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 $r$
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