First slide

Binomial theorem for positive integral Index

Question

The value of $2 C_{0} + \frac{2^{2}}{2} C_{1} + \frac{2^{3}}{3} C_{2} + \dots + \frac{2^{11}}{11} C_{10},$ is

Moderate

A

$\frac{1}{11} (2^{11} - 1)$
B

$\frac{1}{11} (3^{11} - 1)$
C

$\frac{1}{11} (11^{3} - 1)$
D

$\frac{1}{11} (11^{2} - 1)$

Solution

Given expression is equal to
$\begin{array}{l} \int_{0}^{2} (C_{0} + C_{1} x + C_{2} x^{2} + \dots C_{10} x^{10}) d x \\ = \int_{0}^{2} (1 + x)^{10} d x = \frac{1}{11} (3^{11} - 1) \end{array}$

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