The sum of the co-efficients in the expansion of (1-2 x +5 x 2) n is ' a ' and the sum of the co-efficients in the expansion of (1+ x )2 n is b. Then -

Question

The sum of the co-efficients in the expansion of (1-2 x +5 x 2) n is ' a ' and the sum of the co-efficients in the expansion of (1+ x )2 n is b. Then - (A) a = b (B) a=b2 (C) a2=b (D) a b=1

Tardigrade Admin · Accepted Answer

(1-2 x+5 x2)n For sum of coefficients put x =1 ∴ a=(1-2+5)n=4n (1+x)2 n For sum of coefficients put x =1; b =(1+ x )2 n =22 n =(22) n =4 n ∴ a = b

Q. The sum of the co-efficients in the expansion of $(1 - 2 x + 5 x^{2})^{n}$ is ' $a$ ' and the sum of the co-efficients in the expansion of $(1 + x)^{2 n}$ is $b$ . Then -

$a = b$

$a = b^{2}$

$a^{2} = b$

$ab = 1$

$(1 - 2 x + 5 x^{2})^{n}$
For sum of coefficients put $x = 1$
$∴ a = (1 - 2 + 5)^{n} = 4^{n}$
$(1 + x)^{2 n}$
For sum of coefficients put $x = 1$ ;
$b = (1 + x)^{2 n} = 2^{2 n} = (2^{2})^{n} = 4^{n}$
$∴ a = b$

Q. The sum of the co-efficients in the expansion of (1−2x+5x2)n is ' a ' and the sum of the co-efficients in the expansion of (1+x)2n is b. Then -

a=b

a=b2

a2=b

ab=1