Meaning of P(n, r) and C(n, r) — practice questions

Question 1 · difficulty L2 · understanding

The largest $n \in \mathbb{N}$, for which $7^n$ divides $101!$, is :

• A. 18
• B. 15
• C. 19
• D. 16

Question 2 · difficulty L2 · understanding

The number of sequences of ten terms, whose terms are either 0 or 1 or 2 , that contain exactly five 1 s and exactly three 2 s , is equal to :

• A. 360
• B. 2520
• C. 1820
• D. 45

Question 3 · difficulty L2 · understanding

The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition is :

• A. 48
• B. 120
• C. 168
• D. 220

Question 4 · difficulty L2 · understanding

If $${}^n{P_r} = {}^n{P_{r + 1}}$$ and $${}^n{C_r} = {}^n{C_{r - 1}}$$, then the value of r is equal to :

• A. 1
• B. 4
• C. 2
• D. 3

Question 5 · difficulty L2 · understanding

Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to :

• A. 5
• B. 2
• C. 4
• D. 6

Question 6 · difficulty L2 · understanding

A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168 , then $$\mathrm{b}+3 \mathrm{~g}$$ is equal to ____________.

Question 7 · difficulty L2 · understanding

The missing value in the following figure is

Question 8 · difficulty L3 · understanding

The number of elements in the set $S = \left\{ (r, k) : k \in \mathbb{Z} \text{ and } ^{36}C_{r+1} = \frac{6\left(^{35}C_{r}\right)}{(k^2-3)} \right\}$ is :

• A. 2
• B. 4
• C. 8
• D. 16

Question 9 · difficulty L3 · understanding

The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word "UDAYPUR" is

• A. 1579
• B. 1578
• C. 1580
• D. 1581

Question 10 · difficulty L3 · understanding

The largest value of $n$, for which $40^n$ divides $60!$, is

• A. 14
• B. 13
• C. 11
• D. 12