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) =72 = 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. 412/25
B. 53/5
C. 52/5
D. 413/25
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 = 412/25hr
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 30x2 − 15x + 1 = 0, then what is the value of 25x2 + (36x2) −1?
A. 9/2
B. 6 ¼
C. 65/12
D. 55/12
Answer: D.
Explanation:
30x2 − 15x + 1 = 0
Dividing by x,
30x − 15 + 1/x = 0
5x − 15/6 + 1/6x =
5x + 1/6x = 5/2
taking square both side,
(5x + 1/6x)2 = (5/2)2
25x2 + 1/36x2 + 2 × 5x × 1/6x = 25/4
25x2 + 1/36x2 = 25/4 – 5/3
25x2 + 1/36x2 = 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 = πr2h = 22/7 × 302 × 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 sin2 θ − cos2 θ + 2 sin θ = 2, 0∘ < θ < 90∘, then the value of (sec 2θ+cot 2θ)/(cosec 2θ+tan 2θ) is:
A. (2√3+1)/ 3
B. 1
C. ⅕ (1+2√3)
D. ⅖ (1+√3)
Answer: C.
Explanation:
7 sin2 θ − cos2 θ + 2 sin θ = 2
⇒ 7 sin2 θ − cos2 θ + 2 sin θ − 2 = 0
⇒ 7 sin2 θ − (1 − sin2 θ) +2 sin θ − 2 = 0
⇒ 8 sin2 θ + 2 sin θ − 3 = 0
⇒ 8 sin2 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
(7x+4)/(6x−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 − p
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 sec2 θ tan2 θ + tan6 θ − sec6 θ is equal to:
A. -2
B. 1
C. 2
D. -1
Answer: D.
Explanation:
3 sec2 θ tan2 θ + tan6 θ − sec6 θ
= −3 sec2 θ tan2 θ(tan2 θ − sec2 θ) + tan6 θ − sec6 θ
(∵ tan2 θ − sec2 θ = −1)
= (tan2 θ − sec2 θ )3
( ∵ (a − b)3 = a3 − b3 − 3ab(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 x35624 and 1257y4 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 a3 + b3 + c3-3abc is:
A. 469
B. 472
C. 463
D. 479
Answer: A.
Explanation:
We know that,
a3 + b3 + c3 − 3abc = (a + b + c)(a2 + b2 + c2 − (ab + bc + ac))
a + b + c = 7
Squaring both sides,
(a + b + c)2 = 49
a2 + b2 + c2 + 2(ab + bc + ac) = 49
a2 + b2 + c2 = 49 + 12 = 61
a3 + b3 + c3 − 3abc = (a + b + c)(a2 + b2 + c2 − (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{tan2θ – sin2θ}{2 + tan2θ + cot2θ} is:
A. cosec6θ
B. cos4θ
C. sin6θ
D. sec4θ
Answer: C.
Explanation:
{tan2θ – sin2θ}{2 + tan2θ + cot2θ}
={tan2θ – sin2θ}{1 + tan2θ + 1 + cot2θ}
={tan2θ – sin2θ}{sec2θ + cosec2θ}
={tan2θ – sin2θ}{1/cos2θ +1/sin2θ}
={(tan2θ – sin2θ)(sin2θ cos2θ)}{cos2θ + sin2θ}
= (tan2θ – sin2θ)(sin2θcos2θ)
= sin4θ – sin4θ cos2θ
= sin4θ(1 – cos2θ) = sin4θ sin2θ = sin6θ
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 = 280, then the measure of ∠SPR is:
A. 290
B. 340
C. 620
D. 320
Answer: B.
Explanation:
∠QRP = 280
∠ORP = 900 (radius to tangent through PT of contact)
∠QRO = ∠ORP – ∠QRP
∠QRO = 900 – 280 = 620
Now,
∠QRO = ∠OQR
(∵ OQ = OR(radius))
∠OQR = 620
∠RQP + ∠OQR = 1800
∠RQP = 1800 – 620 = 1180
In the ΔOPR,
∠SPR + ∠RQP + ∠QRP = 1800
∠SPR = 1800 – 1180 – 280 = 340
Q. 75 If P ={x4 – 8x}/{x3 – x2 – 2x}, Q ={x2 + 2x + 1}/{x2 – 4x – 5} and R ={2x2 + 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
