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. 4
B. 5
C. 6
D. 2
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. 7
B. 8
C. 9
D. 6
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. O
B. L
C. M
D. K
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. 7
D. 9
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. 5
B. 27
C. 16
D. 9
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) × R
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 = 70∘ and ∠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. 5
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. 1
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. 1
C. 5/4
D. 2
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.
