If the co-efficients of three cosecutive terms in the expansion of (1+x)^{n} are 220, 495 and 792 respectively, find the value of n

  • Option 1)

    10

  • Option 2)

    11

  • Option 3)

    12

  • Option 4)

    14

 

Answers (1)

As we learnt in 

Properties of Binomial Theorem -

\dpi{120} ^{n}c_{r}= \frac{n}{r}\: ^{n-1}c_{r-1}= \frac{n}{r}\cdot \frac{n-1}{r-1}\; \; ^{n-2}c_{r-2}\: and \: so\ on...

-

Let coeffecient be

  ^{n}C_{r-1},^{n}C_{r},^{n}C_{r+1}\\*\\*\frac{^{n}C_{r}}{^{n}C_{r-1}}=\frac{495}{220}=\frac{n-r+1}{r}=\frac{9}{4}\\*\\*4n-13r+4=0\\*\\*and\: \: \: \frac{^{n}C_{r+1}}{^{n}C_{r}}=\frac{792}{495}=\frac{n-r}{r+1}=\frac{8}{5}\\*\\*5n-13r-8=0

On solving n=12


Option 1)

10

Incorrect

Option 2)

11

Incorrect

Option 3)

12

Correct

Option 4)

14

Incorrect

Preparation Products

Knockout BITSAT 2021

It is an exhaustive preparation module made exclusively for cracking BITSAT..

₹ 4999/- ₹ 2999/-
Buy Now
Knockout BITSAT-JEE Main 2021

An exhaustive E-learning program for the complete preparation of JEE Main and Bitsat.

₹ 27999/- ₹ 16999/-
Buy Now
Exams
Articles
Questions