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BITSAT 2024Paper 1

Exam: BITSAT
Year: 2024
Paper: Paper 1
Subject: Mathematics
Chapter: Binomial Theorem

BITSAT 2024 · Paper 1 · Mathematics · Binomial Theorem

If the 17^ th and the 18^ th terms in the expansion of (2+a)^ 50...

If the

17^{\text{th }}

and the

18^{\text{th }}

terms in the expansion of

(2+a)^{50}

are equal, then the coefficient of

x^{35}

in the expansion of

(a+x)^{-2}

is

Options

A $-35$
B $3$
C $36$
D $-36$

Correct answer

D. $-36$

Step-by-step solution

Given,

17^{\text{th }}

and

18^{\text{th }}

terms in the expansion

(2+a)^{50}

are equal

\therefore T_{17}=T_{18}\Rightarrow\binom{50}{16}(2)^{34}(a)^{16}=\binom{50}{17}(2)^{33}(a)^{17}\Rightarrow a=\frac{\binom{50}{16}}{\binom{50}{17}} \times 2=1\therefore

Now, coefficient of

x^{35}

in the expansion

(1+x)^{-2}=-36\because

Coefficient of

x^r

is

(r+1)

in

(1-x)^{-2}

.

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