Water is being poured at the rate of $36 \ m^3 / min$ into a cylindrical vessel,whose circular base has a radius of $3 \ m$. Then the water level in the cylinder is rising at the rate of:

Consider the following reaction equilibrium:
$N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$
Initially,$1 \text{ mole}$ of $N_2$ and $3 \text{ moles}$ of $H_2$ are taken in a $2 \text{ L}$ flask. At equilibrium state,if the number of moles of $N_2$ is $0.6$,what is the total number of moles of all gases present in the flask?

If the function $f$ defined on $\left( \frac{\pi }{6}, \frac{\pi }{3} \right)$ by $f(x) = \begin{cases} \frac{\sqrt{2} \cos x - 1}{\cot x - 1}, & x \neq \frac{\pi}{4} \\ k, & x = \frac{\pi}{4} \end{cases}$ is continuous,then $k$ is equal to

The reaction $X \rightarrow \text{products}$ is a first order reaction. In $40 \text{ minutes}$,the concentration of $X$ changes from $1.0 \text{ M}$ to $0.25 \text{ M}$. What is the rate of reaction when $[X] = 0.1 \text{ M}$? $(\log 4 = 0.60)$

Which one of the following is true for an exothermic reaction $A \rightleftharpoons B$,if $E_f$ and $E_b$ are the activation energies of forward and backward reactions respectively?

The correct match of the group reagents in List$-I$ for precipitating the metal ion given in List$-II$ from solutions, is

List$-I$	List$-II$
$(P)$ Passing $H _2 S$ in the presence of $NH _4 OH$	$(1) \ Cu ^{2+}$
$(Q) \ \left( NH _4\right)_2 CO _3$ in the presence of $NH _4 OH$	$(2) \ Al ^{3+}$
$(R) \ NH _4 OH$ in the presence of $NH _4 Cl$	$(3) \ Mn ^{2+}$
$(S)$ Passing $H _2 S$ in the presence of dilute $\text{HCl}$	$(4) \ Ba ^{2+}$
	$(5) \ Mg ^{2+}$