# If A and B are coefficient of x n in the expansions of (1 + x)2n and (1 + x)2n–1 respectively, then AB equals ______. - Mathematics

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If A and B are coefficient of x n in the expansions of (1 + x)2n and (1 + x)2n–1 respectively, then A/B equals ______.

#### Options

• 1

• 2

• 1/2

• 1/"n"

#### Solution

If A and B are coefficient of x n in the expansions of (1 + x)2n and (1 + x)2n–1 respectively, then A/B equals 2.

Explanation:

Given expression is (1 + x)2n

"T"_(r + 1) = ""^(2n)"C"_r x^r

∴ Coefficient of xn = 2nCn = A  .....(Given)

In the expression (1 + x)2n–1

"T"_(r + 1) = ""^(2n - 1)"C"_rx^r

∴ Coefficient of xn = ""^(2n - 1)"C"_n = B  ....(Given)

So, A/B = (""^(2n)"C"_n)/(""^(2n - 1)"C"_n)

= (""^(2n)"C"_n)/(""^(2n - 1)"C"_n) = 2/1  ....[From Q. no 21]

Concept: Proof of Binomial Therom by Combination
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#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 8 Binomial Theorem
Exercise | Q 23 | Page 145
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