Work done in increasing the size of a soap bubble from a radius of $3\, cm$ to $5\, cm$ is nearly (Surface tension of soap solution $= 0.03\, Nm^{-1}$) (in $\pi \,mJ$)

$A$ pair of substances which gives the same products on reaction with water 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?

An $LCR$ series circuit with a resistance of $100\,\Omega$ is connected to an ac source of $200\,V$ (r.m.s.) and angular frequency $300\,rad/s$. When only the capacitor is removed,the current lags behind the voltage by $60^\circ$. When only the inductor is removed,the current leads the voltage by $60^\circ$. The average power dissipated is......$W$.

Some physical constants are given in List-$I$ and their dimensional formulae are given in List-$II$. Match the following:

List-$I$	List-$II$
$(1)$ Planck's constant	$(i)$ $[ML^{-1} T^{-2}]$
$(2)$ Gravitational constant	(ii) $[ML^{-1} T^{-1}]$
$(3)$ Bulk modulus	(iii) $[ML^2 T^{-1}]$
$(4)$ Coefficient of viscosity	(iv) $[M^{-1} L^3 T^{-2}]$

The correct answer is:

The equation $x^2-5xy+py^2+3x-8y+2=0$ represents a pair of straight lines. If $\theta$ is the angle between them,then $\sin \theta$ is equal to