QJEEM16Ma30f9: JEE Main 2016 Mathematics - Class 11 JEEM16Ma30f9 Solution: If    n + 2 C 6 n − 2 P 2 = 11, then n satisfies the…

Question

Verified Solution • 2025–26 Session moderate

If

\frac{^{n + 2} C_{6}}{^{n - 2} P_{2}}

= 11, then n satisfies the equation :

Accepted Answer

\frac{^{n + 2} C_{6}}{^{n - 2} P_{2}} = 11

\Rightarrow

\frac{(n + 2)!}{6! (n - 4)!} = 11 . \frac{(n - 2)!}{(n - 4)!}

\Rightarrow

(n + 2)! = 11.6! (n

-

2)!

\Rightarrow

(n + 2) (n + 1) n (n

-

1) = 11.6!

\Rightarrow

(n + 2) (n + 1) n (n

-

1) = 11 . 6 . 5 . 4 . 3 . 2 . 1

\Rightarrow

(n + 2) (n + 1) n (n

-

1) = 11 . 10 . 9 . 8

∴

n = 9

This value of n satisfy the equation,

n² + 3n

-

108 = 0

QJEEM16Ma30f9: JEE Main 2016 Mathematics - Class 11 JEEM16Ma30f9 Solution: If &nbsp;&nbsp; n + 2 C 6 n − 2 P 2 = 11, then n satisfies the…