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A transistor is operated in a common emitter configuration at $V_c = 2 \text{ V}$ such that a change in the base current from $100 \text{ } \mu\text{A}$ to $300 \text{ } \mu\text{A}$ produces a change in the collector current from $10 \text{ mA}$ to $20 \text{ mA}$. The current gain is:
A proton and an $\alpha$-particle both enter a region of uniform magnetic field $B$, moving at right angles to the field. If the radius of circular orbits for both particles is equal and the kinetic energy acquired by the proton is $1\text{ MeV}$, the energy acquired by the $\alpha$-particle will be:
The dimensional formula for Planck's constant (h) is
A block A of mass $m_1$ rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of the table and from its other end, another block B of mass $m_2$ is suspended. The coefficient of kinetic friction between block A and the table is $\mu_k$. When block A is sliding on the table, the tension in the string is:
Equation of displacement for any particle is $s = 3t^3 + 7t^2 + 14t + 8$ m. Its acceleration at time $t = 1$ sec is:
The correct Boolean operation represented by the circuit diagram drawn is :
A ball is thrown vertically upwards. Which of the following plots represents the speed-time graph of the ball during its height if the air resistance is not ignored?
In which of the following devices, the eddy current effect is not used?
The unit of e.m.f. is:
A big circular coil with $1000$ turns and an average radius of $10 \text{ m}$ is rotating about its horizontal diameter at a rate of $2 \text{ rad s}^{-1}$. The vertical component of the Earth's magnetic field at that location is $2 \times 10^{-5} \text{ T}$, and the electrical resistance of the coil is $12.56 \Omega$. The maximum induced current in the coil will be:
A square loop with a side length of $1 \text{ m}$ and resistance of $1 \Omega$ is placed in a uniform magnetic field of $0.5 \text{ T}$. The plane of the loop is perpendicular to the direction of the magnetic field. The magnetic flux through the loop is:
Dimensions of charge are:
A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity $4 \text{ m s}^{-1}$. The ball strikes the water surface after $4 \text{ s}$. The height of bridge above water surface is (Take $g = 10 \text{ m s}^{-2}$)
A body of mass $m$ is kept on a rough horizontal surface (coefficient of friction = $\mu$). A horizontal force is applied to the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by $\vec{F}$, where:
If a square loop ABCD carrying a current i is placed near and coplanar with a long straight conductor XY carrying a current I, what will be the net force on the loop?
The Brewsters angle $i_b$ for an interface should be
A full wave rectifier circuit consists of two p-n junction diodes, a centre-tapped transformer, capacitor and a load resistance. Which of these components remove the ac ripple from the rectified output?
In which of the following processes, heat is neither absorbed nor released by a system?
Two identical charged spheres suspended from a common point by two massless strings of lengths l are initially at a distance d (d << l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as:
Two bodies of mass $4 \text{ kg}$ and $6 \text{ kg}$ are tied to the ends of a massless string. The string passes over a pulley, which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity ($g$) is: