JEE Main20203 Sep 2020Evening ShiftMathematicsBinomial TheoremActual

If the term independent of x in the expansion of 3 2 x 2 - 1 3 x 9 is k , then 18 k is equal to:

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Correct answer

D. 7

Step-by-step solution

T r + 1 = 9 C r 3 x 2 2 9 - r - 1 3 x r = 9 C r 3 2 9 - r - 1 3 r x 18 - 3 r For the term independent of x , put r = 6 ⇒ T 7 = 9 C 6 3 2 3 - 1 3 6 = 9 C 3 1 6 3 = 9 × 8 × 7 3 × 2 × 1 1 6 3 = 7 18 ⇒ k = T 7 ⇒ k = 7 18 ⇒ 18 k = 7

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