Test Index

UPSC NDA I 2018 Mathematics Solved Paper

© examsnet.com

Question : 34 of 120

Marks: +1, -0

In the expansion of

(1+x)^{43}

(2r+1)^{\text{th}}

if the coefficients of

(r+2)^{\text{th}}

,

5
14
21
22

Solution:

Concept:

General term in binomial expansion:

\text{ and }

Key property:

\text{,}

Explanation:

We are given that the coefficients of the

\text{ terms are equal, then what is the value of } r (r \neq 1)?

and

T_{(r+1)} = \binom{n}{r} x^{n-r} y^r

terms in

\binom{n}{r} = \binom{n}{n-r}

are equal.

Coefficient of

\left(2r+1\right)^{\text{th}}

term =

\left(r+2\right)^{\text{th}}

Coefficient of

\left(1+x\right)^{43}

term =

\left(2r+1\right)^{\text{th}}

Set them equal:

\binom{43}{2r}

Case 1:

\left(r+2\right)^{\text{th}}

(rejected, since

\binom{43}{r+1}

)

Case 2: Using

\binom{43}{2r} = \binom{43}{r+1}

, we get

2r = r+1 \Rightarrow r = 1

Simplify:

r \neq 1

Answer:

\binom{n}{k} = \binom{n}{n-k}

(Option B)

© examsnet.com

Go to Question:

Prev Question

Next Question