2023 CDS -2 MATH-14457

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2023 CDS -2 MATH (Test Code: 14457)

  1. a

  2. b

  3. c

  4. d

  1. a

  2. b

  3. c

  4. d

A 2-digit number is such that the sum of the number and the number obtained by reversing the order of the digits of the number is 55. Further, the difference of the given number and the number obtained by reversing the order of the digits of the number is 45. What is the product of the digits ?

  1. 5

  2. 2

  3. 1

  4. 0

If A and B can finish a work in 10 days, B and C can finish the same work in 12 days, C and A can finish the same work in 15 days; then in how many days can A, B and C together finish half of the work ?

  1. 8 days

  2. 5 days

  3. 4 days

  4. 3 days

A person borrowed  Rs.10,000 at 12% rate of interest per annum compounded quarterly for a period of 9 months. What is the interest paid by him to settle his account after 9 months ?

  1. Rs.927.27

  2. Rs.947.47

  3. Rs.967.67

  4. Rs.987.87

  1. a

  2. b

  3. c

  4. d

Three persons A, B and C together can do a piece of work in 36 days. A and B together can do five times as much work as C alone; B and C together can do as much work as A alone. If A and C together can do n times as much work as B alone, then what is the value of n ?

  1. 1.5

  2. 2

  3. 2.5

  4. 3

  1. a

  2. b

  3. c

  4. d

  1. 12

  2. 14

  3. 16

  4. 18

If the median of observations

12, 1, 8, 54, 61, 28, 45, 35, 21, 17

is M, then what is the value of 2M + 5 ?

  1. 12

  2. 28

  3. 52

  4. 54

  1. a

  2. b

  3. c

  4. d

  1. 7

  2. 6

  3. 5

  4. 4

Let L be the LCM and H be the HCF of two given numbers. L and H are in the ratio 3 : 2. If the sum of the two numbers is 45, then what is the product of the numbers ?

  1. 243

  2. 486

  3. 504

  4. Cannot be determined due to insufficient data

A man walks at an average speed of 3 km/hr from his home and reaches office 40 minutes early. If he walks at an average speed of 2 km/hr, he would reach office 40 minutes late. What is the distance between his home and office ?

  1. 6 km

  2. 8 km

  3. 10 km

  4. 12 km

  1. 4

  2. 3

  3. 2

  4. 1

  1. a

  2. b

  3. c

  4. d

  1. a

  2. b

  3. c

  4. d

  1. 69

  2. 70

  3. 209

  4. 210

  1. a

  2. b

  3. c

  4. d

  1. -1

  2. 0

  3. 1

  4. 2

  1. a

  2. b

  3. c

  4. d

  1. a

  2. b

  3. c

  4. d

  1. a

  2. b

  3. c

  4. d

  1. 2

  2. 3

  3. 4

  4. 5

  1. 9

  2. 11

  3. 13

  4. 15

  1. a

  2. b

  3. c

  4. d

  1. a

  2. b

  3. c

  4. d

  1. a

  2. b

  3. c

  4. d

  1. a

  2. b

  3. c

  4. d

  1. 0

  2. 1

  3. 2

  4. 3

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

What is the diameter of the circle ?

  1. 120 cm

     

  2. 110 cm

  3. 100 cm

  4. 90 cm

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

If r is the radius of S and R is the radius of S2, 2R2then which one of the following is correct ?

  1. R = 3r

  2. R = 2r

  3. 3R = 4r

  4. 2R = 3r

If m is the area of the circle S and n is the 2r2 tan 9area of semi-circle S1, then which one of the following is correct ?

  1. 9m = 2n

  2. 9m = 4n

  3. 3m = 2n

  4. 7m = 3n

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

What is the monthly electricity bill for a house with 7 rooms consuming 300 units ?

  1. Rs.500

  2. Rs.440

  3. Rs.340

  4. Rs.300

Question:

If average weekly wages earned by a Rs.3,520, then what is the value of k ?

  1. 10

  2. 12

  3. 15

  4. 20

Question:

What is the median (approximate value) of the distribution ?

  1. Rs.3263

  2. Rs.3383

  3. Rs.3413

  4. Rs.3483

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

What is the radius of the sphere passing through the corners of the cuboid with edges 8 cm, 12 cm and 24 cm ?

  1. 10.5 cm

  2. 14 cm

  3. 21 cm

  4. 28 cm

A lamp shade is in the shape of a part of a cone and its top and bottom ends are circles whose circumferences are respectively 30 cm and 40 cm. The perpendicular distance between the ends is 6 cm. If the cone were to be completed, then how far would its vertex be from the top end ?

  1. 20 cm

  2. 18 cm

  3. 12 cm

  4. 9 cm

  1. 23

  2. 24

  3. 25

  4. 26

The corners of an equilateral triangular plate were cut in such a manner that it forms a regular hexagonal plate. What is the ratio of the area of the triangular plate to the area of the hexagonal plate ?

  1. 2 : 1

  2. 3 : 2

  3. 4 : 3

  4. 5 : 3

Two equal arcs of different circles C1 and C2 subtend angles of 600 and 750 respectively, at the centres. What is the ratio of the radius of C1 to the radius of C2 ?

  1. 4 : 5

  2. 5 : 4

  3. 1 : 1

  4. 3 : 2

ABC is a triangle with sides AB = 41 cm, BC = 28 cm and CA = 15 cm. If D, E and F are the mid-points of AB, BC and CA respectively, then what is the area of the triangle DEF ?

  1. 63 square cm

  2. 45 square cm

  3. 31.5 square cm

  4. 22.5 square cm

A triangle has sides 13 cm, 14 cm and 15 cm long. What is the length of the smallest altitude of the triangle ?

  1. 11 cm
     
  2. 11.2 cm

  3. 12 cm

  4. 12.2 cm

  1. 6.24 cm

  2. 6.42 cm

  3. 7.64 cm

  4. 7.84 cm

  1. 10 cm

  2. 9 cm

  3. 2√5 cm

  4. 8 cm

  1. 125 square cm

  2. 132 square cm

  3. 144 square cm

  4. 154 square cm

  1. 88 cm

     

  2. 91 cm

  3. 95 cm

  4. 98 cm

The arch of a bridge is in the form of an arc of a circle. If the span of the bridge is 40 m and height in the middle is 8 m, then what is the radius of curvature of the bridge ?

  1. 25 m
  2. 27m

  3. 29 m

  4. 31 m

  1. a

  2. b

  3. c

  4. d

  1. 18

  2. 21

  3. 24

  4. 27

Three solid lead spheres of diameters 6 cm, 8 cm and 10 cm are melted together and recast as a solid sphere. What is the percentage diminution of the surface area as compared to the sum of the surface areas of the three spheres ?

  1. 25%

  2. 26%

  3. 27%

  4. 28%

A solid sphere of radius 3 cm is melted to form a hollow cylinder of height 4 cm and  external diameter 10 cm. What is the thickness of the cylinder ?

  1. 0.42 cm

  2. 0.46 cm

  3. 0.50 cm

  4. 1.00 cm

  1. 203 : 117

  2. 203 : 157

  3. 172 : 91

  4. 165 : 88

  1. a

  2. b

  3. c

  4. d

  1. a

  2. b

  3. c

  4. d

  1. 1

  2. n -2 

  3. n - 1

  4. n

  1. 1 only

     

  2. 2 only

  3. Both 1 and 2

  4. Neither 1 nor 2

  1. a

  2. b

  3. c

  4. d

  1. a

  2. b

  3. c

  4. d

  1. 9

  2. 4

  3. 1

  4. 0

  1. a

  2. b

  3. c

  4. d

  1. a

  2. b

  3. c

  4. d

  1. 0

  2. 1

  3. 18

  4. 20

  1. 60 m

  2. 62.5 m

  3. 55 m

  4. 67.5 m

A person bought an article and sold it at aWhich of the statements given above is/are profit of 20%. Had he bought it at 20% less,correct ? what would have been the profit percentage if the selling price had been the same ?

  1. 25%
  2. 40%

  3. 50%

  4. 60%

  1. a

  2. b

  3. c

  4. d

  1. a

  2. b

  3. c

  4. d

  1. a

  2. b

  3. c

  4. d

  1. a

  2. b

  3. c

  4. d

  1. a

  2. b

  3. c

  4. d

The mean of p, q, r, s and t is 280. If the mean of p, r and t is 240, what is the mean of q and s ?

  1. 310

  2. 320

  3. 330

  4. 340

Consider the following for the next (05) items that follow :
A, B, C, D, E, F and G are cousins. D is thrice as old as A. Further, C is as many years younger to B, as G to E and E to D. The average age of D and G is
16 years; the average age of A and E is 11 years; the average age of B and C is also 11 years. B and C have equal weight. A's weight is 10 kg less than that of B; D is 4 kg heavier than E; E is 4 kg heavier than F; F is 4 kg heavier than G. Further, D has age-weight in kg; A has age-weight ratio of 2 : 5.
Moreover, none of them is more than 40 kg.

Question:

What is D's age (in years) ?

  1. 15

  2. 16

  3. 17

  4. 18

Consider the following for the next (05) items that follow :
A, B, C, D, E, F and G are cousins. D is thrice as old as A. Further, C is as many years younger to B, as G to E and E to D. The average age of D and G is
16 years; the average age of A and E is 11 years; the average age of B and C is also 11 years. B and C have equal weight. A's weight is 10 kg less than that of B; D is 4 kg heavier than E; E is 4 kg heavier than F; F is 4 kg heavier than G. Further, D has age-weight in kg; A has age-weight ratio of 2 : 5.
Moreover, none of them is more than 40 kg.

Question:

What is the average age (in years) of B, C, D, E and G ?

  1. 12

  2. 13

  3. 14

  4. 15

Consider the following for the next (05) items that follow :
A, B, C, D, E, F and G are cousins. D is thrice as old as A. Further, C is as many years younger to B, as G to E and E to D. The average age of D and G is
16 years; the average age of A and E is 11 years; the average age of B and C is also 11 years. B and C have equal weight. A's weight is 10 kg less than that of B; D is 4 kg heavier than E; E is 4 kg heavier than F; F is 4 kg heavier than G. Further, D has age-weight in kg; A has age-weight ratio of 2 : 5.
Moreover, none of them is more than 40 kg.

Question:

What is the difference between the weights (in kg) of G and C ?

  1. 4

  2. 3

  3. 2

  4. 1

Consider the following for the next (05) items that follow :
A, B, C, D, E, F and G are cousins. D is thrice as old as A. Further, C is as many years younger to B, as G to E and E to D. The average age of D and G is
16 years; the average age of A and E is 11 years; the average age of B and C is also 11 years. B and C have equal weight. A's weight is 10 kg less than that of B; D is 4 kg heavier than E; E is 4 kg heavier than F; F is 4 kg heavier than G. Further, D has age-weight in kg; A has age-weight ratio of 2 : 5.
Moreover, none of them is more than 40 kg.

Question:

  1. a

  2. b

  3. c

  4. d

Consider the following for the next (05) items that follow :
A, B, C, D, E, F and G are cousins. D is thrice as old as A. Further, C is as many years younger to B, as G to E and E to D. The average age of D and G is
16 years; the average age of A and E is 11 years; the average age of B and C is also 11 years. B and C have equal weight. A's weight is 10 kg less than that of B; D is 4 kg heavier than E; E is 4 kg heavier than F; F is 4 kg heavier than G. Further, D has age-weight in kg; A has age-weight ratio of 2 : 5.
Moreover, none of them is more than 40 kg.

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

Question:

  1. a

  2. b

  3. c

  4. d

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