Question

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

• A. 9
• B. 8
• C. 5
• D. None of these

Answer 1

Answer: (B)

${ }^{n+1} C_{n-2}-{ }^{n+1} C_{n-1} \leq 100$
$\Rightarrow { }^{n+1} C_{3}-{ }^{n+1} C_{2} \leq 100$
$\Rightarrow \frac{(n+1) n(n-1)}{6}-\frac{(n+1) n}{2} \leq 100$
$\Rightarrow (n+1) n(n-1)-3 n(n+1) \leq 600$
$\Rightarrow (n+1) n(n-4) \leq 600$
The values of $n$ satisfying this inequality are
$2,3,4,5,6,7,8,9$