If $\frac{d}{d x}\left[(x+1)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\right] = \left(15 x^p-16 x^q+1\right)(x-1)^{-2}$,then $(p, q)$ is equal to

The heating of $NH _4 NO _2$ at $60-70^{\circ} C$ and $NH _4 NO _3$ at $200-250^{\circ} C$ is associated with the formation of nitrogen containing compounds $X$ and $Y$, respectively. $X$ and $Y$, respectively, are

If $(1+x+x^2+x^3)^5 = \sum_{k=0}^{15} a_k x^k$,then $\sum_{k=0}^7 a_{2k}$ is equal to

For the reaction $N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$,the equilibrium constant $(K_c)$ at temperature $T$ is $4 \times 10^{-4}$. What is the value of $K_c$ for the reaction $NO_{(g)} \rightleftharpoons 1/2 N_{2(g)} + 1/2 O_{2(g)}$ at the same temperature?

Using the Trapezoidal rule,find the approximate value of $\int_1^4 y \, dx$ based on the following table:

$x$	$1$	$2$	$3$	$4$
$y$	$0.7111$	$0.7222$	$0.7333$	$0.7444$

(in $.1833$)

An organic compound containing $C$ and $H$ has $92.3 \%$ of carbon. Its empirical formula is: