The coefficient of t4 in the expansion of $${\left( {{{1 - {t^6}} \over {1 - t}}} \right)^3}$$ is :
JEE · Math · previous-year question
- A.14
- B.15correct
- C.10
- D.12
Answer
B. 15
Explanation
$${\left( {{{1 - {t^6}} \over {1 - t}}} \right)^3}$$ = (1 $$-$$ t6)3 (1 $$-$$ t)$$-$$3 = (1 $$-$$ 3C1t6 + 3C2t12 $$-$$ 3C3t18) $$ \times $$ (1 $$-$$ t)$$-$$3 coefficient of t4 is 1 $$ \times $$ coefficient of t4 in (1 $$-$$ t)$$-$$3 = 1 $$ \times $$ 3+4$$-$$1C4 (By multinomial theorem) = 6C4 = 15
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