Ferric sulphate on heating gives:

An $AC$ voltage source of variable angular frequency $\omega$ and fixed amplitude $V_0$ is connected in series with a capacitance $C$ and an electric bulb of resistance $R$ (inductance zero). When $\omega$ is increased:

If $\frac{x+1}{(2x-1)(3x+1)}=\frac{A}{(2x-1)}+\frac{B}{(3x+1)}$,then $16A+9B$ is equal to

The acute angle between the two lines whose direction ratios $(l, m, n)$ satisfy the equations $l+m-n=0$ and $l^2+m^2-n^2=0$ is

Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 ~K$. The piston of $A$ is free to move while that of $B$ is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 ~K$,the rise in temperature of the gas in $B$ is (in $~K$)

If $(1+x+x^2+x^3)^5 = \sum_{k=0}^{15} a_k x^k$,then $\sum_{k=0}^7 a_{2k}$ is equal to