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SSC CGL (Tier - 2) Online Exam Paper - 2017 "held on 17 February 2018" Morning Shift (Quantitate Ability)

SSC CGL (Tier - 2) Online Exam Paper - 2017 "held on 17 February 2018"

Morning Shift (Quantitative Ability)

Exam Name: SSC CGL (Tier - 2)

Year: 2018

EXAM DATE : 17-February-2018

EXAM START TIME : 10:00:00

Total Marks: 200

QID : 1 - What is the unit digit of the sum of first 111 whole numbers?

Options:
1) 4
2) 6
3) 5
4) 0
Correct Answer: 5

QID : 2 - How many 100 digit positive number are there?

Options:
1) 9 × 10⁹⁹
2) 9 × 10¹⁰⁰
3) 10100
4) 11 × 10⁹⁸
Correct Answer: 9 × 10⁹⁹

QID : 3 -

Options:
1) 2
2) 1
3) 3
4) 3/2
Correct Answer: 2

QID : 4 -

Options:
1) 1/4
2) 1/2
3) 1
4) 2
Correct Answer: 2

QID : 5 - What is the unit digit of (217)⁴¹³ × (819)⁵⁴⁷ × (414)⁶²⁴ × (342)⁸¹²?

Options:
1) 2
2) 4
3) 6
4) 8
Correct Answer: 8

QID : 6 -

Options:
1) 6179/15275
2) 6070/14973
3) 7191/15174
4) 5183/16423
Correct Answer: 6070/14973

QID : 7 -

Options:
1) Only I
2) Only II
3) Only III
4) Only IV
Correct Answer: Only III

QID : 8 - N is the largest two digit number, which when divided by 3, 4 and 6 leaves the remainder 1, 2 and 4 respectively. What is the remainder when N is divided by 5?

Options:
1) 4
2) 2
3) 0
4) 1
Correct Answer: 4

QID : 9 -

Options:
1) Only I
2) Only II
3) Only III
4) Only IV
Correct Answer: Only III

QID : 10 - A and B are positive integers. If A + B + AB = 65, then what is the difference between A and B (A, B ≤ 15)?

Options:
1) 3
2) 4
3) 5
4) 6
Correct Answer: 5

QID : 11 - What is the value of 14³ + 16³ + 18³ + … + 30³?

Options:
1) 134576
2) 120212
3) 115624
4) 111672
Correct Answer: 111672

QID : 12 -

Options:
1) 69
2) 68
3) 70
4) 72
Correct Answer: 68

QID : 13 - If x + y + z = 0, then what is the value of (3y² + x² + z²)/(2y² – xz)?

Options:
1) 2
2) 1
3) 3/2
4) 5/3
Correct Answer: 2

QID : 14 - If P = 7 + 4√3 and PQ = 1, then what is the value of 1/P² + 1/Q²?

Options:
1) 196
2) 194
3) 206
4) 182
Correct Answer: 194

QID : 15 - If a³ + 3a² + 9a = 1, then what is the value of a³ + (3/a)?

Options:
1) 31
2) 26
3) 28
4) 24
Correct Answer: 28

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QID : 16 - x, y and z are real numbers. If x³ + y³ + z³= 13,x + y + z = 1 and xyz = 1, then what is the value of xy + yz + zx?

Options:
1) – 1
2) 1
3) 3
4) – 3
Correct Answer: – 3

QID : 17 - If (a + b)/c = 6/5 and (b + c)/a = 9/2, then what is the value of (a + c)/b?

Options:
1) 9/5
2) 11/7
3) 7/11
4) 7/4
Correct Answer: 7/4

QID : 18 - If x³ + y³ + z³ = 3(1 + xyz), P = y + z – x, Q = z + x – y and R = x + y – z, then what is the value of P³ + Q³ + R³– 3PQR?

Options:
1) 9
2) 8
3) 12
4) 6
Correct Answer: 12

QID : 19 - If x₁x₂x₃ = 4(4 + x₁ + x₂ + x₃), then what is the value of [1/(2 + x₁)] + [1/(2 + x₂)] + [1/(2 + x₃)]?

Options:
1) 1
2) 1/2
3) 2
4) 1/3
Correct Answer: 1/2

QID : 20 - If α and β are the roots of equation x² – x + 1 = 0, then which equation will have roots α³ and β³?

Options:
1) x2 + 2x + 1 = 0
2) x2 – 2x – 1 = 0
3) x2 + 3x – 1 = 0
4) x2 – 3x + 1 = 0
Correct Answer: x2 + 2x + 1 = 0

QID : 21 - If 3x + 5y + 7z = 49 and 9x + 8y + 21z = 126, then what is the value of y?

Options:
1) 4
2) 2
3) 3
4) 5
Correct Answer: 3

QID : 22 - Cost of 4 pens, 6 note books and 9 files is Rs 305. Cost of 3 pens, 4 notebooks and 2 files is Rs 145. What is the cost (in Rs) of 5 pens, 8 notebooks and 16 files?

Options:
1) 415
2) 465
3) 440
4) Cannot be determined
Correct Answer: 465

QID : 23 - ABC is a right angled triangle. ∠BAC = 90^o and ∠ACB = 60^o. What is the ratio of the circum radius of the triangle to the side AB?

Options:
1) 1 : 2
2) 1 : √3
3) 2 : √3
4) 2 : 3
Correct Answer: 1 : √3

QID : 24 -

Options:
1) 4√5
2) 4√4
3) 6√3
4) 4√6
Correct Answer: 4√5

QID : 25 - Triangle ABC is similar to triangle PQR and AB : PQ = 2 : 3. AD is the median to the side BC in triangle ABC and PS is the median to the side QR in triangle PQR. What is the value of (BD/QS)2?

Options:
1) 3/5
2) 4/9
3) 2/3
4) 4/7
Correct Answer: 4/9

QID : 26 -

Options:
1) 3√15
2) 5√15
3) 6√15
4) 4√15
Correct Answer: 4√15

QID : 27 -

Options:
1) 18
2) 9
3) 12
4) 15
Correct Answer: 18

QID : 28 - AB and AC are the two tangents to a circle whose radius is 6 cm. If ∠BAC = 60^o, then what is the value (in cm) of √(AB² + AC²)?

Options:
1) 6√6
2) 4√6
3) 9√3
4) 8√3
Correct Answer: 6√6

QID : 29 -

Options:
1) 4
2) 6
3) 4.5
4) 7.5
Correct Answer: 6

QID : 30 -

Options:
1) 67.5
2) 72
3) 78.5
4) 65
Correct Answer: 67.5

QID : 31 -

Options:
1) 3√3
2) 2√6
3) 4√2
4) 6√2
Correct Answer: 4√2

QID : 32 - The radius of two circles is 3 cm and 4 cm. The distance between the centres of the circles is 10 cm. What is the ratio of the length of direct common tangent to the length of the transverse common tangent?

Options:
1) √51 : √68
2) √33 : √17
3) √66 : √51
4) √28 : √17
Correct Answer: √33 : √17

QID : 33 - ABC is a triangle. AB = 5 cm, AC = √41 cm and BC = 8 cm. AD is perpendicular to BC. What is the area (in cm2) of triangle ABD?

Options:
1) 12
2) 6
3) 10
4) 20
Correct Answer: 6

QID : 34 -

Options:
1) (23√21)/4
2) (15√21)/4
3) (17√21)/5
4) (23√21)/5
Correct Answer: (17√21)/5

QID : 35 -

Options:
1) 108.5
2) 94.5
3) 70
4) 120
Correct Answer: 94.5

QID : 36 -

Options:
1) 24√3
2) 18√3
3) 72√3
4) 36√3
Correct Answer: 72√3

QID : 37 - Length and breadth of a rectangle are 8 cm and 6 cm respectively. The rectangle is cut on its four vertices such that the resulting figure is a regular octagon. What is the side (in cm) of the octagon?

Options:
1) 3(√11) – 7
2) 5(√13) – 8
3) 4(√7) – 11
4) 6(√11) – 9
Correct Answer: 3(√11) – 7

QID : 38 -

Options:
1) 31.36
2) 125.44
3) 62.72
4) 156.8
Correct Answer: 31.36

QID : 39 -

Options:
1) 414.46
2) 382.82
3) 406.48
4) 394.24
Correct Answer: 394.24

QID : 40 - A right prism has a square base with side of base 4 cm and the height of prism is 9 cm. The prism is cut in three parts of equal heights by two planes parallel to its base. What is the ratio of the volume of the top, middle and the bottom part respectively?

Options:
1) 1 : 8 : 27
2) 1 : 7 : 19
3) 1 : 8 : 20
4) 1 : 7 : 20
Correct Answer: [ No Correct Answer ]

QID : 41 - Radius of base of a hollow cone is 8 cm and its height is 15 cm. A sphere of largest radius is put inside the cone. What is the ratio of radius of base of cone to the radius of sphere?

Options:
1) 5 : 3
2) 4 : 1
3) 2 : 1
4) 7 : 3
Correct Answer: 5 : 3

QID : 42 - The ratio of curved surface area of a right circular cylinder to the total area of its two bases is 2 : 1. If the total surface area of cylinder is 23100 cm², then what is the volume (in cm³) of cylinder?

Options:
1) 247200
2) 269500
3) 312500
4) 341800
Correct Answer: 269500

QID : 43 -

Options:
1) 3740
2) 3432
3) 3124
4) 2816
Correct Answer: 3432

QID : 44 - 10 identical solid spherical balls of radius 3 cm are melted to form a single sphere. In this process 20% of solid is wasted. What is the radius (in cm) of the bigger sphere?

Options:
1) 24
2) 12
3) 8
4) 6
Correct Answer: 6

QID : 45 - The radius of base of a solid cylinder is 7 cm and its height is 21 cm. It is melted and converted into small bullets. Each bullet is of same size. Each bullet consisted of two parts viz. a cylinder and a hemisphere on one of its base. The total height of bullet is 3.5 cm and radius of base is 2.1 cm. Approximately how many complete bullets can be obtained?

Options:
1) 83
2) 89
3) 74
4) 79
Correct Answer: 83

QID : 46 - A cuboid of size 50 cm × 40 cm × 30 cm is cut into 8 identical parts by 3 cuts. What is the total surface area (in cm²) of all the 8 parts?

Options:
1) 11750
2) 14100
3) 18800
4) 23500
Correct Answer: 18800

QID : 47 -

Options:
1) 48[(√3) + 1]
2) 24[4 + (√3)]
3) 28[6 + (√3)]
4) 32[3 + (√3)]
Correct Answer: 32[3 + (√3)]

QID : 48 - What is the value of [(sin x + sin y) (sin x – sin y)]/[(cosx + cosy) (cosy – cosx)]?

Options:
1) 0
2) 1
3) – 1
4) 2
Correct Answer: 1

QID : 49 - What is the value of [(tan 5θ + tan 3θ)/4 cos 4θ (tan 5θ – tan 3θ)]?

Options:
1) sin 2θ
2) cos 2θ
3) tan 4θ
4) cot 2θ
Correct Answer: cos 2θ

QID : 50 - What is the value of (4/3) cot² (p/6) + 3 cos² (150^o) – 4 cosec² 45^o + 8 sin (p/2)?

Options:
1) 25/4
2) 1
3) – 7/2
4) 13/2
Correct Answer: 25/4

QID : 51 - What is the value of sin (B – C) cos (A – D) + sin (A – B) cos (C – D) + sin (C – A) cos (B – D)?

Options:
1) 3/2
2) – 3
3) 1
4) 0
Correct Answer: 0

QID : 52 -

Options:
1) 1
2) – 1
3) 0
4) 2
Correct Answer: – 1

QID : 53 - What is the value of cos [(180 – θ)/2] cos [(180 – 9θ)/2] + sin [(180 – 3θ)/2] sin [(180 – 13θ)/2]?

Options:
1) sin 2θ sin 4θ
2) cos 2θ cos 6θ
3) sin 2θ sin 6θ
4) cos 2θ cos 4θ
Correct Answer: cos 2θ cos 6θ

QID : 54 - What is the value of [tan² (90 – θ) – sin² (90 – θ)] cosec² (90 – θ) cot² (90 – θ)?

Options:
1) 0
2) 1
3) – 1
4) 2
Correct Answer: 1

QID : 55 - Two points P and Q are at the distance of x and y (where y > x) respectively from the base of a building and on a straight line. If the angles of elevation of the top of the building from points P and Q are complementary, then what is the height of the building?

Options:
1) xy
2) √( y/ x)
3) √( x/ y)
4) √( xy)
Correct Answer: √( xy)

QID : 56 - The tops of two poles of height 60 metres and 35 metres are connected by a rope. If the rope makes an angle with the horizontal whose tangent is 5/9 metres, then what is the distance (in metres) between the two poles?

Options:
1) 63
2) 30
3) 25
4) 45
Correct Answer: 45

QID : 57 - A Navy captain going away from a lighthouse at the speed of 4[(√3) – 1] m/s. He observes that it takes him 1 minute to change the angle of elevation of the top of the lighthouse from 60o to 45o. What is the height (in metres) of the lighthouse?

Options:
1) 240√3
2) 480[(√3) – 1]
3) 360√3
4) 280√2
Correct Answer: 240√3

QID : 58 -

If A equals to 15% of total applicants who are present at exam centre F and B equals to present applicants at exam centre K, then A is what percent of B?

Options:
1) 18.18
2) 11.25
3) 13.33
4) 14.28
Correct Answer: 11.25

QID : 59 -

Total number of offline applicants from exam centre H, K and F are how much less than the total number of present applicants from exam centre G and J?

Options:
1) 111420
2) 100920
3) 127370
4) 109990
Correct Answer: 100920

QID : 60 -

What are the total number of offline applicants from the exam centre F, H, J and G?

Options:
1) 393720
2) 963000
3) 564720
4) 428540
Correct Answer: 564720

QID : 61 -

What is the ratio of total number of present applicants from exam centre K to total number of offline applicants from exam centre J?

Options:
1) 40 : 41
2) 80 : 81
3) 10 : 9
4) 7 : 11
Correct Answer: 80 : 81

QID : 62 -

What are the total number of present applicants from exam centre H and G together?

Options:
1) 238200
2) 151800
3) 388200
4) 442650
Correct Answer: 388200

QID : 63 - Solution A contains 10% acid and solution B contains 30% acid. In what ratio should solution A be mixed with Solution B to obtain a mixture with 25% acid?

Options:
1) 1 : 2
2) 3 : 1
3) 1 : 3
4) 2 : 1
Correct Answer: 1 : 3

QID : 64 - In what ratio should coffee powder costing Rs 2500/kg be mixed with coffee powder costing Rs 1500/kg so that the cost of the mixture is Rs 2250/kg?

Options:
1) 1 : 4
2) 4 : 1
3) 3 : 1
4) 1 : 3
Correct Answer: 3 : 1

QID : 65 - A and B started a partnership business investing in the ratio of 3 : 8. C joined them after 4 months with an amount equal to 3/4th of B. What was their profit (in Rs) at the end of the year if C got Rs 24,000 as his share?

Options:
1) 120000
2) 150000
3) 90000
4) 180000
Correct Answer: 90000

QID : 66 - A and B invest in a business in the ratio 4 : 5. After 10 months B leaves the business after withdrawing his investment. In the first year the business made a profit of Rs 49,000. What is B's share (in Rs) of this profit?

Options:
1) 25000
2) 20000
3) 18000
4) 22000
Correct Answer: 25000

QID : 67 - Working together A and B can do a job in 40 days, B and C in 36 days and all three together in 24 days. In how many days can B alone do the job?

Options:
1) 60
2) 90
3) 72
4) 120
Correct Answer: 90

QID : 68 - A, B and C can do a job working alone in 50, 75 and 20 days respectively. They all work together for 4 days, then C quits. How many days will A and B take to finish the rest of the job?

Options:
1) 20
2) 30
3) 18
4) 24
Correct Answer: 20

QID : 69 - A can do 50% of the job in 16 days, B can do 1/4th of the job in 24 days. In how many days can they do 3/4th of the job working together?

Options:
1) 24
2) 9
3) 21
4) 18
Correct Answer: 18

QID : 70 - A and B can together complete a task in 18 hours. After 6 hours A leaves. B takes 36 hours to finish rest of the task. How many hours would A have taken to do the task if he worked alone?

Options:
1) 54
2) 45
3) 21
4) 27
Correct Answer: 27

QID : 71 - 1 packet of biscuits costs Rs 16 but a pack of 4 of the same packet of biscuits costs Rs 56. What is the effective discount (in %) on the pack?

Options:
1) 8
2) 10
3) 7.5
4) 12.5
Correct Answer: 12.5

QID : 72 - The cost price of an article is Rs x. It is marked up by 200%. It is sold at Rs 540 after giving 25% discount. What is the value of x (in Rs)?

Options:
1) 360
2) 250
3) 300
4) 240
Correct Answer: 240

QID : 73 - A Rs 750 tin of cheese is offered at 8% discount and a Rs 1,250 tin of butter at 20% discount. If we buy 5 tins of cheese and 3 tins of butter, what is the effective discount we get (in %)?

Options:
1) 12
2) 15
3) 14
4) 16
Correct Answer: 14

QID : 74 - The selling price of an article is Rs 816 if the discount on it is 15%. What would be the selling price of the article (in Rs) if the discount on it is 25%?

Options:
1) 750
2) 720
3) 800
4) 700
Correct Answer: 720

QID : 75 - The entry ticket at a fun park was increased in the ratio 7 : 9, due to which footfalls fell in the ratio 13 : 11. What is the new daily collection (in Rs), if the daily collection before the price hike was Rs 2,27,500?

Options:
1) 237500
2) 247500
3) 232500
4) 242500
Correct Answer: 247500

QID : 76 - If 6A = 4B = 9C; What is A : B : C?

Options:
1) 6 : 4 : 9
2) 9 : 4 : 6
3) 4 : 9 : 6
4) 6 : 9 : 4
Correct Answer: 6 : 9 : 4

QID : 77 - If 50 less had applied and 25 less selected, the ratio of selected to unselected would have been 9 : 4. So how many candidates had applied if the ratio of selected to unselected was 2 : 1.

Options:
1) 125
2) 250
3) 375
4) 500
Correct Answer: 375

QID : 78 - What is the fourth proportional to 189, 273 and 153?

Options:
1) 117
2) 299
3) 221
4) 187
Correct Answer: 221

QID : 79 - Rs 11,550 has to be divided between X, Y & Z such that X gets 4/5 of what Y gets and Y gets 2/3 of what Z gets. How much more does Z get over X (in Rs)?

Options:
1) 7200
2) 1800
3) =13*9
4) 2450
Correct Answer: 2450

QID : 80 - Before a battle the ratio of tanks to planes in an army was 5 : 3. During the war 1000 tanks were destroyed and 800 planes were destroyed. The ratio of tanks to planes became 2 : 1. What is the number of tanks after the war.

Options:
1) 2000
2) 1000
3) 3000
4) 4000
Correct Answer: 2000

QID : 81 - The average marks of 50 students in an examination was 65. It was later found that the marks of one student had been wrongly entered as 83 instead of 38. The correct average is?

Options:
1) 63.9
2) 64.5
3) 64.7
4) 64.1
Correct Answer: 64.1

QID : 82 - In a class of 50 students there are 22 girls who scored an average of 35 marks in the test. What is the average marks of the boys if the class average is 42 marks?

Options:
1) 50
2) 52.5
3) 47.5
4) 55
Correct Answer: 47.5

QID : 83 - The average of 41 consecutive odd numbers is 49. What is the largest number.

Options:
1) 89
2) 91
3) 93
4) 95
Correct Answer: 89

QID : 84 - A batsman scores 87 runs in the 21st match of his career. His average runs per match increases by 2. What was his average before the 21st match.

Options:
1) 45
2) 46
3) 44
4) 43
Correct Answer: 45

QID : 85 - Oil equal to 20% of the weight of ground nut is extracted in a mill. The matter left after extraction is sold as cattle feed at the rate of Rs 12.5/kg. The groundnuts are bought at Rs 20/kg. The processing cost is Rs 5/kg. At what price (Rs per kg) should the oil be sold to earn 20% profit on total costs (Total cost = Cost of groundnuts and Processing costs)?

Options:
1) 250
2) 150
3) 200
4) 100
Correct Answer: 100

QID : 86 - If a vendor sells a coconut at Rs 14.4 he makes 10% loss. If he wants to make 25% profit, then at what price (in Rs) should he sell?

Options:
1) 18
2) 20
3) 16
4) 22
Correct Answer: 20

QID : 87 - At a village trade fair a man buys a horse and a camel together for Rs 51,250. He sold the horse at a profit of 25 % and the camel at a loss of 20 %. If he sold both the animals at the same price, then the cost price of the cheaper animal was Rs ____________.

Options:
1) 6600
2) 7500
3) 25000
4) 20000
Correct Answer: 20000

QID : 88 - On a certain item profit is 150%. If the cost price increases by 25% what will be the new profit margin (in %)?

Options:
1) 25
2) 50
3) 100
4) 75
Correct Answer: 100

QID : 89 - 40% are the passing marks. A student gets 250 marks yet fails by 38 marks. What is the maximum marks?

Options:
1) 720
2) 750
3) 800
4) 840
Correct Answer: 720

QID : 90 - Ravi is 12 years younger than Surya. Ravi's age is 40% of the sum of his and Surya's age. What will be Surya's age 9 years hence?

Options:
1) 36
2) 24
3) 33
4) 45
Correct Answer: 45

QID : 91 - 5% of a = b, then b% of 20 is the same as __________.

Options:
1) 20% of a/2
2) 50% of a/20
3) 50% of a/2
4) 20% of a/20
Correct Answer: 20% of a/20

QID : 92 - A man's annual income has increased by Rs 5 lakhs but the tax on income that he has to pay has reduced from 12% to 10%. He now pays Rs 10,000 more income tax. What is his increased income (in Rs lakhs)?

Options:
1) 20
2) 25
3) 15
4) 10
Correct Answer: 25

QID : 93 - A racing car going at an average speed of 108 km/hr takes 15 minutes to complete a lap on a racing track. By how much should it increase its speed (in km/hr) to complete the lap in 12 minutes?

Options:
1) 24
2) 21
3) 27
4) 30
Correct Answer: 27

QID : 94 - Train A takes 45 minutes more than train B to travel a distance of 450 km. Due to engine trouble speed of train B falls by a quarter, so it takes 30 minutes more than Train A to complete the same journey. What is the speed of Train A (in km/hr)?

Options:
1) 90
2) 120
3) 100
4) 110
Correct Answer: 100

QID : 95 - Two cars A and B travel from one city to another, at speeds of 72 km/hr and 90 km/hr respectively. If car B takes 1 hour lesser than car A for the journey, then what is the distance (in km) between the two cities?

Options:
1) 270
2) 360
3) 240
4) 400
Correct Answer: 360

QID : 96 - B starts 4 minutes after A from the same point, for a place at a distance of 7 miles from the starting point. A on reaching the destination turns back and walks a mile where he meets B. If A's speed is a mile in 8 minutes then B's speed is a mile in ____ minutes.

Options:
1) 9
2) 12
3) 10
4) 8
Correct Answer: 10

QID : 97 - If the amount on a certain principal in 3 years at 12% rate of interest compounded annually is Rs 12,000, what will be the amount (in Rs) after the 4th year?

Options:
1) 14330
2) 15440
3) 13440
4) 14550
Correct Answer: 13440

QID : 98 - The amount (in Rs) received at 10% per annum compound interest after 3 yrs is Rs 1,19,790. What was the principal?

Options:
1) 90000
2) 1,00,000
3) 80000
4) 75000
Correct Answer: 90000

QID : 99 - In how many months will Rs 8,000 yield Rs 2,648 as compound interest at 20% per annum compounded semi-annually?

Options:
1) 18
2) 24
3) 12
4) 30
Correct Answer: 18

QID : 100 - What is the rate of interest (in %) if simple interest earned on a certain sum for the 3rd year is Rs 2,000 and compound interest earned in 2 years is Rs 4,160?

Options:
1) 8
2) 10
3) 12
4) 6
Correct Answer: 8