The major product of the following reaction is

Let the relation $R$ be defined on the set of natural numbers $N$ by $a R b$ if $3 a + 2 b = 27$. Then $R$ is:

The foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{b^2} = 1$ and the hyperbola $\frac{x^2}{144} - \frac{y^2}{81} = \frac{1}{25}$ coincide. Then the value of $b^2$ is

What is the unit of $K_p$ for the reaction?
$CS_{2(g)} + 4H_{2(g)} \rightleftharpoons CH_{4(g)} + 2H_2S_{(g)}$

One end each of a resistance $r$,a capacitor $C$,and a resistance $2r$ are connected together. The other ends are respectively connected to the positive terminals of batteries $P, Q,$ and $R$ having emf's $E, E,$ and $2E$. The negative terminals of the batteries are then connected together. In this circuit,with steady current,the potential drop across the capacitor is:

The sum of two numbers is $20$. If the product of the square of one number and the cube of the other is maximum,then the numbers are: