Question

$(1 + x + x^{2} + x^{3})^{5}$term in expansion of $x^{r}\lbrack 0 \leq r \leq (n - 1)\rbrack$ is.

• A. $nC_{r}(3^{r} - 2^{n})$
• B. $nC_{r}(3^{n - r} - 2^{n - r})$
• C. $nC_{r}(3^{r} + 2^{n - r})$
• D. None of these

Answer 1

Answer: (B)

$nC_{r}(3^{n - r} - 2^{n - r})$

Answer 2

Applying $nC_{r + 1} = 70$for $\frac{nC_{r}}{nC_{r - 1}} = \frac{n - r + 1}{r} = \frac{56}{28} = 2$

Hence $\frac{nC_{r + 1}}{nC_{r}} = \frac{n - r}{r + 1} = \frac{70}{56} = \frac{5}{4}$

$n + 1 = 3r$.