First slide

Binomial theorem for positive integral Index

Question

If $(1 + p x)^{n} = 1 + 24 x + 2642 x^{2} + \dots . . .$ then

Moderate

A

$p = 2, n = 6$
B

$p = 2, n = 12$
C

$p = 3, n = 6$
D

none of these

Solution

$\begin{array}{l} (1 + p x)^{n} = 1 + n p x + \frac{1}{2} n (n - 1) p^{2} x^{2} + \dots \\ ∴ n p = 24, \frac{1}{2} n (n - 1) p^{2} = 264 \end{array}$
Solve to obtain $n = 12, p = 2 .$

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