SSC CGL Tier-2 01-December-2016 Maths

SSC CGL Tier-2 01-December-2016 Maths - Question 1

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Let $$ 0 < x < 1$$. Then the correct inequality is

A

$$ x < \surd x < x^2 $$

B

$$  \surd x < x < x^2 $$

C

$$  x^2 < x <  \surd x $$

D

$$  \surd x < x^2 < x $$

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SSC CGL Tier-2 01-December-2016 Maths - Question 2

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Three bells ring at interval of 36 seconds, 40 seconds and 48 seconds respectively. They start ringing together at a particular time. They will ring together after every

A

6 minutes

B

12 minutes

C

18 minutes

D

24 minutes

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SSC CGL Tier-2 01-December-2016 Maths - Question 3

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f the sum of the digits of a three digit numberis subtracted from that number, then it will always be divisible by

A

3 only

B

9 only

C

both 3 and 9

D

all of 3,6 and 9

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SSC CGL Tier-2 01-December-2016 Maths - Question 4

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Which ofthe following is correct ?

A

$$ \frac{2}{3} < \frac{3}{5}< \frac{11}{5} $$

B

$$ \frac{3}{5} < \frac{2}{3}< \frac{11}{5} $$

C

$$ \frac{11}{5} < \frac{3}{5}< \frac{2}{3} $$

D

$$ \frac{3}{5} < \frac{11}{15}< \frac{2}{3} $$

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SSC CGL Tier-2 01-December-2016 Maths - Question 5

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The greater of the two numbers whose product is 900 and sum exceeds their difference by 30 is

A

60

B

75

C

90

D

100

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SSC CGL Tier-2 01-December-2016 Maths - Question 6

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The smallest fraction, which should be added to the sum of $$ 2 \frac{1}{2} , 3 \frac{1}{3} ,4 \frac{1}{4}  and   5\frac{1}{5} $$ to make the result a whole number, is 

A

$$ \frac{13}{60}$$ 

B

$$  \frac{1}{4}  $$

C

$$  \frac{17}{60}  $$

D

$$  \frac{43}{60}  $$

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SSC CGL Tier-2 01-December-2016 Maths - Question 7

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Find the cube root of (-13824) 

OR 

Find the value of $$ \sqrt[3]{-13824} $$

A

38

B

-38

C

24

D

-24

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SSC CGL Tier-2 01-December-2016 Maths - Question 8

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The sum of three positive numbersis 18 and their product is 162. If the sum of two numbersis equal to the third then the sum of squares of the numbersis

A

120

B

126

C

132

D

138

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SSC CGL Tier-2 01-December-2016 Maths - Question 9

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The sum of three consecutive even numbers is 28 more than the average of these three numbers. Then the smallest of these three numbers is

A

6

B

12

C

14

D

16

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SSC CGL Tier-2 01-December-2016 Maths - Question 10

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In a division sum, the divisor 'd' is 10 times the quotient 'q' and 5 times the remainder'r'. If r = 46, the dividend will be

A

5042

B

5348

C

5336

D

4276

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SSC CGL Tier-2 01-December-2016 Maths - Question 11

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A man can do a piece of workin 30 hours. If he works with his son then the same piece of work is finished in 20 hours. If the son works alone he can do the work in

A

60 hours

B

50 hours

C

25 hours

D

10 hours

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SSC CGL Tier-2 01-December-2016 Maths - Question 12

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A water tap fills a tub in 'p' hours and a sink at the bottom empties it in 'q' hours. If p < q and both tap and sink are open, the tank is filled in 'r' hours; then 

A

$$ \frac{1}{r} = \frac{1}{p} + \frac{1}{q}  $$

B

$$ \frac{1}{r} = \frac{1}{p} - \frac{1}{q}  $$

C

$$ r = p + q$$  

D

$$ r = p - q$$  

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SSC CGL Tier-2 01-December-2016 Maths - Question 13

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John does $$ \frac{1}{2} $$ piece of work in 3 hours, Joe does $$ \frac{1}{4} $$ of the remaining work in 1 hour and George finishes remaining work in 5 hours. How long would it have taken the three working together to do the work ?

A

$$ 2 \frac{1}{7} hours $$

B

$$ 3 \frac{1}{7} hours $$

C

$$ 3 \frac{8}{11} hours $$

D

$$ 2 \frac{8}{11} hours $$

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SSC CGL Tier-2 01-December-2016 Maths - Question 14

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A does $$  \frac{2}{5} $$ of a work in 9 days. Then B joined him and they together completed the remaining work in 6 days. B alone can finish the whole work in

A

$$ 6 \frac{12}{13} days $$

B

$$ 8 \frac{2}{11} days $$

C

$$ 10 days $$

D

$$ 18 days $$

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SSC CGL Tier-2 01-December-2016 Maths - Question 15

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The daily wagesof A and B respectively are Rs.3.50 and 2.50 . When A finishes a certain work, he gets a total wage of Rs. 63. When B does the same work, he gets a total wage Rs.75. If both of them do it together what is the cost of the work ?

A

Rs. 67.50

B

Rs. 27.50

C

Rs. 60.50

D

Rs. 70.50

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SSC CGL Tier-2 01-December-2016 Maths - Question 16

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A man does double the work done by a boy in the same time. The number of days that 3 men and 4 boys will take to finish a work which can be done by 10 men in 8 days is

A

4

B

16

C

$$ \frac{3}{11} $$

D

$$ \frac{4}{5} $$ 

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SSC CGL Tier-2 01-December-2016 Maths - Question 17

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The marked price of an article is 30% higher than the cost price. If a trader sells the articles allowing 10% discount to customer, then the gain percent will be

A

17

B

20

C

19

D

15

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SSC CGL Tier-2 01-December-2016 Maths - Question 18

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A merchant marked the price of an article by increasing its production cost by 40%. Now he allows 20%discount and gets a profit of Rs. 48 after selling it. The production cost is

A

Rs. 320

B

Rs. 360

C

Rs. 400

D

Rs. 440

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SSC CGL Tier-2 01-December-2016 Maths - Question 19

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A watch dealer pays 10% customs duty on a watch which costs Rs.500 abroad. He desires to make a profit of 20% after giving a discount of 25% to the buyer, The marked price should be

A

Rs. 950

B

Rs. 800

C

Rs. 880

D

Rs. 660

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SSC CGL Tier-2 01-December-2016 Maths - Question 20

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A shopkeeper allows 20% discount on his advertised price and to make a profit of 25% on his outlay. What is the advertised price (in Rs.) on which he gains Rs.6000?

A

36000

B

37500

C

39000

D

42500

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SSC CGL Tier-2 01-December-2016 Maths - Question 21

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Rs.2420 were divided among A, B, C so that A: B=5 : 4 and B : C = 9 : 10 then C gets

A

680

B

800

C

900

D

950

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SSC CGL Tier-2 01-December-2016 Maths - Question 22

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49 Kg of blended tea contain Assam and Darjeeling tea in the ratio 5 : 2. Then the quantity of Darjeeling tea is to be added to the mixture to make the ratio of Assam to Darjeeling tea 2 : 1 is

A

4.5 kg

B

3.5 kg

C

5 kg

D

6 kg

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SSC CGL Tier-2 01-December-2016 Maths - Question 23

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Among 132 examineesof a certain school, the ratio of successful to unsuccessful students is 9 : 2, Had 4 more students passed, then the ratio of successful to unsuccessful students will be

A

14:3

B

14:5

C

28:3

D

28:5

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SSC CGL Tier-2 01-December-2016 Maths - Question 24

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Ina regiment the ratio between the numberofofficers to soldiers was 3 : 31 before battle. In a battle 6 officers and 22 soldiers werekilled and theratio became 1 : 13, the number of officers in the regiment before battle was

A

31

B

38

C

21

D

28

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SSC CGL Tier-2 01-December-2016 Maths - Question 25

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Three containers have their volumesin the ratio 3 : 4: 5. They are full of mixtures of milk and water. The mixtures contain milk and water in the ratio of(4:1), (3 : 1) and (5 : 2) respectively. The contents ofall these three containers are poured into a fourth container. The ratio of milk and water in the fourth container is

A

4:1

B

151:48

C

157:53

D

5:2

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SSC CGL Tier-2 01-December-2016 Maths - Question 26

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In what proportion must a grocer mix sugar at Rs.12 a kg and Rs.7 a kg so as to make a mixture worth Rs.8 a kg ?

A

7:12

B

1:4

C

2:3

D

12:7

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SSC CGL Tier-2 01-December-2016 Maths - Question 27

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Fifteen movie theatres average 600 customers per theatre per day.If six of the theatres close down but the total theatre attendence stays the same,then the average daily attendence per theatre among the remaining theatres is

A

900

B

1000

C

1100

D

1200

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SSC CGL Tier-2 01-December-2016 Maths - Question 28

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The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg andthat of B and C be 43 kg, then the weight of B is:

A

31 kg

B

32 kg

C

29.5kg

D

35 kg

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SSC CGL Tier-2 01-December-2016 Maths - Question 29

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The batting average for 40 innings of a cricket player is 50 runs. His highest score exceeds his lowest score by 172 runs, If these twoinnings are excluded, the average of the remaining 38 innings is 48 runs. The highest score of the player is

A

165

B

170

C

172

D

174

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SSC CGL Tier-2 01-December-2016 Maths - Question 30

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The average of 7 consecutive numbersis 20. The largest of these numbersis

A

20

B

23

C

24

D

26

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SSC CGL Tier-2 01-December-2016 Maths - Question 31

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Mukesh has twice as much money as Soham, Soham has 50% more moneythan Pankaj. If the average money with them is Rs.110, then Mukesh has

A

155

B

160

C

180

D

175

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SSC CGL Tier-2 01-December-2016 Maths - Question 32

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The average daily income of 7 men, 11 womenand 2 boysis Rs.257.50. If the average daily income of the men is Rs.10 more than that of women and the average daily income of the womenis Rs.10 more than that of boys, the average daily income of a man is

A

Rs.277.5

B

Rs.250

C

Rs.265

D

Rs.257

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SSC CGL Tier-2 01-December-2016 Maths - Question 33

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The profit on selling an article for Rs.425 is the same as the loss on selling it for Rs.355, then the cost price of the article is

A

410

B

380

C

400

D

390

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SSC CGL Tier-2 01-December-2016 Maths - Question 34

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A & B jointly made a profit of Rs.1650 and they decided to share it such that $$ \frac{1}{3} $$ of A's profit is equal to $$ \frac{2}{5} $$of B's profit. Then profit of B is

A

Rs.700

B

Rs.750

C

Rs.850

D

Rs.800

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SSC CGL Tier-2 01-December-2016 Maths - Question 35

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4%of the selling price of an article is equal to 5% of its cost price. Again 20% of the selling price is Rs.120 more than 22%ofits cost price. The ratio ofcostprice & selling price is

A

2:3

B

3:2

C

4:5

D

5:4

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SSC CGL Tier-2 01-December-2016 Maths - Question 36

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Due to 25% fall in the rate of eggs, one can buy 2 dozen eggs morethan before by investing Rs.162. Then the orignal rate per dozen of the eggsis

A

Rs. 22

B

Rs. 24

C

Rs. 27

D

Rs. 30

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SSC CGL Tier-2 01-December-2016 Maths - Question 37

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Last year Mr. A bought two paintings. This year he sold them for Rs, 20,000 each. On one, he made a 25% profit and on the other he had a 25% loss.Then his net profit or loss is

A

He lost more than Rs.2000

B

He lost less than Rs, 2000

C

He earned more than than Rs, 2000

D

He earned less than Rs.2000

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SSC CGL Tier-2 01-December-2016 Maths - Question 38

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A shopkeeper sells rice at 10% profit and uses weight 30% less than the actual measure. His gain percent is

A

$$ 57 \frac{2}{3}$$ %

B

$$ 57 \frac{1}{7}$$ %

C

$$ 57 \frac{2}{5}$$%

D

$$ 57 \frac{3}{7}$$%

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SSC CGL Tier-2 01-December-2016 Maths - Question 39

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What % of a day is 30 minutes ?

A

2.83

B

2.083

C

2.09

D

2.075

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SSC CGL Tier-2 01-December-2016 Maths - Question 40

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A businessman's earning increase by 25%in one year but decreases by 4%in the next. Goingby this pattern, after 5 years, his total earnings would be Rs.72000. Whatis his present earning?

A

Rs.10000

B

Rs.80000

C

Rs.40000

D

Rs.54000

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SSC CGL Tier-2 01-December-2016 Maths - Question 41

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In an examination 73%of the candidates passed in quantitative aptitude test, 70% passed in General awareness and 64% passedin both. If 6300 failed in both subjects the total number of examinees were

A

60000

B

50000

C

30000

D

25000

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SSC CGL Tier-2 01-December-2016 Maths - Question 42

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A man spends 75% of his income. His income increases by 20% and his expenditure also increases by 10%. Find the percentage increase in his savings.

A

25%

B

50%

C

15%

D

10%

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SSC CGL Tier-2 01-December-2016 Maths - Question 43

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On river, Q is the mid-point between two points P and R on the same bank ofthe river. A boat can go from P to Q and back in 12 hours, and from P to R in 16 hours 40 min. How long would it take to go from R to P ?

A

$$ 3 \frac{1}{3} hr $$.

B

$$ 5 hr $$.

C

$$ 6 \frac{2}{3} hr $$.

D

$$ 7 \frac{1}{3} hr $$.

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SSC CGL Tier-2 01-December-2016 Maths - Question 44

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A car can finish a certain journey in 10 hours at a speed of 42 kmph. In order to cover the same distance in 7 hours, the speed of the car (km/h) must be increased by

A

12

B

15

C

18

D

24

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SSC CGL Tier-2 01-December-2016 Maths - Question 45

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A man travels 450 km to his home partly by train and partly by car. He takes 8 hrs 40 minsif he travels 240 km bytrain and rest by car. He takes 20 mins moreif he travels 180 km by train and the rest by car. The speed of the car in km/hr is

A

45

B

50

C

60

D

48

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SSC CGL Tier-2 01-December-2016 Maths - Question 46

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A train 'B' speeding with 100 kmph crosses another train C, running in the same direction, in 2 mins. If the length of the train B and C be 150m and 250m respectively, what is the speed of the train C (in kmph) ?

A

75

B

88

C

95

D

110

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SSC CGL Tier-2 01-December-2016 Maths - Question 47

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The compound interest on Rs. 30,000 at 7%per annum for n years is Rs. 4347. The value of n is

A

3

B

2

C

4

D

5

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SSC CGL Tier-2 01-December-2016 Maths - Question 48

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If A borrowed Rs. P at x% and B borrowed Rs. Q (>P) at y% per annum at simple interest at the same time, then the amountof their debts will be equal after

A

$$ 100 \left (\frac{Q - P}{Px - Qy}\right) years $$

B

$$ 100 \left (\frac{Px - Qy}{ Q - P}\right) years $$

C

$$ 100 \left (\frac{Px - Qy}{ P - Q}\right) years $$

D

$$ 100 \left (\frac{P - Q}{Px - Qy}\right) years $$

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SSC CGL Tier-2 01-December-2016 Maths - Question 49

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A man invested a sum of money at compoundinterest. It amounted to Rs. 2420 in 2 years and to Rs. 2662 in 3 years. Find the sum.

A

RS.1000

B

RS.2000

C

RS.5082

D

RS.3000

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SSC CGL Tier-2 01-December-2016 Maths - Question 50

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if a sum of money becomes 4000 in 2 yrs and 5500 in 4 yrs 6 months at the same rate of simple interest per annum. Then the rate of simple interest is

A

$$ 21 \frac{3}{7}\% $$

B

$$ 21 \frac{2}{7}\% $$

C

$$ 21 \frac{1}{7}\% $$

D

$$ 21 \frac{5}{7}\% $$

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SSC CGL Tier-2 01-December-2016 Maths - Question 51

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A hollow cylindrical tube 20 cm long is madeofiron andits external and internal diameters are 8 cm and 6 cm respectively. The volume (in cubic cm) of iron used in making the tube is (Take $$ \pi = \frac{22}{7} $$)

A

1760

B

440

C

220

D

880

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SSC CGL Tier-2 01-December-2016 Maths - Question 52

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 If the areas of three adjacent faces of a rectangular box which meet in a corner are $$ 12 cm^2,   15 cm^2    and   20 cm^2$$  respectively. Then the volume of the box is

A

$$ 3600  cm^3 $$

B

$$ 300  cm^3 $$

C

$$ 60  cm^3 $$

D

$$ 180  cm^ 3$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 53

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The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundaryof the park at the speed of 12 km/hour completes one round in 8 minutes, then the area of the park is

A

$$ 153650  m^2 $$

B

$$ 135600  m^2 $$

C

$$ 153600  m^2 $$

D

$$ 156300  m^2 $$

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SSC CGL Tier-2 01-December-2016 Maths - Question 54

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If the radius of a right circular cylinder open at both the ends, is decreased by 25% and the height of the cylinder is increased by 25%. Then the curved surface areaofthe cylinder thus formed

A

remains unaltered

B

is increased by 25%

C

is increased by 6.25%

D

is decreased by 6.25%

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SSC CGL Tier-2 01-December-2016 Maths - Question 55

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A cylindrical pencil of diameter 1.2 cm has one of its end sharpened into a conical shape of height 1.4 cm. The volume of the material removed is

A

1.056 $$cm^3$$

B

4.224 $$cm^3$$

C

10.56 $$cm^3$$

D

42.24 $$cm^3$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 56

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A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 $$m^2$$ then the width of the road is

A

3 m

B

5 m

C

6 m

D

2 m

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SSC CGL Tier-2 01-December-2016 Maths - Question 57

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Four circles of equal radii are described about the four corners of a square so that each touches two of the other circles. If each side of the square is 140 cm then area of the space enclosed between the circumference of the circle is (take $$\pi = \frac{22}{7}$$)

A

4200 $$cm^2$$

B

2100 $$cm^2$$

C

7000 $$cm^2$$

D

2800 $$cm^2$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 58

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The amount of concrete required to build a concrete cylindrical pillar whose base has a perimeter 8.8 metre and curved surface area 17.6 sq. metre, is (Take $$\pi = \frac{22}{7}$$)

A

8.325 $$m^3$$

B

9.725 $$m^3$$

C

10.5 $$m^3$$

D

12.32 $$m^3$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 59

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A hemispherical bowlof internal radius 9 cm, contains a liquid. This liquid is to befilled into small cylindrical bottles of diameter 3 cm and height 4 cm.Then the numberof bottles necessary to empty the bowlis

A

18

B

45

C

27

D

54

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SSC CGL Tier-2 01-December-2016 Maths - Question 60

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A rectangular water tank is 80 m $$x\times$$ 40 m. Water flows into it through a pipe of 40 sq.cm at the opening at a speed of 10 km/hr. The water level will rise in the tank in half an hour is

A

$$\frac{3}{2}$$ cm

B

$$\frac{4}{9}$$ cm

C

$$\frac{5}{9}$$ cm

D

$$\frac{5}{8}$$ cm

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SSC CGL Tier-2 01-December-2016 Maths - Question 61

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A square and a regular hexagon are drawn such that all the vertices of the square and the hexagon are on circle of radius r cm. The ratio of area of the square and the hexagon is

A

$$3 : 4$$

B

$$4 : 3\surd3$$

C

$$\surd2 : \surd3$$

D

$$1 :  \surd2$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 62

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A solid cylinder has the total surface area 231 sq.cm. If its curved surface area is $$\frac{2}{3}$$ of the total surface area, then the volume of the cylinder is

A

154 cu.cm

B

308 cu.cm

C

269.5 cu.cm

D

370 cu.cm

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SSC CGL Tier-2 01-December-2016 Maths - Question 63

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The lateral surface area of frustum of a right circular cone,if the area of its base is $$16 \pi  cm^2$$ and the diameter of circular upper surface is 4 cm and slant height 6 cm, will be

A

$$30 \pi  cm^2$$

B

$$48 \pi  cm^2$$

C

$$36 \pi  cm^2$$

D

$$60 \pi  cm^2$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 64

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The diameter of a sphere is twice the diameter of another sphere, The surface area ofthefirst sphere is equal to the volume of the second sphere, The magnitude of the radius ofthefirst sphereis

A

12

B

24

C

16

D

48

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SSC CGL Tier-2 01-December-2016 Maths - Question 65

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A right circular cylinder having diameter 21 cm & height 38 cm is full of ice cream. The ice cream is to be filled in cones of height 12 cm and diameter 7 cm having a hemispherical shape on the top. The numberof such conesto befilled with ice cream is

A

54

B

44

C

36

D

24

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SSC CGL Tier-2 01-December-2016 Maths - Question 66

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The Simplified value of $$  \left(1 - \frac{2xy}{x^2 + y^2}\right) \div \left(\frac{x^3 - y^3}{x - y} - 3xy\right)$$ is

A

$$\frac{1}{x^2 - y^2}$$

B

$$\frac{1}{x^2 + y^2}$$

C

$$\frac{1}{x - y}$$

D

$$\frac{1}{x + y}$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 67

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If $$a + b + c = 0$$ then the value of $$\frac{1}{(a + b)(b + c)} + \frac{1}{(b + c)(c + a)} + \frac{1}{(c + a)(a + b)}$$ is

A

0

B

1

C

3

D

2

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SSC CGL Tier-2 01-December-2016 Maths - Question 68

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If $$x^2 + y^2 + 2x + 1 = 0$$, then the value of $$x^{31} + y{35}$$ is

A

-1

B

0

C

1

D

2

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SSC CGL Tier-2 01-December-2016 Maths - Question 69

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If $$x = \frac{\sqrt{5} + 1}{\sqrt{5} - 1}  and  y = \frac{\sqrt{5} - 1}{\sqrt{5} + 1}$$, the value of $$\frac{x^2 + xy + y^2}{x^2 - xy + y^2}$$ is

A

$$\frac{3}{4}$$

B

$$\frac{4}{3}$$

C

$$\frac{3}{5}$$

D

$$\frac{5}{3}$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 70

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If $$\left(x - \frac{1}{x}\right)^2 = 3$$, then the value of $$x^6 + \frac{1}{x^6}$$ equals

A

90

B

100

C

110

D

120

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SSC CGL Tier-2 01-December-2016 Maths - Question 71

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If $$x^4 + 2x^3 + ax^2 + bx + 9$$ is a perfect square, where a and b are positive real numbers,then the value of a and b are

A

a = 5, b = 6

B

a = 6, b = 7

C

a = 7, b = 6

D

a = 7, b = 8

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SSC CGL Tier-2 01-December-2016 Maths - Question 72

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If $$a^2 + b^2 + c^2 = 16, x^2 + y^2 + z^2 = 25  and  ax + by + cz = 20$$, then the value of $$\frac{a + b + c}{x + y + z}$$

A

$$\frac{3}{5}$$

B

$$\frac{5}{3}$$

C

$$\frac{4}{5}$$

D

$$\frac{5}{4}$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 73

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The value of x which satisfies the equation $$\frac{x + a^2 + 2c^2}{b + c} + \frac{x + b^2 + 2a^2}{c  + a} + \frac{x + c + 2b^2}{a + b} = 0$$ is

A

$$(a^2 + b^2 + c^2)$$

B

$$-(a^2 + b^2 + c^2)$$

C

$$(a^2 + 2b^2 + c^2)$$

D

$$-(a^2 + b^2 + 2c^2)$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 74

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If $$a^3 = 117 + b^3$$ and $$a = 3 + b$$, then the value of $$a + b$$ is:

A

$$\pm 7$$

B

$$\pm 49$$

C

$$\pm 13$$

D

0

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SSC CGL Tier-2 01-December-2016 Maths - Question 75

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If $$a + \frac{1}{a} = -2$$ then the value of $$a^{1000} + a^{-1000}$$ is

A

2

B

0

C

1

D

$$\frac{1}{2}$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 76

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$$\triangle ABC$$ is similar to $$\triangle DEF$$. If area of $$\triangle ABC$$ is 9 sq.cm. and area of $$\triangle DEF$$ is 16 sq.cm. and BC = 2.1 cm. Then the length of EF will be

A

5.6 cm

B

2.8 cm

C

3.7 cm

D

1.4 cm

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SSC CGL Tier-2 01-December-2016 Maths - Question 77

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A chord of a circle is equal to its radius. The angle subtended by this chord at a point on the circumference is

A

$$80^\circ$$

B

$$60^\circ$$

C

$$30^\circ$$

D

$$90^\circ$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 78

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Let two chords AB and AC of the larger circle touch the smaller circle having same centre at X and Y. Then XY = ?

A

BC

B

$$\frac{1}{2}$$ BC

C

$$\frac{1}{3}$$ BC

D

$$\frac{1}{4}$$ BC

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SSC CGL Tier-2 01-December-2016 Maths - Question 79

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Let G be the centroid of the equilateral triangle ABC of perimeter 24 cm. Then the length of AG is

A

$$2 \surd3$$ cm

B

$$\frac{8}{\surd3}$$ cm

C

$$8 \surd3$$ cm

D

$$4 \surd3$$ cm

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SSC CGL Tier-2 01-December-2016 Maths - Question 80

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A and B are the centres of two circles with radii 11 cm and 6 cm respectively. A common tangent touches these circles at P & Q respectively. If AB =13 cm, then the length of PQ is

A

13 cm

B

17 cm

C

8.5 cm

D

12 cm

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SSC CGL Tier-2 01-December-2016 Maths - Question 81

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ABC is an isosceles triangle inscribed in a circle. If $$AB = AC = 12\surd5$$ and $$BC = 24  cm$$ then radius of circle is

A

10 cm

B

15 cm

C

12 cm

D

14 cm

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SSC CGL Tier-2 01-December-2016 Maths - Question 82

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ABC is an isosceles triangle where AB = AC whichis circumscribed abouta circle. If P is the point where the circle touches the side BC, then which of the following is true ?

A

$$BP = PC$$

B

$$BP > PC$$

C

$$BP < PC$$

D

$$BP = \frac{1}{2}PC$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 83

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If D and E are the mid points of AB and AC respectively of $$\triangle$$ABC, then the ratio of the areas of ADE and BCED is ?

A

1 : 2

B

1 : 4

C

2 : 3

D

1 : 3

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SSC CGL Tier-2 01-December-2016 Maths - Question 84

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O is the circumcentre of the isosceles $$\triangle$$ABC. Given that AB = AC = 17 cm and BC = 6 cm. The radius of the circle is

A

3.015 cm

B

3.205 cm

C

3.025 cm

D

3.125 cm

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SSC CGL Tier-2 01-December-2016 Maths - Question 85

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$$B_1$$ is a point on the side $$AC$$ of $$\triangle ABC$$ and $$B_1B$$ is joined. line is drawn through A parallel to $$B_1B$$ meeting $$BC$$ at $$A_1$$ and another line is drawn through $$C$$ parallel to $$B_1B$$ meeting $$AB$$ produced at $$C_1$$. Then

A

$$\frac{1}{CC_1} - \frac{1}{AA_1} = \frac{1}{BB_1}$$

B

$$\frac{1}{CC_1} + \frac{1}{AA_1} = \frac{1}{BB_1}$$

C

$$\frac{1}{BB_1} - \frac{1}{AA_1} = \frac{1}{CC_1}$$

D

$$\frac{1}{AA_1} - \frac{1}{CC_1} = \frac{2}{BB_1}$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 86

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The value of the expression $$(1 + \sec 22^\circ + \cot 68^\circ)(1 - \cosec 22^\circ + \tan 68^\circ)$$is

A

0

B

1

C

-1

D

2

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SSC CGL Tier-2 01-December-2016 Maths - Question 87

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If $$x \sin^3 \theta + y \cos^3 \theta = \sin \theta \cos \theta  and  x \sin \theta - y \cos \theta = 0$$, then the value of $$x^2 + y^2$$ equals

A

1

B

$$\frac{1}{2}$$

C

$$\frac{3}{2}$$

D

2

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SSC CGL Tier-2 01-December-2016 Maths - Question 88

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If $$\sec \theta + \tan \theta = m (>1)$$, then the value of $$\sin \theta  is  (0^\circ < \theta < 90^\circ)$$

A

$$\frac{1 - m^2}{1 + m^2}$$

B

$$\frac{m^2 - 1}{m^2 + 1}$$

C

$$\frac{m^2 + 1}{m^2 - 1}$$

D

$$\frac{1 + m^2}{1 - m^2}$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 89

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If $$(a^2 - b^2)\sin \theta + 2ab \cos \theta = a^2 + b^2$$, then $$\tan \theta =$$

A

$$\frac{2ab}{a^2 - b^2}$$

B

$$\frac{a^2 - b^2}{2ab}$$

C

$$\frac{ab}{a^2 - b^2}$$

D

$$\frac{a^2 - b^2}{ab}$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 90

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A person from the top of a hill observes a vehicle moving towards him at a uniform speed. It takes 10 minutes for the angle of depression to change from $$45^\circ$$ to $$60^\circ$$. After this the time required by the vehicle to reach the bottom of the hill is

A

12 min 20 sec

B

13 min

C

13 min 40 sec

D

14 min 24 sec

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SSC CGL Tier-2 01-December-2016 Maths - Question 91

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If $$2y \cos \theta = x \sin \theta  and  2x \sec \theta - y \cosec \theta = 3$$, then the value of $$x^2 + 4y^2$$ is

A

1

B

2

C

3

D

4

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SSC CGL Tier-2 01-December-2016 Maths - Question 92

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From the top of a cliff 100 metre high, the angles of depression of the top and bottom of a tower are $$45^\circ$$ and $$60^\circ$$ respectively. The height of the tower is

A

$$\frac{100}{3}(3 - \sqrt3)$$ metre

B

$$\frac{100}{3}(\sqrt3 - 1)$$ metre

C

$$\frac{100}{3}(2\sqrt3 - 1)$$ metre

D

$$\frac{100}{3}(\sqrt3 - \sqrt2)$$ metre

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SSC CGL Tier-2 01-December-2016 Maths - Question 93

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A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angle of elevation of the bottom of the flag staff is $$\alpha$$ and that of the top of the flag staff is $$\beta$$. Then the height of the tower is

A

$$h \tan \alpha$$

B

$$\frac{h \tan \alpha}{\tan \beta - \tan \alpha}$$

C

$$\frac{h \tan \alpha}{\tan \alpha - \tan \beta}$$

D

None of these

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SSC CGL Tier-2 01-December-2016 Maths - Question 94

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A man on the top of a tower, standing on the sea-shore, finds that a boat coming towards him takes 10 minutes for the angle of depression to change from $$30^\circ$$ to $$60^\circ$$. How soon the boat reach the sea-shore ?

A

5 minutes

B

7 minutes

C

10 minutes

D

15 minutes

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SSC CGL Tier-2 01-December-2016 Maths - Question 95

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The expression of $$\frac{\cot \theta + \cosec \theta - 1}{\cot \theta + \cosec \theta + 1}$$ is equal to

A

$$\frac{1 + \cos \theta}{\sin \theta}$$

B

$$\frac{1 - \cos \theta}{\sin \theta}$$

C

$$\frac{\cot \theta + 1}{\cosec \theta}$$

D

$$\frac{\cot \theta - 1}{\cosec \theta}$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 96

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Whatis the total monthly income of the family ?

A

Rs. 8025

B

Rs. 8250

C

Rs. 8520

D

Rs. 8052

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SSC CGL Tier-2 01-December-2016 Maths - Question 97

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What percent of the total income does the family save

A

15%

B

50%

C

20%

D

25%

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SSC CGL Tier-2 01-December-2016 Maths - Question 98

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Whatis the ratio of expenses on food and miscellaneous ?

A

$$3 : 4$$

B

$$2 : 3$$

C

$$3 : 2$$

D

$$2 : 5$$

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SSC CGL Tier-2 01-December-2016 Maths - Question 99

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Whatis the average of expensesonclothing and rent?

A

Rs. 1443.75

B

Rs. 1344.57

C

Rs. 1574.34

D

Rs. 1734.45

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SSC CGL Tier-2 01-December-2016 Maths - Question 100

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The ratio of average of expenses on food, clothing and miscellaneous items to the average of expenses on savings and rent is

A

$$3 : 2$$

B

$$1 : 3$$

C

$$2 : 1$$

D

$$1 : 1$$

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