Modern Maths — Practice

Question 1

In how many ways can 4 books be selected from 9 different books (order irrelevant)?

Accepted Answer

C

Question 2

In how many ways can 8 people be seated around a round table?

Accepted Answer

A

Question 3

Two fair dice are rolled. Find the probability that the sum is 7.

Accepted Answer

B

Question 4

Find the sum of the first 12 odd natural numbers.

Accepted Answer

C

Question 5

Find the number of distinct arrangements of the letters of 'ENGINEERING' (11 letters: E×3, N×3, G×2, I×2, R×1).

Accepted Answer

B

Question 6

In how many ways can 12 identical chocolates be distributed among 4 children, with no restriction on the number each child gets?

Accepted Answer

B

Question 7

How many diagonals does a convex dodecagon (12 sides) have?

Accepted Answer

C

Question 8

Four fair coins are tossed. Find the probability of getting at least 3 heads.

Accepted Answer

B

Question 9

Two cards are drawn without replacement from a standard 52-card deck. Find the probability that the first is a king and the second is a queen.

Accepted Answer

B

Question 10

From 6 men and 3 women, a committee of 4 is to be formed. In how many ways can the committee include at least one woman?

Accepted Answer

C

Question 11

In how many ways can 5 letters be placed into 5 addressed envelopes so that no letter goes into its correct envelope?

Accepted Answer

This is the derangement D₅ = 5!(1 − 1 + 1/2! − 1/3! + 1/4! − 1/5!) = 120 × (1 − 1 + 0.5 − 0.1667 + 0.0417 − 0.0083) = 44.

D₅ = 44.

Question 12

Find the sum: 1/(1×2) + 1/(2×3) + 1/(3×4) + 1/(4×5) + 1/(5×6).

Accepted Answer

C

Practice — Modern Maths