number of students initially in the class, were: **

**A. **30

**B. **35

**C. **25

**D. **40

**Answer: **B.

**Explanation: **

The average weight of some students in a class = 58.4 kg

Let the total number of students be n.

Total weight of n students = 58.4n kg

The average weight of 5 students = 62.8 kg

Total weight of 5 students = 62.8 × 5 = 314 kg

The average weight of (n + 5) students = 58.4 + 0.55 = 58.95 kg

Total weight of (n + 5) students = 58.95(n + 5) kg

Total weight of n students + Total weight of 5 students = 58.95(n + 5)

58.4n + 314 = 58.95(n + 5)

58.4n + 314 = 58.95n + 294.75

0.55n = 19.25

n = 1925/55 = 35

∴ 35 students were initially in the class.

**Q. 74 PRT is a tangent to a circle with centre O, at the point R on it. Diameter SQ of the circle is produced to meet the tangent at P and QRis joined. If ****∠****QRP = 28**^{0}**, then the measure of ****∠****SPR is: **

**A. **29^{0}

**B. **34^{0}

**C. **62^{0}

**D. **32^{0}

**Answer: **B.

**Explanation: **

∠QRP = 28^{0}

∠ORP = 90^{0} (radius to tangent through PT of contact)

∠QRO = ∠ORP – ∠QRP

∠QRO = 90^{0} – 28^{0} = 62^{0}

Now,

∠QRO = ∠OQR

(∵ OQ = OR(radius))

∠OQR = 62^{0}

∠RQP + ∠OQR = 180^{0}

∠RQP = 180^{0} – 62^{0} = 118^{0}

In the ΔOPR,

∠SPR + ∠RQP + ∠QRP = 180^{0}

∠SPR = 180^{0} – 118^{0} – 28^{0} = 34^{0}

**Q. 75 If P ={x**^{4}** – 8x}/{x**^{3}** – x**^{2}** – 2x}, Q ={x**^{2}** + 2x + 1}/{x**^{2}** – 4x – 5} and R ={2x**^{2}** + 4x + 8}{x – 5}, then (P**×**Q) ÷ R is equal to: **

**A. **½

**B. **1

**C. **2

**D. **4

**Answer: **A.

**Explanation: **

**English Comprehension **

**Instructions **

For the following questions answer them individually

**Q. 76 Select the most appropriate word to fill in the blank. **

**A reward is a ______ which motivates a person to achieve excellence in his field. **

**A. **memorial

**B. **collection

**C. **recognition

**D. **monument

**Answer: **C.

**Q. 77 Select the most appropriate meaning of the given Idiom. **

**The bee’s knees **

**A. **Observant

**B. **Extraordinary

**C. **Problematic

**D. **Foolish

**Answer: **B.

**Q. 78 Select the correctly spelt word. **

**A. **Embarasment

**B. **Encouragement

**C. **Comotion

**D. **Conscinteous

**Answer: **B.

**Q. 79 Select the most appropriate ANTONYM of the given word. **

**Obsolete **

**A. **Rigid

**B. **Remote

**C. **Outdated

**D. **Recent

**Answer: **D.

**Instructions **

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

**Q. 80 A. sudden rush of a large number of frightened people or animals. **

**A. **Lunacy

**B. **Recluse

**C. **Stampede

**D. **Scapegoat

**Answer: **C.

**Q. 81 One who loads and unloads ships. **

**A. **Spinster

**B. **Stevedore

**C. **Rustic

**D. **Captain

**Answer: **B.

**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:

Discipline is doing any work with rules and regulations. It is (1)______ misunderstood as a restriction to freedom but it makes our life organized. Discipline is a (2)______ for students

and people in different professions. A. disciplined person always (3)______ in each and every field of life. Disciplined people (4)______ a disciplined society and a powerful nation. Discipline should not be (5)______ upon the people, rather it should come from within.

**Q. 82 Select the most appropriate option for blank number (1) **

**A. **happily

**B. **usually

**C. **proudly

**D. **slowly

**Answer: **B.

**Q. 83 Select the most appropriate option for blank number (2) **

**A. **virtue

**B. **curse

**C. **dream

**D. **disadvantage

**Answer: **A.

**Q. 84 Select the most appropriate option for blank number (3) **

**A. **successful

**B. **success

**C. **succeeds

**D. **succeed

**Answer: **C.

**Q. 85 Select the most appropriate option for blank number (4) **

**A. **made

**B. **makes

**C. **had made

**D. **make

**Answer: **D.

**Q. 86 Select the most appropriate option for blank number (5) **

**A. **adorned

**B. **imposed

**C. **curbed

**D. **reposed

**Answer: **B.

**Instructions **

For the following questions answer them individually

**Q. 87 Given below are four jumbled sentences. Out of the given options pick the one that gives their correct order. **

**A. They can then purchase them on subsidized rates with additional loan facilities. **

**B. It will import technologically advanced medical instruments and provide them to entrepreneurs. **

**C. The Indian Government has announced certain facilities in the budget session. **

**D. This will help in strengthening the economic condition of entrepreneurs. **

**A. **CBAD.

**B. **CADB.

**C. **BDCA.

**D. **DCAB.

**Answer: **A.

**Q. 88 Select the most appropriate synonym of the given word. **

**Acknowledgement **

**A. **Confirmation

**B. **Elimination

**C. **Compensation

**D. **Confusion

**Answer: **A.

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

**A. This is because of its aroma, flavour and variety in the market. **

**B. Thus, it leads to poor health and mental disorders among children. **

**C. Children as well as teenagers are tempted towards junk food. **

**D. It has no or negligible nutritional value and high content of sugar and salt. **

**A. **BCDA.

**B. **CADB.

**C. **CDAB.

**D. **ACDB.

**Answer: **B.

**Q. 90 In the sentence identify the segment which contains the grammatical error. **

**When I reached the cinema hall, the movie had already began. **

**A. **already began

**B. **the movie had

**C. **the cinema hall

**D. **When I reached

**Answer: **A.

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

**The government should take stringent steps against terrorists and foil their ______ designs. **

**A. **conducive

**B. **benevolent

**C. **malicious

**D. **exemplary

**Answer: **C.

**Q. 92 Select the most appropriate meaning of the given idiom. **

**To throw a fit **

**A. **Caution someone about fitness

**B. **Become unconscious

**C. **Faint and fall down

**D. **Express extreme anger

**Answer: **D.

**Q. 93 Select the correctly spelt word. **

**A. **Rehersal

**B. **Employeed

**C. **Seperable

**D. **Veterinary

**Answer: **D.

**Q. 94 Select the most appropriate synonym of the given word. **

**Prodigal **

**A. **Humble

**B. **Trivial

**C. **Arrogant

**D. **Extravagant

**Answer: **D.

**Q. 95 Select the correct passive form of the given sentence. **

**His elder sister taught him English. **

**A. **He has been taught English by his elder sister.

**B. **He was taught English by his elder sister.

**C. **He is being taught English by his elder sister.

**D. **His elder sister is taught English by him.

**Answer: **B.

**Q. 96 Select the most appropriate option to substitute the underlined segment in the given sentence. If there is no need to substitute it, select No improvement. **

**The mathematical calculation of this problem is**** easy than a**** previous one. **

**A. **easiest than the

**B. **No Improvement

**C. **easy than the

**D. **easier than the

**Answer: **D.

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

**Those who follow a healthy routine is likely enjoying good health. **

**A. **is likely enjoying

**B. **good health

**C. **Those who follow

**D. **a healthy routine

**Answer: **A.

**Q. 98 Select the correct indirect form of the given sentence. **

**The teacher said to me, “You have not submitted the assignment.” **

**A. **The teacher said to me that I have not submitted the assignment.

**B. **The teacher said me that I had not submitted the assignment.

**C. **The teacher told to me that I have not submitted that assignment.

**D. **The teacher told me that I had not submitted the assignment.

**Answer: **D.

**Q. 99 Select the most appropriate option to substitute the underlined segment in the given sentence. No effort has been made by the Indian cricket team**** to cash off on**** its vibrant image in the World Cup. **

**A. **to cash in on

**B. **for cash through in

**C. **to cash up on

**D. **for cashing off on

**Answer: **A.

**Q. 100 Select the most appropriate ANTONYM of the given word. **

**Derogatory **

**A. **Depreciating

**B. **Insulting

**C. **Intricate

**D. **Complimentary

**Answer: **D

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