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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)

best_answer

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

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