Q33 / 90 · JEE Main 2019 (09 Jan Shift 2) · Mathematics

The coefficient of $t^{4}$ in the expansion of ${(\frac{1 - t^{6}}{1 - t})}^{3}$ is

A
$10$
B
$14$
Correct answer
C
$15$
D
$12$

Solution

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

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

∴

Co-efficient of

t^{4} = 1 \times^{3 + 4 - 1} C_{4} =^{6} C_{4} = 15

Hence, the correct answer is option: 'C'.

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