The number of ways by which 6 distinct balls can be put in 5 distinct boxes are

• (A) 7776
• (B) 15625
• (C) 720
• (D) 120

Find the number of whole number solutions to \(a + b + c = 8\)

• (A) \(^{8}P_{3}\)
• (B) \(^{8}C_{3}\)
• (C) \(8^{3}\)
• (D) none of these

Find the number of natural number solutions to \(a + b + c = 8\)

• (A) 24
• (B) 28
• (C) 30
• (D) none of these

In how many ways 5 identical envelopes be placed among 3 distinct boxes such that any number of envelopes can be placed in any box.

• (A) 21
• (B) 35
• (C) 6
• (D) 42
• (E) None of the above

In how many ways can 8 identical pens be distributed among Aal, Bal, and Cal so that Aal gets at least 1 pen, Bal gets at least 2 pens, and Cal gets at least 3 pens?

• (A) 4
• (B) 3
• (C) 2
• (D) 6
• (E) 5

In how many ways 11 identical toys be placed in 3 distinct boxes such that no box is empty?

• (A) 33
• (B) 44
• (C) 42
• (D) 72
• (E) 45

A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that the cube is colored with green on one set of adjacent faces, red on the second and blue on the third set. How many minimum cuts you have made?

• (A) 15
• (B) 18
• (C) 12
• (D) 7
• (E) 13

In a solid cube which is made up of 27 small cubes, two opposite sides are painted red, two painted yellow and the other two with white. How many cubes have two colours?

• (A) 8
• (B) 12
• (C) 16
• (D) 24

A cube whose two adjacent faces are coloured is cut into 64 identical small cubes. How many of these small cubes are not coloured at all? (CAPF, 2005)

• (A) 24
• (B) 36
• (C) 48
• (D) 60

Ankit is 18th from right in the class of 50 students. What is the position from left?

• (A) 50
• (B) 32
• (C) 33
• (D) 31

Nitin ranks eighteenth in a class of 49 students. What is his rank from the last?

• (A) 18
• (B) 19
• (C) 31
• (D) 32
• (E) 33

Mohan and Ramesh are ranked seventh and eleventh respectively from the top in a class of 41 students. What will be their respective ranks from the bottom in the class?

• (A) 30th and 34th
• (B) 35th and 31st
• (C) 34th and 30th
• (D) 34th and 31st
• (E) 36th and 32nd