KC Sinha Mathematics Solution Class 11 Chapter 14 Permutations Exercise 14.2

 Exercise 14.1

Page no 14.16

Question 1

Evaluate the following :

(i) $7 !$ (ii) 5 ! (iii) 8 !

(iv) $8 !-5 !$

(v) $4 !-3$ !

(vi) $7 !-5 !$

(vii) $\frac{6 !}{5 !}$

(viii) $\frac{7 !}{5 !}$

(ix) $\frac{8 !}{6 ! 2 !}$

(x) $\frac{9 !}{4 ! 5 !}$

(xi) $\frac{12 !}{(10 !) 2 \times 1}$

Question 2

Compute

(i) $(3 !)(5 !)$

(ii) $\frac{20 !}{18 !(20-18) !}$

(iii) $\frac{1}{5 !}+\frac{1}{6 !}+\frac{1}{7 !}$

Question 3

Evaluate $\frac{n !}{r !(n-r) !}$, when

(i) $n=7, r=3$

(ii) $n=15, r=12$

(iii) $n=5, r=2$

Question 4

Evaluate $\frac{n !}{(n-r) !}$, when

(i) $n=9, r=5$

(ii) $n=6, r=2$

Question 5

Convert the following into factorials :

(i) $1.3 .5 .7 .9 .11$

(ii) $(n+1)(n+2)(n+3) \ldots 2 n$

Question 6

State whether 'true' or 'false' :

(i) $2 !+3 !=5 !$

(ii) $2 ! \times 3 !=6 !$

(iii) $\frac{8 !}{4 !}=2$ !

(iv) $5 !-3 !=2$ !

(v) $3 !+4 !=7$ !

Question 7

Find $x$ if:

(i) $\frac{1}{8 !}+\frac{1}{9 !}=\frac{x}{10 !}$

(ii) $\frac{1}{6 !}+\frac{1}{7 !}=\frac{x}{8 !}$

Question 8

Find the value of $n$ if :

(i) $(n+1) !=12 \cdot(n-1) !$

(ii) $2 n ! n !=(n+1)(n-1) !(2 n-1) !$

Question 9

If $\frac{n !}{2 !(n-2) !}$ and $\frac{n !}{4 !(n-4) !}$ are in ratio $2: 1$, find the value of $n$.

Question 10

Show that $n !(n+2)=n !+(n+1) !$

Question 11

Find the value of $x$ if $\frac{(x+2) !}{(2 x-1) !} \cdot \frac{(2 x+1) !}{(x+3) !}=\frac{72}{7}$ where $x \in N$.

Question 12

Show that $27 !$ is divisible by $2^{12}$. What is the largest natural number $n$ such that 27 ! is divisible by $2^{n}$ ?

Question 13

Show that $24 !+1$ is not divisible by any number between 2 to 24 .