A body of mass \(2 \mathrm{~kg}\) thrown vertically from the ground with a velocity of \(8 \mathrm{~ms}^{-1}\) reaches a maximum height of \(3 \mathrm{~m}\). The work done by the air resistance is (acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )

An inductor is connected to an ac source of frequency 50 \(\mathrm{Hz}\). The frequency of the instantaneous power developed in the circuit is

A particle executes simple harmonic motion between $x=-A$ and $x=+A$. If it takes a time $T_1$ to $g_0$ from $x=0$ to $x=A/2$ and $T_2$ to go from $x=A/2$ to $x=A$. Then

The surface tension and vapour pressure of a liquid at \(25^{\circ} \mathrm{C}\) are \(8 \times 10^{-2} \mathrm{Nm}^{-1}\) and \(2.5 \times 10^3 \mathrm{~Pa}\) respectively. The radius of the smallest spherical water droplet which can from without evaporating at \(25^{\circ} \mathrm{C}\) is

Two bodies are projected from points \((0,0)\) and \((\sqrt{3}-1,0)\) with velocities \(10 \mathrm{~ms}^{-1}\) and \(\mathrm{v} \mathrm{ms}^{-1}\) respectively, as shown in the figure. The time after which they collide in space is ________.

The ratio of energies of photons produced due to transition of an electron in hydrogen atom from second energy level to first energy level and fifth energy level to second energy level is

An observer moves towards a stationary source of sound with a speed \(\frac{1}{5}^{\text {th }}\) of the speed of sound. The wavelength and frequency of the waves emitted by the source are \(\lambda\) and \(f\) respectively. The apparent frequency and wavelength heard by the observer are respectively,

In the common-base configuration, a transistor has current amplification factor 0.95 . If the transistor is used in common-emitter configuration and base current changes by \(2 \mu \mathrm{A}\), then the change in the collector current is

Two dice are thrown and the sum of the numbers appeared on the dice is noted. If \(A\) is the event of getting a prime number as their sum and \(B\) is the event of getting a number greater than 8 as their sum, then \(\mathrm{P}(\mathrm{A} \cap \overline{\mathrm{B}})=\)

\(\mathrm{XeF}_4\) is square planar where as \(\mathrm{CCl}_4\) is tetrahedral because

Which of the following nuclear reactions is possible?

If \(y=\frac{\alpha x+\beta}{\gamma x+\delta}\), then \(2 y_1 y_3=\)

When ' \(\mathrm{X}\) ' \(\mathrm{g}\) of graphite is completely burnt in a bomb calorimeter in excess of \(\mathrm{O}_2\) at \(298 \mathrm{~K}\) and \(1 \mathrm{~atm}\) pressure as given in the equation
\(\mathrm{C}\) (graphite) \(+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})\)
The temperature of calorimeter raised from \(298 \mathrm{~K}\) to \(302 \mathrm{~K}\). If the heat capacity of the calorimeter and molar enthalpy change for the reaction at \(1 \mathrm{~atm}\) and \(298 \mathrm{~K}\) are \(20.7 \mathrm{~kJ} \mathrm{~K}^{-1}\) and \(-248.4 \mathrm{~kJ} \mathrm{~mol}^{-1}\), ' \(\mathrm{X}^{\prime}\) in \(\mathrm{g}\) is