The sum of the coefficients of all the even powers of x in the expansion of (2 x2-3 x+1)11 is

Question

The sum of the coefficients of all the even powers of x in the expansion of (2 x2-3 x+1)11 is (A) 2 × 610 (B) 3 × 610 (C) 611 (D) None of these

Tardigrade Admin · Accepted Answer

Let (2 x2-3 x+1)11=a0+a1 x+a2 x2+⋅s+a22 x22 to find a0+a2+a4+⋅s+a22, we find that SE+S0=P(1)=0 where P(x)=(2 x2-3 x+1)11 SE-S0=P(-1)=611 ⇒ 2 SE=611 ⇒ SE=3 × 610

Q. The sum of the coefficients of all the even powers of $x$ in the expansion of $(2 x^{2} - 3 x + 1)^{11}$ is

$2 \times 6^{10}$

$3 \times 6^{10}$

$6^{11}$

None of these

Q. The sum of the coefficients of all the even powers of x in the expansion of (2x2−3x+1)11 is

2×610

3×610

611

None of these

Let (2x2−3x+1)11=a0​+a1​x+a2​x2+⋯+a22​x22 to find a0​+a2​+a4​+⋯+a22​, we find that SE​+S0​=P(1)=0 where P(x)=(2x2−3x+1)11 SE​−S0​=P(−1)=611⇒2SE​=611⇒SE​=3×610

Q. The sum of the coefficients of all the even powers of $x$ in the expansion of $(2 x^{2} - 3 x + 1)^{11}$ is

$2 \times 6^{10}$

$3 \times 6^{10}$

$6^{11}$