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JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Binomial Theorem

The coefficient of

x^{7}

in the expression

(1 + x)^{10} + x (1 + x)^{9} + x^{2} (1 + x)^{8} + \dots + x^{10}

is:

(A)120
(B)420
(C)330✓ Correct
(D)210

Answer: (C)

Solution

The sum

(1 + x)^{10} + x (1 + x)^{9} + \dots + x^{10}

is a geometric series with first term

(1 + x)^{10}

, common ratio

\frac{x}{1 + x}

and

11

terms. It collapses to

(1 + x)^{10} \cdot \frac{1 - ( \frac{x}{1 + x} ) ^{11}}{1 - \frac{x}{1 + x}} = (1 + x)^{11} - x^{11}

. The coefficient of

x^{7}

is therefore

(7 11) = (4 11) = 330

.

JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Single correct option

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