In the binomial expansion of $(p-q)^{14}$,if the sum of $7^{\text{th}}$ term and $8^{\text{th}}$ term is zero,then $\frac{p+q}{p-q}=$

If $a>0$ and the coefficient of $x^2$ in the expansion of $\left(a x^3+\frac{c}{x}\right)^6$ is $60$,then $a c^2=$

If $a^3 + b^6 = 2$,then the maximum value of the term independent of $x$ in the expansion of $(ax^{1/3} + bx^{-1/6})^9$ is,where $(a > 0, b > 0)$.

If $n$ is the degree of the polynomial,$\left[ {\frac{1}{{\sqrt {5{x^3} + 1} - \sqrt {5{x^3} - 1} }}} \right]^8 + \left[ {\frac{1}{{\sqrt {5{x^3} + 1} + \sqrt {5{x^3} - 1} }}} \right]^8$ and $m$ is the coefficient of $x^{12}$ in it,then the ordered pair $(n, m)$ is equal to

The number of integral terms in the expansion of $(5^{\frac{1}{2}} + 7^{\frac{1}{8}})^{1016}$ 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 $8K$ is equal to $....$