List of practice Questions

The phenomena of lowering freezing point of water by the application of pressure is known as:
A steel ball of mass 200 g falls freely from a height of 20 m and bounces to a height of 10.8 m from the ground. If the energy lost in this process is absorbed by the ball, the rise in its temperature is:
A work of 166.28 J is done to adiabatically compress one mole of a gas. If the increase in the temperature of the gas is \( 8^\circ C \), the gas is:
In a Carnot’s engine, as the gas absorbs heat energy from the source, then the temperature of the source:
A ball of mass 10 g is allowed to fall down from 10 m height. After collision with the ground, if 50\% of its energy is lost, then the height reached by the ball is:
A bomb at rest explodes into three pieces of equal masses. If two pieces move perpendicular to each other, each with a speed \( v \), then the speed of the third piece is:
A body rotating with uniform acceleration about its geometrical axis makes 8 rotations in the first 2 seconds. The number of rotations the body makes in the next 3 seconds is (Initially the body is at rest):
A solid sphere is pushed on a horizontal surface such that it slides with a speed 3.5 m/s initially without rolling. The sphere will start rolling without slipping when its velocity becomes:
The mechanical energy of a damped oscillator becomes half of its initial energy in 4 seconds. In another \( t \) seconds its mechanical energy becomes 12.5\% of its initial mechanical energy. Then \( t = \):
When an external force with angular frequency \( \omega_0 \) acts on a system of natural angular frequency \( \omega \), the system oscillates with angular frequency \( \omega_d \). The condition for the amplitude of oscillations to be maximum is:
Which one of the following is a homogeneous differential equation?
The number of significant figures in 4.870 m is:
Among the following, velocity \( v \) - time \( t \) graph representing the motion of a vertically projected body is:
The resultant of two vectors \( \mathbf{A} \) and \( \mathbf{B} \) is perpendicular to vector \( \mathbf{A} \), and the resultant magnitude is equal to half of the magnitude of \( \mathbf{B} \). The angle between \( \mathbf{A} \) and \( \mathbf{B} \) is:
At any instant \( t \), the vertical distance \( Y \) and horizontal distance \( X \) of a projectile are given by \[ 2Y = 6t - g t^2 \quad \text{and} \quad X = 4t, \] The initial velocity of the projectile is:
A lorry is moving on a smooth circular path of radius 50 m with a velocity of 20 m/s. Then the banking angle of the road is:
A body of mass 1 kg is moving with a velocity 10 m/s due to a constant force on a horizontal rough surface having coefficient of kinetic friction 0.4. If the constant force is removed, the body comes to rest in a time:
Evaluate the following integral: \[ \int (x^3 + x^2 m + x^m) (2x^{2m} + 3x^m + 6x^m) \, dx \]
If \( a \in \mathbb{Z}^+ \), \([x]\) is the greatest integer not more than \( x \) and \[ \int_0^a \left\lfloor x \right\rfloor \, dx = 127, \text{ then } a = ? \]
Evaluate the integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin x \cdot \sin^2 x \cdot \cos x \, dx \]
The positive value of \( x \) satisfying the equation \[ \int_0^x (1 - t) \, dt = \frac{1}{2} \] is:
The area (in square units) bounded by \[ x = 4, \quad y = -4, \quad \text{and} \quad y = x \quad \text{is:} \]
The particular solution of the differential equation \[ (1 + y^2) \, dx - xy \, dy = 0, \quad y(1) = 0 \quad \text{represents:} \]
If \( c \) and \( d \) are arbitrary constants, then \[ y = e^{2x} \left( \cosh \sqrt{2} x + d \sinh \sqrt{2} x \right) \] is the general solution of the differential equation:
The function \( f(x) = x^2 + \dfrac{54}{x} \)