The number of integral values of $k$ for which the equation $7 \cos x + 5 \sin x = 2k + 1$ has a solution is:

$A$ liquid is in equilibrium with its vapour in a sealed container at a fixed temperature. The volume of the container is suddenly increased.
$a$. What is the initial effect of the change on vapour pressure?
$b$. How do rates of evaporation and condensation change initially?
$c$. What happens when equilibrium is restored finally and what will be the final vapour pressure?

Two rotating bodies $A$ and $B$ of masses $m$ and $2m$ with moments of inertia $I_A$ and $I_B$ $(I_B > I_A)$ have equal kinetic energy of rotation. If $L_A$ and $L_B$ are their angular momenta respectively,then:

$CrO_4^{2-}$ (Yellow) changes to $Cr_2O_7^{2-}$ (orange) in $pH = x$ and vice versa in $pH = y$,hence $x$ and $y$ are respectively:

What are organisms that obtain energy from reduced inorganic compounds called?

If $f(x) = (p - x^n)^{1/n}$,$p > 0$ and $n$ is a positive integer,then $f[f(x)]$ is equal to