List of practice Questions

The energy equivalent of 1 g of a substance in joules is:
Mass numbers of two nuclei are in the ratio 2:3. The ratio of the nuclear densities would be:
Four hydrogen atoms combine to form an \( ^4_2He \) atom with a release of 26.7 MeV of energy. This is:

In the circuit given below, the current is: 

Electric conduction in a semiconductor is due to:
If the displacement of a body moving on a horizontal surface is 151.25 cm in a time interval of 2.25 s, then the velocity of the body in the correct number of significant figures in cm s\(^{-1}\) is:
The dimensions of torque are:
A particle is projected at an angle \( \theta \) with the x-axis in the xy-plane with a velocity \( \mathbf{v} = 6\hat{i} - 4\hat{j} \). The velocity of the body on reaching the x-axis again is:
The displacement-time graph of a moving body is a straight line making a 45\(^{\circ}\) angle with the time axis. The body moves with:
A ball is thrown up vertically at a speed of 6.0 m/s. The maximum height reached by the ball (Take \( g = 10 { m/s}^2 \)) is:
The INCORRECT statement is:
A bullet of 10 g, moving at 250 m/s, penetrates 5 cm into a tree limb before coming to rest. Assuming uniform force being exerted by the tree limb, the magnitude of the force is:
A block of mass \( M \) is placed on the floor of a lift at the center. The acceleration required for the lift to descend so that the block exerts a force of \( \frac{Mg}{4} \) on the lift floor is:
A particle of mass 40 g executes simple harmonic motion with an amplitude of 2.0 cm. If the time period of oscillation is \( \frac{\pi}{20} \) s, the total mechanical energy of the system is:
If the points \( (2, -3), (\lambda, -1) \) and \( (0, 4) \) are collinear, then the value of \( \lambda \) is equal to:
If \( B = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix} \) is the adjoint of a \( 3 \times 3 \) matrix \( A \) and \( |A| = 4 \), then the value of \( \alpha \) is:

If 

then the value of \( x - y \) is:

The constant term in the expansion of \( \left( x^3 + \frac{1}{x^2} \right)^{10} \) is:
If \( _nP_r = 480 \) and \( _nC_r = 20 \), then the value of \( r \) is equal to:
The coefficient of \( x^3 \) in the binomial expansion of \( \left( \frac{1}{\sqrt{x}} - x \right)^6 \) is:
Evaluate \( \binom{10}{1} + \binom{10}{2} + \dots + \binom{10}{10} \):
The numbers \( a, b, c, d \) are in G.P. with common ratio \( r \). If \( \frac{1}{a^3 + b^3} + \frac{1}{b^3 + c^3} + \frac{1}{c^3 + d^3} \) are also in G.P., then the common ratio is:
The second term of a G.P. is 4, then the product of the first three terms is:
If \( z_1 \) and \( z_2 \) are two complex numbers with \( |z_1| = 1 \), then \( \left| \frac{z_1 - z_2}{1 - z_1 \overline{z_2}} \right| \) is equal to:
If \( \left( \frac{1 - i}{1 + i} \right)^{10} = a + ib \), then the values of \( a \) and \( b \) are, respectively: