List of practice Questions

When unpolarised light from air incidents on the surface of a medium of refractive index $\sqrt{3}$, then the reflected light is totally polarised. The angle of refraction is
An alpha particle and a proton are accelerated from rest in a uniform electric field. The ratio of the times taken by proton and alpha particle to attain equal displacements is
A parallel plate capacitor with air as dielectric has a capacitance of 4 $\mu$F. The space between the plates of the capacitor is completely filled with a material of dielectric constant 5 and charged to a potential of 100 V. The work done to completely remove the dielectric material after the capacitor is disconnected from the battery is
The potential difference between the terminals of a cell is 20 V when a current of 2 A flows through the circuit. When the direction of current in the circuit is reversed, the potential difference between the terminals of the cell is 30 V. The internal resistance of the cell is
A straight uniform wire of resistance 36 $\Omega$ is bent in the form of a semi-circular loop. The effective resistance between the ends of the diameter of the semi-circular loop is
A rectangular ice box of total surface area of 1000 cm$^2$ initially contains 1.5 kg of ice at 0 $^\circ$C. If the thickness of the walls of the box is 2 mm and the temperature outside the box is 42 $^\circ$C, then the mass of the ice remaining in the box after 160 minutes is (Thermal conductivity of the material of the box = $10^{-2}$ Wm$^{-1}$K$^{-1}$ and latent heat of the fusion of ice = $336\times10^3$ Jkg$^{-1}$)
At constant pressure, equal amounts of heat are supplied to a monatomic gas and a diatomic gas separately. The ratio of the increases in internal energies of the two gases is
If the rms speed of the molecules of a gas at a temperature of 77 $^\circ$C is 50 ms$^{-1}>$, then the rms speed of the same gas molecules at a temperature of 150.5 $^\circ$C is
Two tuning forks of frequencies 320 Hz and 323 Hz are vibrated together. The time interval between a maximum sound and its adjacent minimum sound heard by an observer is
The frequency of sound heard by an observer moving towards a stationary source with certain speed is $n_1$ and if the observer moves away from the same source with same speed, the frequency of sound heard by the observer is $n_2$. If the speed of sound in air is 340ms$^{-1}$ and $n_1 : n_2 = 71:65$, then speed of observer is
A Cassegrain telescope uses two mirrors of radii of curvature 25 cm and 16 cm separated by a distance of 2.5 cm. The position of the final image of an object at infinity is
At a given place, to increase the number of oscillations made by a simple pendulum in one minute from 72 to 90, the length of the pendulum is to be decreased by
If the orbital speed of a body revolving in a circular path near the surface of the earth is 8 kms$^{-1}$, then the orbital speed of a body revolving around the earth in a circular orbit at height of 19,200 km from the surface of earth is (Radius of the earth = 6400 km)
The Young's modulus and Poisson's ratio of a material are respectively Y and $\sigma$. The force required to decrease the area of cross-section of a wire made of this material by $\Delta A$ is
A thin film of water is formed between two straight parallel wires each of length 8 cm separated by distance of 0.6 cm. The work done to increase the distance between the wires to 0.8 cm is (Surface tension of water = 0.07 Nm$^{-1}$)
A rain drop of diameter 1 mm falls with a terminal velocity of 0.7 ms$^{-1}$ in air. If the coefficient of viscosity of air is $2\times10^{-5}$ Pas, the viscous force on the rain drop is
The temperature at which the reading on Fahrenheit scale becomes 90% more than the reading on Celsius scale is
A ball projected at an angle of 45$^\circ$ with the horizontal crosses two points at equal heights separated by a distance at times 2 s and 8 s respectively. The horizontal distance between the two points is (Acceleration due to gravity = 10 ms$^{-2}$)
A truck of mass 8 ton is carrying a block of mass 2 ton. If a breaking force of 25 kN is applied on the truck, then the frictional force acting on the block is (Coefficient of static friction between the block and the truck is 0.3)
The work done in displacing a particle from $y=a$ to $y = 2a$ by a force $F = -\frac{K}{y^2}$ acting along y-axis is
Due to the presence of air resistance, if a body dropped from a height of 20 m reaches the ground with a speed of 18ms$^{-1}$, then the time taken by the body to reach the ground is nearly
A balance is made using a uniform metre scale of mass 100 g and two plates each of mass 200 g fixed at the two ends of the scale and the balance is pivoted at 45 cm mark of the scale. The error when 300 g weight is placed in the plate at 0 cm to weigh vegetables placed in the plate at 100 cm is
The ratio of radii of gyration of a thin circular ring and a circular disc of same radius about a tangential axis in their own planes is $\sqrt{12}:\sqrt{K}$. The value of K is
$\int_{-2}^{4} |2-x^2| dx =$
The general solution of the differential equation $\frac{dy}{dx} + (\sec x \csc x)y = \cos^2 x$ is