In the expansion of ${({5^{1/2}} + {7^{1/8}})^{1024}}$, the number of integral terms is
$128$
$129$
$130$
$131$
Write the general term in the expansion of $\left(x^{2}-y x\right)^{12}, x \neq 0$
The coefficient of $x^8$ in the expansion of $(1 -x^4)^4 (1 + x)^5$ is :-
If $7^{th}$ term from beginning in the binomial expansion ${\left( {\frac{3}{{{{\left( {84} \right)}^{\frac{1}{3}}}}} + \sqrt 3 \ln \,x} \right)^9},\,x > 0$ is equal to $729$ , then possible value of $x$ is
If the non zero coefficient of $(2r + 4)th$ term is greater than non zero coefficient of $(r - 2)th$ term in expansion of $(1 + x)^{18}$, then number of possible integral values of $r$ is
If the maximum value of the term independent of $t$ in the expansion of $\left( t ^{2} x ^{\frac{1}{5}}+\frac{(1- x )^{\frac{1}{10}}}{ t }\right)^{15}, x \geq 0$, is $K$, then $8\,K$ is equal to $....$