Suppose $2-p, p, 2-\alpha, \alpha$ are the coefficient of four consecutive terms in the expansion of $(1+x)^n$. Then the value of $p^2-\alpha^2+6 \alpha+2 p$ equals
$4$
$10$
$8$
$6$
${6^{th}}$ term in expansion of ${\left( {2{x^2} - \frac{1}{{3{x^2}}}} \right)^{10}}$ is
If sum of the coefficient of the first, second and third terms of the expansion of ${\left( {{x^2} + \frac{1}{x}} \right)^m}$ is $46$, then the coefficient of the term that doesnot contain $x$ is :-
If the coefficients of the three consecutive terms in the expansion of $(1+ x )^{ n }$ are in the ratio $1: 5: 20$, then the coefficient of the fourth term is $............$.
Number of integral tems in the expansion of $\left\{7^{\left(\frac{1}{2}\right)}+11^{\left(\frac{1}{6}\right)}\right\}^{824}$ is equal to..................
The term independent of $x$ in expansion of ${\left( {\frac{{x + 1}}{{{x^{2/3}} - {x^{\frac{1}{3}}} + 1\;}}--\frac{{x - 1}}{{x - {x^{1/2}}}}} \right)^{10}}$ is