MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Combination

If n+1C4=9n...

Question

If $^{n + 1} C_{4} = 9^{n} C_{2}$ , then $n =$

A

10

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

B

9

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

C

12

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

D

11

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

Open in App

Solution

The correct option is D $11$
$^{n + 1} C_{4} = 9^{n} C_{2}$
$\frac{(n + 1)!}{(n - 3) 14!} = 9 \frac{n!}{(n - 2)! 2!}$
$\frac{(n + 1) n!}{(n - 3)! 4!} = \frac{9 n!}{(n - 2) (n - 3)! 2!}$
$\frac{n + 1}{4 \times 3 \times 2!} = \frac{9}{(n - 2) 2!}$
$(n + 1) (n - 2) = 12 \times 9$
$n^{2} - 2 n + n - 2 = 108$
$n^{2} - n - 2 = 108$
$n^{2} - n = 110$
$n^{2} - n - 110 = 0$
On simiplying, we get
$n = 11$
$∵ n^{2} - 11 n + 10 n - 110 = 0$
$n (n - 11) + 10 (n - 11) = 0$
$(n + 10) (n - 11) = 0$
$n = 11, - 10$
$∵ n \neq - 10$
$\Rightarrow n = 11$

Suggest Corrections

thumbs-up

0

Similar questions

^{n} C_{4} = \frac{10}{6} \times^{n} C_{2}

, find the value of "n".

If $C_{r}$ means $^{n} C_{r}$ then $\frac{C_{0}}{1} + \frac{C_{2}}{3} + \frac{C_{4}}{5} + \dots =$

A_{n} = (n, n + 1)

10 (A_{10} A_{11})^{2} + 11 (A_{11} + A_{12})^{2} + . . . . . . + 20 (A_{20} A_{21})^{2}

\frac{5 + 9 + 13 + . . . t o n t e r m s}{7 + 9 + 11 + . . . t o (n + 1) t e r m s} = \frac{17}{16},

then n =

(a) 8

(b) 7

(c) 10

(d) 11

A = {4^{n} - 3 n - 1 : n \in N}

B = {9 (n - 1) : n \in N}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Combinations

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon