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Question 51

AP Police SI 2018• Test

A person packs sweets boxes of dimensions 15cm × 15cm × 15cm in a basket of size 120cm × 120cm × 120cm. If he now wants to carry the maximum number of cubical boxes having the maximum integer dimensions but less than the dimensions of the earlier boxes without leaving any space unused, the number of such boxes he can carry is

  1. AOption (a)

    1,72,8000

  2. BOption (b)

    512

  3. COption (c)

    3375

  4. DOption (d)

    14,400

View answer & explanation

Correct answer

Answer: (a)A.

1,72,8000

Explanation not yet available.

Question 52

AP Police SI 2018• Test

From a circle of radius 12cm centered at O, a sector OAB of arc length 8π cm is cut and from it a cone is formed by joining OA and OB. If the volume of the cone is V cubic cm and its lateral surface area is S square cm, then V : S =

  1. AOption (a)

    4√2 ∶ 3

  2. BOption (b)

    9√2 ∶ 8

  3. COption (c)

    8√2 ∶ 9

  4. DOption (d)

    3√2 ∶ 8  

View answer & explanation

Correct answer

Answer: (a)A.

4√2 ∶ 3

Explanation not yet available.

Question 53

AP Police SI 2018• Test

A solid sphere of radius r is melted and with that material a solid cone and twenty two identical solid cubes were made. If the height of cone and edge of each cube are each equal to half the radius of the sphere, then the ratio of the radius of the cone to its height is

  1. AOption (a)

    11 ∶ 1

  2. BOption (b)

    \(\sqrt{11} ∶ 1\)

  3. COption (c)

    √3 ∶ 1  

  4. DOption (d)

    3 ∶ 1

View answer & explanation

Correct answer

Answer: (a)A.

11 ∶ 1

Explanation not yet available.

Question 54

AP Police SI 2018• Test

What is the area (in sq. cms) of the shaded portion of the following diagram in which each side of the triangle is 14 cms and its vertices being the centres of three mutually touching circles?

  1. AOption (a)

    7.3

  2. BOption (b)

    77

  3. COption (c)

    385

  4. DOption (d)

    154

View answer & explanation

Correct answer

Answer: (a)A.

7.3

Explanation not yet available.

Question 55

AP Police SI 2018• Test

Let Δ be the area of the circumcircle of a right angled triangle ABC with ∠B = 90°. Let Δ1 and Δ2 be areas of the two circles with diameters BC and BA respectively. Then

  1. AOption (a)

    \(\Delta^2=\Delta_1^2+\Delta_2^2\)

  2. BOption (b)

    Δ = Δ1Δ2

  3. COption (c)

    Δ = Δ1 + Δ2

  4. DOption (d)

    \(\frac{\Delta_1}{\Delta_2}=\Delta\)

View answer & explanation

Correct answer

Answer: (a)A.

\(\Delta^2=\Delta_1^2+\Delta_2^2\)

Explanation not yet available.

Question 56

AP Police SI 2018• Test

From each of the corners of a rectangular sheet of dimensions 36cm × 24cm, a small square of dimensions 4cm × 4cm is removed. If the edges on the four sides are folded and a box is formed then the volume of the box so formed (in cm3) is

  1. AOption (a)

    1792

  2. BOption (b)

    2234

  3. COption (c)

    2560

  4. DOption (d)

    2460

View answer & explanation

Correct answer

Answer: (a)A.

1792

Explanation not yet available.

Question 57

AP Police SI 2018• Test

In a square of side 8 cm, 5 identical circles are placed as shown in the figure. Then the radius (in cms) of each of the circle is

  1. AOption (a)

    8√2

  2. BOption (b)

    8√2 - 2

  3. COption (c)

    4(√2 - 1)

  4. DOption (d)

    4(√2 + 1)2

View answer & explanation

Correct answer

Answer: (a)A.

8√2

Explanation not yet available.

Question 58

AP Police SI 2018• Test

Two identical circles intersect such that their centers and their points of intersection, form a square of side 4cm. Then the area (in sq.cms) of the portion that is common to the two circles is

  1. AOption (a)

    8(π - 2)

  2. BOption (b)

    8π

  3. COption (c)

    8π - 4

  4. DOption (d)

    \(\frac{\pi^2}{4}-\frac{\pi}{2}\)

View answer & explanation

Correct answer

Answer: (a)A.

8(π - 2)

Explanation not yet available.

Question 59

AP Police SI 2018• Test

The number of Positive integers x such that 2018, 1998 and x are the sides of a triangle is 

  1. AOption (a)

    3998

  2. BOption (b)

    3996

  3. COption (c)

    4001

  4. DOption (d)

    3995

View answer & explanation

Correct answer

Answer: (a)A.

3998

Explanation not yet available.

Question 60

AP Police SI 2018• Test

An equilateral triangular plate is completely cut into n number of identical small equilateral triangular plates. Which one of the following can be a possible value for n

  1. AOption (a)

    206

  2. BOption (b)

    216

  3. COption (c)

    256

  4. DOption (d)

    296

View answer & explanation

Correct answer

Answer: (a)A.

206

Explanation not yet available.
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