COMPASSLearning

Talk to us Register Login

JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Binomial Theorem

The coefficient of

t^{4}

in the expansion of

(\frac{1 - t ^{6}}{1 - t})^{3}

is

(A)12
(B)15✓ Correct
(C)10
(D)14

Answer: (B)

Solution

Write

(\frac{1 - t ^{6}}{1 - t})^{3} = (1 - t^{6})^{3} (1 - t)^{- 3}

. Since

(1 - t^{6})^{3} = 1 - 3 t^{6} + 3 t^{12} - t^{18}

has no term below

t^{6}

, the coefficient of

t^{4}

comes entirely from the leading

1

multiplying the

t^{4}

term of

(1 - t)^{- 3}

. That expansion is

\sum_{k} (2 k + 2) t^{k}

, whose

t^{4}

coefficient is

(2 6) = 15

.

JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Binomial Theorem →

More JEE Main questions on Binomial Theorem