KC Sinha Mathematics Solution Class 11 Chapter 15 Combinations Exercise 15.1

 Exercise 15.1

Page no 15.9

Type 1

Question 1

Find $n$ if ${ }^{2 n} C_{3}:{ }^{n} C_{2}=12: 1$

Question 2

If ${ }^{n} C_{30}={ }^{\prime \prime} C_{4}$, find $n$

Question 3

If ${ }^{n} C_{12}={ }^{n} C_{8}$, find ${ }^{n} C_{17}$ and ${ }^{22} C_{n}$

Question 4

If ${ }^{18} C_{r}={ }^{18} C_{r+2}$, find ${ }^{r} C_{6}$

Question 5

If ${ }^{n} C_{n-4}=15$, find $n$

Question 6

If ${ }^{15} C_{r}:{ }^{15} C_{r-1}=11: 5$, find $r$

Question 7

Evaluate (i) ${ }^{10} C_{4}+{ }^{10} C_{5}$

(ii) ${ }^{13} C_{6}+{ }^{13} C_{5}$

(iii) ${ }^{19} C_{18}+{ }^{19} C_{17}$

Question 8

Evaluate

(i) ${ }^{31} C_{26}-{ }^{30} C_{26}$

(ii) ${ }^{61} C_{57}-{ }^{60} C_{56}$

Question 9

(i) If ${ }^{n} C_{9}={ }^{n} C_{8}$, find ${ }^{n} C_{17}$

(ii) If ${ }^{n} C_{8}={ }^{n} C_{2}$, find ${ }^{n} C_{2}$

Question 10

If ${ }^{n} C_{10}={ }^{n} C_{12}$, determine $n$ and hence ${ }^{n} C_{5}$

Question 11

Prove that (i) $1+{ }^{3} C_{1}+{ }^{4} C_{2}={ }^{5} C_{3}$

(ii) $2 \times{ }^{7} C_{4}={ }^{8} C_{4}$

(iii) ${ }^{2} C_{1}+{ }^{3} C_{1}+{ }^{4} C_{1}={ }^{5} C_{3}-1$

Question 12

If ${ }^{n} P_{r}=2520$ and ${ }^{n} C_{r}=21$, find $r$

Question 13

Show that ${ }^{20} C_{13}+{ }^{20} C_{14}-{ }^{20} C_{6}-{ }^{20} C_{7}=0$

Question 14

Prove that ${ }^{n-1} C_{3}+{ }^{n-1} C_{4}>{ }^{n} C_{3}$, if $n>7$

Question 15

If ${ }^{n} C_{r-1}=36,{ }^{n} C_{r}=84$ and ${ }^{n} C_{r+1}=126$, find $n$ and $r$