KVPY Sample Paper KVPY Stream-SX Model Paper-16

If \[^{m}{{C}_{3}}+\,{{\,}^{m}}{{C}_{4}}>\,{{\,}^{m+1}}{{C}_{3}},\] then the least value of m is-

A) 6

B) 7

C) 5

D) none of these

Correct Answer: B

Solution :

\[^{m}{{C}_{3}}+\,{{\,}^{m}}{{C}_{4}}>{{\,}^{m+1}}{{C}_{3}}\]

\[\Rightarrow {{\,}^{m+1}}{{C}_{4}}>\,{{\,}^{m+1}}{{C}_{3}}\]

\[\Rightarrow \,\,\frac{(m+1)!}{(m-3)!4!}>\frac{(m+1)!}{(m-2)!3!}\]

\[\Rightarrow m-2>4\]

\[\Rightarrow \,\,m>6\]

\[\Rightarrow \]The least value of m is 7.