List of practice Questions

If \( \frac{\sec^2 15^\circ - 1}{\sec^2 15^\circ} \) equals:
Let \( A = (a_{ij}) \) be a square matrix of order 3 and let \( M_{ij} \) be the minors of \( a_{ij} \). If \( M_{11} = -40, M_{12} = -10, M_{13} = 35 \), and \( a_{11} = 1, a_{12} = 3, a_{13} = -2 \), then the value of \( |A| \) is equal to:
If the determinant of the matrix \( \begin{bmatrix} |x| & 1 & 2 \\ 4 & 1 & x \\ 1 & -1 & 3 \end{bmatrix} \) equals -10, then the values of \( x \) are:
The magnetic field at the centre of a circular coil having a single turn of the wire carrying current \( I \) is \( B \). The magnetic field at the centre of the same coil with 4 turns carrying the same current is:
A current carrying square loop is suspended in a uniform magnetic field acting in the plane of the loop. If \( \vec{F} \) is the force acting on one arm of the loop, then the net force acting on the remaining three arms of the loop is:
In an LCR circuit, at resonance, the value of the power factor is:
An electromagnetic wave is propagating in a medium with velocity \( \vec{v} = v \hat{i} \). The instantaneous oscillating magnetic field of this electromagnetic wave is along positive \( z \)-direction. Then the direction of the oscillating electric field is in the:
Focal length of a convex lens of refractive index 1.5 is 3 cm. When the lens is immersed in water of refractive index \( \frac{4}{3} \), its focal length will be:
A narrow single slit of width \( d \) is illuminated by white light. If the first minimum for violet light (\( \lambda = 4500 \, {Å} \)) falls at \( \theta = 30^\circ \), the width of the slit \( d \) in microns is (1 micron = \( 10^{-6} \) m):
Threshold frequency for photoelectric effect from a metallic surface corresponds to a wavelength of 6000 \({Å}\). The photoelectric work function for the metal is \( h = 6.6 \times 10^{-34} \, {Js} \):
Bohr atom model is invalid for:
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: