Question

Coefficient of $x^{50}$ in the polynomial
$\left(x{+}^{50}{C}_0\right)(x+{3.}^{50}{C}_1)(x+{5.}^{50}{C}_2).....[x+(101\left){.}^{50}{C}_{50}\right]$ is

• A. ${50.2}^{50}$
• B. ${50.2}^{51}$
• C. ${51.2}^{50}$
• D. $50(2^{50}+2)$

Answer 1

The correct option is B ${50.2}^{51}$

$\left(x{+}^{50}{c}_0\right)\left(x+{3.}^{50}{c}_1\right)\left(x+{5.}^{50}{c}_2\right).........\left[x+\left(2n+1\right){.}^{50}{c}_{50}\right]$

Then coefficient of $x^{50}$ is ${50.2}^{51}$