Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its \((i)\) second permitted energy level to the first level, and \((ii)\) the highest permitted energy level to the first permitted level.

Water drops are falling from a nozzle of a shower onto the floor, from a height of \(9.8\, {m}\). The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.  (In \(m\))

Light travels in two media \(M _{1}\) and \(M _{2}\) with speeds \(1.5 \times 10^{8} ms ^{-1}\) and \(2.0 \times 10^{8} ms ^{-1}\) respectively. The critical angle between them is.

A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from \(440\, Hz\) to \(480 \,Hz ,\) when it gets reflected from the wall. If the speed of sound in air is \(345 \,m / s ,\) then the speed of the car is \(.......km/hr\)

A simple pendulum of length \(L\) is placed between the plates of a parallel plate capacitor having electric field \(E,\) as shown in figure. Its bob has mass \(m\) and charge \(q.\) the time period of the pendulum is given by

Consider the efficiency of Carnot's engine is given by \(\eta=\frac{\alpha \beta}{\sin \theta} \log _{e} \frac{\beta x}{k T}\), where \(\alpha\) and \(\beta\) are constants. If \(T\) is temperature, \(k\) is Boltzman constant, \(\theta\) is angular displacement and \(x\) has the dimensions of length. Then, choose the incorrect option.

A telescope has an objective lens of focal length \(150\,\,cm\) and an eyepiece of focal length \(5 \,\,cm.\) If a \(50\,\,m\) tall tower at a distance of \(1\,\,km\) is observed through this telescope in normal setting, the angle formed by the image of the tower is \(\theta \), then \(\theta \) is close to.....\(^o\)

According to Bohr's theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the \(n^{th}\) orbit is proportional to (\(n =\) principal quantum number)

Two projectiles are projected with the same initial velocities at the \(15^\circ\) and \(30^\circ\) with respect to the horizontal. The ratio of their ranges is \(1:x\). The value of \(x\) is:

An electric field is given by \((6 \hat{i}+5 \hat{j}+3 \hat{k}) \ N / C\). The electric flux through a surface area \(30 \hat{\mathrm{i}}\; m^2\) lying in \(YZ-\)plane (in SI unit) is _______.

The displacement and the increase in the velocity of a moving particle in the time interval of \(t\) to \((t+1) \mathrm{s}\) are \(125 \mathrm{~m}\) and \(50 \mathrm{~m} / \mathrm{s}\), respectively. The distance travelled by the particle in \((\mathrm{t}+2)^{\mathrm{th}} \mathrm{s}\) is __________ \(\mathrm{m}\).

A spherical body of radius \(r\) and density \(\sigma\) falls freely through a viscous liquid having density \(\rho\) and viscosity \(\eta\) and attains a terminal velocity \(v _0\). Estimated maximum error in the quantity \(\eta\) is : (Ignore errors associated with \(\sigma, \rho\) and g , gravitational acceleration)

A beam of plane polarised light of large cross sectional area and uniform intensity of \(3.3 \,Wm ^{-2}\) falls normally on a polariser (cross sectional area \(3 \times 10^{-4}\, m ^{2}\) ) which rotates about its axis with an angular speed of \(31.4\, rad/s.\) The energy of light passing through the polariser per revolution, is close to ........ \( \times 10^{-4} \,J\)