Question

If n is even positive integer, then the condition that the greatest term in the expansion of $x^{2}$may have the greatest coefficient also, is.

• A. $(x + a)^{n}$
• B. $T_{0},T_{1},T_{2},....$
• C. $(T_{0} - T_{2} + T_{4} - ....)^{2}$
• D. None of these

Answer 1

Answer: (A)

$(x + a)^{n}$

Answer 2

If n is even, the greatest coefficient is $924x^{6}$

Therefore the greatest term

$\left( x + \frac{1}{x} \right)^{10}$

$10C_{4}\frac{1}{x}$

and $10C_{5}$

⇒ $10C_{5}x$and $10C_{7}x^{4}$

⇒ $\left( x^{2} - \frac{3\sqrt{3}}{x^{3}} \right)^{10}$ and $(1 + x)^{10}$

⇒ $\frac{10!}{5!6!}$and $\frac{10!}{(5!)^{2}}$