List of top Questions asked in Assam Combined Entrance Examination

In the circuit below, A and B represent two inputs and C represents the output. The circuit represents:
A particle is moving in a uniform circular motion of radius \( R \) with angular velocity \( \omega \) in the anti-clockwise direction. Another particle is also moving along the same circular path but in the clockwise direction with the same angular velocity \( \omega \). Suppose, both the particles start at \( t = 0 \) from the same point (R, 0) in opposite directions. The minimum time \( t \) after which the velocities of the two particles become orthogonal to each other is:
The current I drawn from the 5 volt source will be:
A wire of length \( L \) meter carrying current \( i \) ampere is bent in the form of a circle. The magnitude of its magnetic moment in SI units is:
A point object is placed at a distance of 25 cm from a thin plano-convex lens of focal length 20 cm. The plane surface of the lens is now silvered. The image created by the system is at:
The temperature of an ideal gas is increased from 75 K to 300 K. If at 75 K the r.m.s. velocity of the gas molecules is \(v\), at 300 K it becomes:
A liquid drop of radius \(R = 0.1 \, \text{m}\) having surface tension \(S = \frac{0.01}{4\pi} \, \text{N/m}\) divides itself into \(n\) identical drops. In the process, the total change in the surface energy \(\Delta U = 10^{-4} \, \text{J}\). The value of \(n\) is
The work function of a given metal is 4 eV. The longest wavelength of light that can cause photoelectron emission from this metal is:
A ray of light passes through four transparent media with refractive index \(n_1, n_2, n_3, n_4\) as shown in the figure. The surfaces of all media are parallel. If the emergent ray ST is parallel to the incident ray PQ, we must have:
A particle moves in a circle of radius \( R \). In half the period of revolution its displacement and distance covered respectively are:
Four closed surfaces and corresponding charge distributions are shown below. The respective electric fluxes through the surfaces \( S_1, S_2, S_3, S_4 \) are \( \Phi_1, \Phi_2, \Phi_3, \Phi_4 \). Then, which of the following is correct?
Two bodies (A and B) of masses 7 kg and 3 kg are attached to each other in the following way. If a force of 100 N is applied on A along the x direction, the force on A on B will be
The dimension of force constant is
A system goes from state a to b along the path abc, when 20 kJ of heat flows into the system and the system does 7.6 kJ of work. If the system is returned back from b to a along the curved path bca due to a work of 5 kJ done on it, then
The efficiency of a Carnot engine operating between a reservoir and an sink is \( \eta \). If the temperature of the reservoir is increased by 50% and that of the sink is decreased by 50%, the new efficiency will be:
For a straight wire carrying steady current in the vertically upward direction as shown below
Two very long, straight, and insulated wires are kept at a 90° angle from each other in the x-y plane as shown in the figure. These wires carry equal currents of magnitude \( I \), whose directions are shown in the figure. The net magnetic field at point P will be:
At temperature \( T \), the probability of ideal gas molecules with mass \( m \) having speed \( v \) is given by \( P(v) \). Two quantities \( I_1 \) and \( I_2 \) are defined in terms of \( P(v) \) as follows:
\[ I_1 = \int_0^\infty P(v) v^3 \, dv \quad \text{and} \quad I_2 = \int_0^\infty P(v) v \, dv \] Which of the following relationship is true?
In a Doppler effect experiment, initially an observer and the source are moving towards each other with equal speeds. The observed frequency in this case is found to be \( f_0 \). The observed frequency once they cross each other is found to be \( f' \). If \( f \) is the frequency at the source, \( f' \) is equal to:
Consider a viscous fluid having uniform density \( \rho \) and coefficient of viscosity \( \eta \). Two solid spheres with radius \( R_1 \) and \( R_2 \) fall into this liquid and acquire terminal velocities of \( V \) and \( 8V \) respectively. If the densities of the two spheres are \( 2\rho \) and \( 3\rho \) respectively, then \( R_1 \) is equal to \( R_2 \)?
Consider two radioactive materials A and B. When A decays into 6.25 percent of its original amount, B decays into 25 percent of its original amount. The ratio of their decay constants \( \lambda_A \) and \( \lambda_B \) is:
1 gm of ice at 0°C is mixed with 1 gm of water at 100°C. At thermal equilibrium, the temperature of the mixture will be:
A pulse of light of duration 50 ns is absorbed completely by a small object initially at rest. Power of the pulse is 60 mW and speed of light is \( 3 \times 10^8 \) m/s. The final momentum of the object is:
A series R-C combination is connected to an AC voltage of angular frequency \( \omega = 1000 \) rad/s. If the impedance of the RC circuit is \( R/\sqrt{2} \), the time constant (in milliseconds) of the circuit is:
In the uranium radioactive series the initial nucleus is \(^{238}U\) and the final nucleus is \(^{206}Pb\). When the uranium nucleus decays to lead, the number of \(\alpha\)-particles and \(\beta\)-particles emitted respectively are: