Two blocks of masses $10\,kg$ and $4\,kg$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $14\,m/s$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is ......... $m/s$.

The pressure and density of a given mass of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$ change adiabatically from $(P, d)$ to $(P^{\prime}, d^{\prime})$. If $\frac{d^{\prime}}{d} = 32$,then $\frac{P^{\prime}}{P}$ is $(\gamma = \text{ratio of specific heats})$

$A$ meter bridge is set up as shown,to determine an unknown resistance '$X$' using a standard $10 \, \Omega$ resistor. The galvanometer shows a null point when the tapping-key is at the $52 \, cm$ mark. The end corrections are $1 \, cm$ and $2 \, cm$ respectively for the ends $A$ and $B$. The determined value of '$X$' is $.......... \Omega$.

What is the concentration of nitrate ions if equal volumes of $0.1 \ M$ $AgNO_3$ and $0.1 \ M$ $NaCl$ are mixed together (in $M$)?

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

If a plant is deficient in the element $Zinc$,which plant hormone's biosynthesis will be affected in that plant?