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Sainik School Entrance Test

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The sum of the squares of the prime numbers between 20 and 30 is

  1. 1570

  2. 1282

  3. 1370

  4. 1258

  5. None of these


Correct Option: C
Explanation:

Between 20 and 30, there are only two prime numbers 23 and 29. Therefore, 23 x 23 + 29 x 29 = 529 + 841 = 1370

Which of the following is a perfect square?

  1. 12548

  2. 12543

  3. 15427

  4. 14641

  5. 25412


Correct Option: D
Explanation:

It is the square of 121.

If the angles of a quadrilateral are in the ratio 5 : 2 : 4 : 1, then the greatest angle (in degrees) of the quadrilateral is

  1. 120o

  2. 30o

  3. 60o

  4. 150o

  5. None of these


Correct Option: D
Explanation:

Let the angles of quadrilateral be 5k, 2k, 4k & k. Now, 5k + 2k + 4k + k = 360o Then, 12k = 360o k = 30o 5k = 150o

What is cost of painting 4 walls of the room at the rate of Rs. 54 per sq. m, if the the dimension of the room is 10 m x 12 m x 14 m?

  1. Rs. 28080

  2. Rs. 30800

  3. Rs. 33264

  4. Rs. 31104

  5. None of these


Correct Option: C
Explanation:

Area of 4 walls of the room = [2 x 14 x (10 + 12) ] sq. m = [28 x 22] sq. m = 616 sq. m Therefore, cost of painting = Rs. ( 616 x 54 ) = Rs. 33264

The cost of painting a cube of edge length 5 m at the rate of Rs. 20 per sq. m is

  1. Rs. 300

  2. Rs. 1200

  3. Rs. 3000

  4. Rs. 30000

  5. None of these


Correct Option: C
Explanation:

Total surface area of the cube = 6 x 5 m x 5 m = 150 sq. m Therefore, cost of painting the cube = Rs. (20 x 150) = Rs. 3000

Let K be the solution of the linear equation 3x - 21 = 7x - 29 and M be the solution of the linear equation 2y + 6 = y + 12. Now, if 2z + M = K, then the value of z is

  1. -2

  2. -4

  3. 4

  4. -1

  5. None of these


Correct Option: A
Explanation:

3x - 21 = 7x - 29 Or, 4x = 8 Or, x = 2 = K Also, 2y + 6 = y + 12 Or, y = 6 = M Now,  2z + 6 = 2 Or, 2z = - 4 Or, z = - 2 Ans.

What is the total cost of painting if the faces containing only length and breadth are to be painted with yellow colour?

The length, breadth and height of a cuboid are 10 cm, 8 cm and 2 cm, respectively. All the faces of the cuboid are to be painted. The cost of painting with red colour is Rs. 5 per sq. cm. with green colour is Rs. 6 per sq. cm and with yellow is Rs. 10 per sq. cm. Now, answer the questions.

  1. Rs. 800

  2. Rs. 80

  3. Rs. 1600

  4. Rs. 960

  5. None of these


Correct Option: C
Explanation:

Area to be painted = 2 (lb) = (2 x 10 x 8) sq. cm = 160 sq. cm Cost of painting = Rs. (10 x 160) = Rs. 1600

What is the total cost of painting if only the faces containing length and height are to be painted with red colour?

The length, breadth and height of a cuboid are 10 cm, 8 cm and 2 cm, respectively. All the faces of the cuboid are to be painted. The cost of painting with red colour is Rs. 5 per sq. cm. with green colour is Rs. 6 per sq. cm and with yellow is Rs. 10 per sq. cm. Now, answer the questions.

  1. Rs. 100

  2. Rs. 200

  3. Rs. 160

  4. Rs. 240

  5. None of these


Correct Option: B
Explanation:

Total area to be painted = 2 (lh) = (2 x 10 x 2) sq. cm = 40 sq cm Cost of painting = Rs. (5 x 40) = Rs. 200

The cost of painting the cuboid with green colour is

The length, breadth and height of a cuboid are 10 cm, 8 cm and 2 cm, respectively. All the faces of the cuboid are to be painted. The cost of painting with red colour is Rs. 5 per sq. cm. with green colour is Rs. 6 per sq. cm and with yellow is Rs. 10 per sq. cm. Now, answer the questions.

  1. Rs. 2320

  2. Rs. 1160

  3. Rs. 1392

  4. Rs. 580

  5. None of these


Correct Option: C
Explanation:

Total surface area of the cuboid = 2 (lb + bh + hl) = 2 (10 x 8 + 8 x 2 + 2 x 10) sq. cm = 2 (80 + 16 + 20) sq. cm = 2 (116) = 232 sq. cm Cost of painting = Rs. (6 x 232) = Rs. 1392

The digit which can appear at the units' place of a perfect square is

  1. 2

  2. 9

  3. 3

  4. 7

  5. 8


Correct Option: B
Explanation:

A perfect square can have 9 at its units' place.

Which of the following is a pair of co-prime numbers?

  1. 11, 13

  2. 14, 15

  3. 23, 29

  4. All of the above

  5. 51, 53


Correct Option: D
Explanation:

All of the above are pairs of co-prime numbers. 51 = 17 x 3 x 1 53 = 53 x 1 H.C.F. = 1 Therefore, it is a pair of co-prime numbers.

Solve for k if 4k + 3 = 6k - 5.

  1. 1/4

  2. 4

  3. -4

  4. 1

  5. None of these


Correct Option: B
Explanation:

4k + 3 = 6k - 5 Or, 2k = 8 Or, k = 4

What should be multiplied to - 7/4 to get 3/8?

  1. -14/3

  2. 3/14

  3. -3/14

  4. 14/3

  5. None of these


Correct Option: C
Explanation:

Let x be the number to be multiplied then, (-7/4) (x) = 3/8 Or, x = -3/14

What is the cost of painting the cuboid with Red colour?

The length, breadth and height of a cuboid are 10 cm, 8 cm and 2 cm, respectively. All the faces of the cuboid are to be painted. The cost of painting with red colour is Rs. 5 per sq. cm. with green colour is Rs. 6 per sq. cm and with yellow is Rs. 10 per sq. cm. Now, answer the questions.

  1. Rs. 1392

  2. Rs. 1160

  3. Rs. 2320

  4. Rs. 580

  5. None of these


Correct Option: B
Explanation:

Total surface area of the cuboid = 2 (lb + bh + hl) = 2 (10 x 8 + 8 x 2 + 2 x 10) sq. cm = 2 (80 + 16 + 20) sq. cm = 2 (116) = 232 sq. cm Cost of painting = Rs. (5 x 232) = Rs. 1160

What is the total cost of painting if 4 such cuboids are to be painted? Two cuboids with red colour and other two cuboids with green and yellow, respectively.

The length, breadth and height of a cuboid are 10 cm, 8 cm and 2 cm, respectively. All the faces of the cuboid are to be painted. The cost of painting with red colour is Rs. 5 per sq. cm. with green colour is Rs. 6 per sq. cm and with yellow is Rs. 10 per sq. cm. Now, answer the questions.

  1. Rs. 6032

  2. Rs. 6496

  3. Rs. 6022

  4. Rs. 3016

  5. None of these


Correct Option: A
Explanation:

Total surface area of 1 cuboid = 2 (lb + bh + hl) = 2 (10 x 8 + 8 x 2 + 2 x 10) sq. cm = 2 (80 + 16 + 20) sq. cm = 2 (116) = 232 sq. cm Total surface area of 2 such cuboids which is to be painted red = 2 x 232 sq cm = 464 sq. cm and the cost of painting will be Rs. (464 x 5) = Rs. 2320 Also, cost of painting 1 cuboid with green colour = Rs. (232 x 6) = Rs. 1392. Again, cost of painting 1 cuboid with yellow colour = Rs. (232 x 10) = Rs. 2320 Therefore, total cost of painting = Rs. (2320 + 1392 + 2320) = Rs. 6032

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