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

9

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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

Suggest Corrections

Similar questions

^{n + 1} C_{n - 2} -^{n + 1} C_{n - 1} \leq 100

S_{n} = \sum_{k = 0}^{n} (- 1)^{K} .^{3 n} C_{k}, w h e r e n = 12, . . . . . .

$^{n + 1} C_{n + 1} = ? n \in N$

$^{n} C_{0} \times^{n + 1} C_{n} +^{n} C_{1}^{n} C_{n - 1} +^{n} C_{2} \times^{n - 1} C_{n - 2} + . . . . .^{n} C_{n}$ =

m \sum r = 0

^{n + r} C_{n} =

Join BYJU'S Learning Program