General and middle terms

If $p_1$ and $p_2$, respectively, are the second largest and the fourth largest prime numbers in the factorization of the coefficient of $x^{30}$ in the expression of $\left(x^2+2+\dfrac1{x^2}\right)^{-5}(1+x^2)^{40}$, then $p_1+p_2$ is equal to _______

The coefficient of $x^{-5}$ in the binomial expansion of $\left(\dfrac{x+1}{x^{2/3}-x^{1/3}+1}-\dfrac{x-1}{x-x^{1/2}}\right)^{10}$, where $x\ne0,1$, is :

If the coefficients of $x^{-2}$ and $x^{-4}$ in the expansion of $\left(x^{1/3}+\dfrac1{2x^{1/3}}\right)^{18}$, (x > 0), are m and n respectively, then $\dfrac mn$ is equal to :

If the coefficients of the three successive terms in the binomial expansion of $(1+x)^n$ are in the ratio 1 : 7 : 42, then the first of these terms in the expansion is :

The term independent of $x$ in the binomial expansion of
$$\left(1-\frac1x+3x^5\right)\left(2x^2-\frac1x\right)^8$$
is :

If the coefficients of $x^3$ and $x^4$ in the expansion of $(1+ax+bx^2)(1-2x)^{18}$ in powers of $x$ are both zero, then $(a,b)$ is equal to :

If $\left(2+\dfrac x3\right)^{55}$ is expanded in the ascending powers of $x$ and the coefficients of powers of $x$ in two consecutive terms of the expansion are equal, then these terms are :

The coefficient of $x^{1012}$ in the expansion of $(1+x^n+x^{253})^{10}$, (where $n\le22$ is any positive integer), is :