The number of zeros at the end of $70!$ is

Important Questions on Permutation and Combination

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 6 - Permutation and Combination>Work Book Exercise 6.2>Q 5

Sum of the series $\sum _{r=1}^n\left(r^2+1\right)r!$ is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 6 - Permutation and Combination>Work Book Exercise 6.3>Q 1

If ${}^{15}P_r={}^{14}P_8+8·{}^{14}P_7,$ then $r$ is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 6 - Permutation and Combination>Work Book Exercise 6.3>Q 2

Which of the following is incorrect ?

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 6 - Permutation and Combination>Work Book Exercise 6.3>Q 3

If ${}^{n+2}C_8:{}^{n-2}P_4=57:16$, then the value of $n$ is:

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 6 - Permutation and Combination>Work Book Exercise 6.3>Q 4

The exponent of $7$ in ${}^{100}\mathrm{C}_{50}$ is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 6 - Permutation and Combination>Work Book Exercise 6.3>Q 5

If ${}^{n-1}C_r=\left(k^2-3\right){}^{n}C_{r+1}$, then $k$ belongs to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 6 - Permutation and Combination>Work Book Exercise 6.3>Q 6

If $n$ is even and ${}^{n}C_0<{}^{n}C_1<{}^{n}C_2<\dots <{}^{n}C_r$$>{}^{n}C_{r+1}>{}^{n}C_{r+2}>\dots >{}^{n}C_n,$ then $r$ is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 6 - Permutation and Combination>Work Book Exercise 6.3>Q 7

The number of positive integers satisfying the inequality ${}^{n+1}C_{n-2}-{}^{n+1}C_{n-1}\le 100$ are