Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of \(10 cm / s\) coalesce to form a bigger drop. The terminal velocity of bigger drop is _________ \(cm / s\).

In the below circuit the current in each resistance is

The number of electrons flowing per second in the filament of a \(110 \mathrm{~W}\) bulb operating at \(220 \mathrm{~V}\) is _______. (Given \(\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\) )

When a hydrogen atom going from \(\mathrm{n}=2\) to \(\mathrm{n}=1\) emits a photon, its recoil speed is \(\frac{\mathrm{x}}{5} \mathrm{~m} / \mathrm{s}\). Where \(\mathrm{x}=\) _______. (Use : mass of hydrogen atom\(\left.=1.6 \times 10^{-27 /} \ \mathrm{kg}\right)\)

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of \(3\,s\) and \(4\,s\) respectively. If their moments of inertia are in the ratio of \(3: 2\) then the ratio of their magnetic moments will e.

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field \(\vec{E}_1=E_0\hat{x}\). If another electric field \(\vec{E}_2=2E_0(\hat{y}+\hat{z})\) is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

A convex lens (of focal length \(20\, cm\)) and a concave mirror, having their principal axes along the same lines, are kept \(80\, cm\) apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of \(30\, cm\) to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be.....\(cm\)

A beam of light consisting of wavelengths 650 nm and 550 nm illuminates the Young's double slits with separation of 2 mm such that the interference fringes are formed on a screen, placed at a distance of 1.2 m from the slits. The least distance of a point from the central maximum, where the bright fringes due to both the wavelengths coincide, is ___________ \(\times 10^{-5} m\).

The position of a particle related to time is given by \(x =\left(5 t ^2-4 t +5\right) m\). The magnitude of velocity of the particle at \(t=2\,s\) will be \(...........ms^{-1}\)

Two identical positive charges \(Q\) each are fixed at a distance of ' \(2 a\) ' apart from each other. Another point charge qo with mass ' \(m\) ' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge \(q_{0}\) executes \(SHM\). The time period of oscillation of charge \(q_{0}\) will be.