Question

If p and q be positive, then the coefficients of $(r + 1)^{th}$ and $(1 - x)^{- 4}$ in the expansion of $\frac{x^{r}}{r!}$will be.

• A. Equal
• B. Equal in magnitude but opposite in sign
• C. Reciprocal to each other
• D. None of these

Answer 1

Answer: (A)

Equal

Answer 2

Coefficient of $\therefore r = 0,8,16,24,.....,256$ is $\left( \frac{256 - r}{2} \right)$ and coefficient of $a_{0} + a_{1}x + a_{2}x^{2} + ..... + a_{2n}x^{2n} = (1 + x + x^{2})^{n}$ is $a_{1} + 2a_{2}x + ... + 2na_{2n}x^{2n - 1}$.

But $3^{2 \times 2} - 2 \times 2 + 1 = 81 - 4 + 1 = 78$, $x^{2n - 1} + y^{2n - 1}$.