If $\tanh ^{-1} x = a \log \left(\frac{1+x}{1-x}\right)$,$|x| < 1$,then $a$ is equal to

Heat is supplied to a diatomic gas at constant pressure. The ratio of $\Delta Q : \Delta U : \Delta W$ is

The variation of radiant energy emitted by the sun, the filament of a tungsten lamp, and a welding arc as a function of its wavelength is shown in the figure. Which of the following options is the correct match?

Let $P(6, 3)$ be a point on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. If the normal at point $P$ intersects the $x$-axis at $(9, 0)$,then the eccentricity of the hyperbola is:

Passage cells are thin-walled cells found in

$20 \text{ mL}$ of $0.1 \text{ M}$ acetic acid is mixed with $50 \text{ mL}$ of potassium acetate. $K_a$ of acetic acid $= 1.8 \times 10^{-5}$ at $27^\circ \text{C}$. Calculate the concentration of potassium acetate if the $pH$ of the mixture is $4.8$. (in $\text{ M}$)