According to Abbe, in the formula for resolving power of microscope, the
numerical aperture is represented by

A particle of mass ' \(\mathrm{m}\) ' moving east ward with a speed ' \(v\) ' collides with another particle of same mass moving north-ward with same speed ' \(v\) '. The two particles coalesce after collision. The new particle of mass ' \(2 \mathrm{~m}\) ' will move in north east direction with a speed (in \(\mathrm{m} / \mathrm{s}\) )

Two inductors of \(60 \mathrm{mH}\) each are joined in parallel. The current passing through this combination is \(2.2 \mathrm{~A}\). The energy stored in this combination of inductors in joule is

A hollow cylinder has a charge \(q\) coulomb within it. If \(\phi\) is the electric flux associated with the surface \(B\), the flux linked with the plane surface A will be

In the given circuit, current flowing through the circuit is

Moving coil galvanometers \(\mathrm{M}_{1}\) and \(\mathrm{M}_{2}\) have resistance, number of turns, area of coil and magnetic field as follows.
\(\mathrm{R}_{1}=10 \Omega, \mathrm{R}_{2}=14 \Omega, \mathrm{N}_{1}=30, \mathrm{~N}_{2}=42\)
\(\mathrm{A}_{1}=3 \cdot 6 \times 10^{-3} \mathrm{~m}^{2}, \mathrm{~A}_{2}=1 \cdot 8 \times 10^{-2} \mathrm{~m}^{2},\) \(\mathrm{~B}_{1}=0 \cdot 25 \mathrm{~T}, \mathrm{~B}_{2}=0 \cdot 50 \mathrm{~T}\)
(Spring constants are same for both materials)
The ratio of (i) current sensitivity and (ii) voltage sensitivity for galvanometer
\(\left(\mathrm{M}_{2}\right.\) to \(\left.\mathrm{M}_{1}\right)\) is respectively

The critical angle is \(\theta\) for a light going from medium \(P\) to medium Q. If speed of light in medium \(\mathrm{P}\) is \(\mathrm{V}_{\mathrm{P}}\) then speed of light in medium \(\mathrm{Q}\) is

Progeny resulting from cross pollination are

For a gas at a particular temperature on an average, the quantity which remains same for all molecules is

Calculate the solubility product of sparingly soluble salt BA at 300 K if its solubility is \(9.1 \times 10^{-3} \mathrm{moldm}^{-3}\) at same temperature.

In a first order reaction \(60 \%\) of the reactant converts into product in 45 minute. Calculate rate constant of the reaction.

Figure shows three forces \(\overrightarrow{\mathrm{F}}_{1}, \overrightarrow{\mathrm{F}}_{2}\) and \(\overrightarrow{\mathrm{F}}_{3}\) acting along the sides of an equilateral
triangle. If the total torque acting at point ' 0 ' (centre of the triangle) is zero then the
magnitude of \(\overrightarrow{\mathrm{F}}_{3}\) is

A piece of metal weighing \(100 \mathrm{~g}\) is heated to \(80^{\circ} \mathrm{C}\) and dropped into \(1 \mathrm{~kg}\) of cold water in an insulated container at \(15^{\circ} \mathrm{C}\). If the final temperature of the water in the container is \(15.69^{\circ} \mathrm{C}\), the specific heat of the metal in \(\mathrm{J} / \mathrm{g}^{\circ} \cdot \mathrm{C}\) is: