$A$ and $B$ are two radioactive substances whose half-lives are $1$ and $2$ years respectively. Initially, $10 \, g$ of $A$ and $1 \, g$ of $B$ are taken. The time (approximate) after which they will have the same quantity remaining is ........... $years$.

$A$ ball falls from a height $h$ and rebounds after striking the floor. The coefficient of restitution is $e$. The total distance covered before it comes to rest is

In an $LCR$ circuit,the capacitance is changed from $C$ to $2C$. For the resonant frequency to remain unchanged,the inductance should be changed from $L$ to:

Match the following columns:

Column-$I$	Column-$II$
$a$. Superior Vena Cava	$p$. Carries deoxygenated blood to the lungs
$b$. Inferior Vena Cava	$q$. Carries oxygenated blood to the heart
$c$. Pulmonary Artery	$r$. Brings deoxygenated blood from lower body parts to the right atrium
$d$. Pulmonary Vein	$s$. Brings deoxygenated blood from upper body parts to the right atrium

$A$ body is moving up an inclined plane of angle $\theta$ with an initial kinetic energy $E$. The coefficient of friction between the plane and the body is $\mu$. The work done against friction before the body comes to rest is

$A$ cylinder of radius $R$ made of a material of thermal conductivity $K_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of material of thermal conductivity $K_2$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is