If the coefficient of x2 r is greater than half of the coefficient of x2 r+1 in the expansion of (1+x)15 then the possible value of r is -

Question

If the coefficient of x2 r is greater than half of the coefficient of x2 r+1 in the expansion of (1+x)15 then the possible value of r is - (A) 5 (B) 6 (C) 7 (D) 8

Tardigrade Admin · Accepted Answer

15 C 2 r >(1/2) 15 C 2 r +1 2>( 15 C 2 r +1/ 15 C 2 r ) ⇒ 2>(15-(2 r +1)+1/2 r +1) ⇒ 4 r +2>15-2 r ⇒ 6 r >13 ⇒ r >(13/6) 2 r +1 ≤ 15 ⇒ 2 r ≤ 14 ⇒ r ≤ 7 ∴ Options A, B C are correct.

Q. If the coefficient of x2r is greater than half of the coefficient of x2r+1 in the expansion of (1+x)15 then the possible value of r is -

5

6

7

8

15C2r​>21​15C2r+1​ 2>15C2r​15C2r+1​​⇒2>2r+115−(2r+1)+1​⇒4r+2>15−2r⇒6r>13⇒r>613​ & 2r+1≤15⇒2r≤14⇒r≤7 ∴ Options A, B & C are correct.

Q. If the coefficient of $x^{2 r}$ is greater than half of the coefficient of $x^{2 r + 1}$ in the expansion of $(1 + x)^{15}$ then the possible value of $r$ is -