List of practice Questions

What is the path followed by a charge entering a uniform magnetic field with its initial velocity along the direction of the magnetic field?

Find the pressure on an air bubble of radius \( r \) at a height \( h \) from the surface of the water.

What is the work done to stretch a string?

Three forces are acting on a particle in which \( F_1 \) and \( F_2 \) are perpendicular. If \( F_1 \) is removed, find the acceleration of the particle.

Acceleration of the freely falling metal rod in a cycling ring?

The ratio of frequency of the 3rd mode of vibration for the closed organ pipe and the open pipe of length \( L \)?

To have the same RMS value as that of hydrogen at 30K, what will be the temperature of the oxygen molecule?

If \( \frac{C_p}{C_v} \) is unity for a process, \( PV^{\gamma} = \text{constant} \), then the process is:

If a bar magnet is doped into a circular ring placed horizontally, then what change will happen?

If fringe width obtained in a YDSE is 1.3mm. If the whole system is dipped in a liquid of refractive index 1.3, then the new fringe width will be:

Band gap energy of Si is:

Which of the following is incorrect?

If \( B = 400\sqrt{2} \sin(\omega t - kx) \), find the peak value of the magnetic field of the electromagnetic wave.

3 capacitors of capacitance \( 12 \mu \text{F} \) each is connected in series. If the voltage is 12V, what charge is drawn from the cell?

The power dissipated by a particle with constant force and constant acceleration is proportional to the:

The dimension of \( \lambda \times t \) (decay constant \(\lambda\) multiplied by time \(t\)) is:

Arrange the following in the order of conductivity: Na, Ag, Fe, Cu

Find pH of the solution if \([H^+] = 2 \times 10^{-4} \, \text{mol/L}\)

Which among the following acts as a Lewis acid?

Solution set of \( -12x > 38 \text{ for } x \in \mathbb{N} \) \[ -12x > 38 \]

Evaluate the following integral: \[ \int e^x \left[\frac{1}{1+x(1+x)^2}\right] dx \]

Evaluate the following sum: \[ \sum_{n=1}^{2025} i^n (1+i) \]

Evaluate the following statement: \[ f(x) = \sin(|x|) - |x| \text{ is not differentiable at } x = \underline{\hspace{2cm}} \]

Evaluate the derivative of the function: \[ f(x) = x |x|, \quad \text{find} \quad f'(-10) \]

Given the following probabilities: \[ P(A) = 0.7, P(B) = 0.5, P(A \cup B) = 0.9, \quad \text{find} \quad P(A/B) \]