The expression $[x + (x^3-1)^{1/2}]^5 + [x - (x^3-1)^{1/2}]^5$ is a polynomial of degree :
$5$
$6$
$7$
$8$
If the coefficients of $x^7$ & $x^8$ in the expansion of ${\left[ {2\,\, + \,\,\frac{x}{3}} \right]^n}$ are equal , then the value of $n$ is :
Let $a$ and $b$ be two nonzero real numbers. If the coefficient of $x^5$ in the expansion of $\left(a x^2+\frac{70}{27 b x}\right)^4$ is equal to the coefficient of $x^{-5}$ is equal to the coefficient of $\left(a x-\frac{1}{b x^2}\right)^7$, then the value of $2 b$ is
In the expansion of ${\left( {3x - \frac{1}{{{x^2}}}} \right)^{10}}$ then $5^{th}$ term from the end is :-
In the expansion of ${\left( {\frac{{3{x^2}}}{2} - \frac{1}{{3x}}} \right)^9}$,the term independent of $x$ is
The first $3$ terms in the expansion of ${(1 + ax)^n}$ $(n \ne 0)$ are $1, 6x$ and $16x^2$. Then the value of $a$ and $n$ are respectively