If $b+c=3a$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :

Let $PQR$ be a right-angled isosceles triangle,with the right angle at $P(2, 1)$. If the equation of the line $QR$ is $2x + y = 3$,then the equation representing the pair of lines $PQ$ and $PR$ is:

The rate constant of a first order reaction at $27^{\circ} C$ is $10^{-3} \ min^{-1}$. The temperature coefficient of this reaction is $2$. What is the rate constant (in $min^{-1}$) at $17^{\circ} C$ for this reaction?

Which property among the following is the same for both hydrogen and deuterium molecules?

The coefficient of $x^{24}$ in the expansion of $(1+x^2)^{12}(1+x^{12})(1+x^{24})$ is

$A$ parallel plate capacitor with air between the plates has a capacitance of $9 \, pF$. The separation between its plates is $d$. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_1 = 3$ and thickness $d/3$,while the other one has dielectric constant $K_2 = 6$ and thickness $2d/3$. The new capacitance of the capacitor is .... $pF$.