Maths Binomial Theorem & Mathematical Induction No of Term, General Term, Coefficient of Any Power of X, Independent Term, Middle Term and Greatest Term & Greatest Coefficient Single Correct MCQ
Published on: August 12, 2026

In the expansion of a term containing the power x 13 :

A
Does not exist
B
Exists and the coefficient is divisible by 29
C
Exists and the coefficient is divisible by 63
D
Exists and the coefficient is divisible by 65

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Text Solution

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The correct answer is:
CHECK THE SOLUTION.

(b, c, d)

T r+1 = 30 C r (x 2/3 ) 30 –r (–x –1/2 ) r

= 30 C r (–1) r

⇒ 20 – = 13

= 7

⇒ r = 6

the coefficient of x 13 will be 30 C 6 = 593775 which is divisible 29, 63 and 65

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