List of practice Questions

The magnetic field at the center of a long solenoid having 400 turns per unit length and carrying a current $I = 6.24 \times 10^{-7$ A is}
If a proton of kinetic energy 8.35 MeV enters a uniform magnetic field of 10 T at right angles to the direction of the field, then the force acting on the proton is
If the rms speed of the molecules of a diatomic gas at a temperature of 322K is 2000 m/s, then the gas is
The equation of a transverse wave propagating along a stretched string of length 80 cm is $y = 1.5 \sin ( (5 \times 10^3)x + 20t )$, here 'x' and 'y' are in cm and the time 't' is in seconds. If the mass of the string is 3 g, then the tension in the string is
When an object is placed in front of a convex mirror at a distance 'u' from the pole of the mirror such that the size of the image is 'n' times that of the object, then the object distance 'u' is
A narrow slit of width 2 mm is illuminated with monochromatic light of wavelength 500 nm. If the distance between the slit and the screen is 1 m, then first minima are separated by a distance of
The force between two conducting spheres of same radius having charges +8 μC and -4 μC separated by some distance in air is F. If the spheres are connected by a conducting wire and after some time the wire is removed, then the magnitude of the force between the two conducting spheres is
The potential energy of a satellite of mass \( m \) revolving around the earth at a height of \( R \) from the surface of the earth is:
When the temperature increases, the viscosity of
If a body cools from a temperature of 62°C to 50°C in 10 minutes and to 42°C in the next 10 minutes, then the temperature of the surroundings is
If the ratio of universal gas constant and specific heat capacity at constant volume of a gas is given by 0.67, then the gas is
The internal energy of 4 moles of a monoatomic gas at a temperature of 77°C is
If 5.6 liters of a monoatomic gas at STP is adiabatically compressed to 0.7 liters, then the work done on the gas is nearly
A motor can pump 7560 kg of water per hour from a well of depth 100 m. If the efficiency of the pump is 70%, then the power of the pump is:
A circular disc of diameter 0.8 m and mass 4 kg is rolling on a smooth horizontal plane. If 2.56 N torque is acting on the disc, then its angular acceleration is:
A particle is executing simple harmonic motion with amplitude \( A \). The ratio of the kinetic energies of the particle when it is at displacements of \( \frac{A}{4} \) and \( \frac{A}{2} \) from the mean position is:
If the potential energy of a particle of mass \(0.1 \, \text{kg}\) moving along the x-axis is \(5x(x - 4)\), then the speed of the particle is maximum at a position of:
The general solution of the differential equation \((1 + \sin^2 x) \, \frac{dy}{dx} + \sin 2x = 0\) is?
The displacement (\(x\)) and time (\(t\)) graph of a particle moving along a straight line is shown in the figure. The average velocity of the particle in the time of 10s is:
If the horizontal range of a body projected with a velocity \(u\) is 3 times the maximum height reached by it, then the range of the body is:
Evaluate \[ \int \sin^3 x \cos^2 x \, dx = ? \]
Evaluate \[ \lim_{n \to \infty} \frac{1}{2n} \left( \sin \frac{\pi}{2n} + \sin \frac{\pi}{n} + \sin \frac{2\pi}{2n} + \dots \right) = ? \]
Evaluate \[ \int_0^\pi \left( \sin^3 x \cos^3 x + \sin^4 x \cos^4 x + \sin^3 x \cos^3 x \right) dx = ? \]
Evaluate \[ \int \frac{1}{x^4 + 1} \, dx = ? \]
The area of the region (in sq.units) bounded by the curves \(x^2 + y^2 = 16\) and \(x^2 + y^2 = 6x\) is?