First slide

Binomial theorem for positive integral Index

Question

If the coefficients of x³⁹ and x⁴⁰ are equal in the expansion of (p + qx)⁴⁹ ,then the possible values of p and q, respectively, are

Moderate

A

4, 16
B

1, 4
C

5, 20
D

3, 9

Solution

We have,
$^{49} C_{39} p^{10} q^{39} =^{49} C_{40} p^{9} q^{40}$
$\begin{array}{l} \Rightarrow p = \frac{^{49} C_{40}}{^{49} C_{39}} q \\ \Rightarrow p = \frac{49 - 40 + 1}{40} q \\ \Rightarrow p = \frac{1}{4} q \end{array}$

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