Question

$\left( x^{4} - \frac{1}{x^{3}} \right)^{15}$

• A. $x^{32}$; for all even values of n
• B. $15C_{5}$; for all values of n i.e., all even odd values
• C. 0
• D. None of these

Answer 1

Answer: (B)

$15C_{5}$; for all values of n i.e., all even odd values

Answer 2

Multiplying each term by n! the question reduces to

$2^{15}$

$2^{14}$.

Thus $\frac { 1 } { 1 ! ( n - 1 ) ! } + \frac { 1 } { 3 ! ( n - 3 ) ! } + \frac { 1 } { 5 ! ( n - 5 ) ! } + \ldots$ $C_{0} + 2C_{1} + 3C_{2} + .... + (n + 1)C_{n}$.