List of practice Questions

A hollow insulated conduction sphere is given a positive charge of 10 μC. What will be the electric field at the centre of the sphere if its radius is 2 meters?
Two mercury drops (each of radius \( r \)) merge to form a bigger drop. The surface energy of the bigger drop is, if \( T \) is the surface tension, is
Resistances 1 \( \Omega \), 2 \( \Omega \), and 3 \( \Omega \) are connected to form a triangle. If a 1.5 V cell of negligible internal resistance is connected across the 3 \( \Omega \) resistor, the current flowing through this resistor will be
A current carrying coil is subjected to a uniform magnetic field. The coil will orient so that its plane becomes
The value of \( \tan(90^\circ - \theta) \) in the graph gives
A conducting circular loop of radius \( r \) carries a constant current \( i \). It is placed in a uniform magnetic field \( \vec{B} \) such that \( \vec{B} \) is perpendicular to the plane of the loop. The magnetic force acting on the loop is
A vessel of depth 2d cm is half-filled with a liquid of refractive index \( \mu_1 \) and the upper half with a liquid of refractive index \( \mu_2 \). The apparent depth of the vessel seen perpendicularly is
A smooth sphere of mass \( M \) moving with velocity \( u \) directly collides elastically with another sphere of mass \( m \) at rest. After collision, their final velocities are \( V \) and \( v \) respectively. The value of \( v \) is
Two capacitors \( C_1 \) and \( C_2 \) in a circuit are joined as shown in the figure. The potentials of points A and B are \( V_1 \) and \( V_2 \), respectively. Then the potential of point D will be
Light of wavelength 500 nm is incident on a metal with work function \( 2.28 \, \text{eV} \). The de Broglie wavelength of the emitted electron is:
Kerosene oil rises up in a wick of a lantern because of
The current in a coil of \( L = 40 \, \text{mH} \) is to be increased uniformly from 1 A to 11 A in 4 milli sec. The induced e.m.f. will be
If the kinetic energy of a moving particle is \( E \), then the de-Broglie wavelength is
Two bodies A and B having masses in the ratio of 3 : 1 possess the same kinetic energy. The ratio of linear momentum of B to A is
In which sequence the radioactive radiations are emitted in the following nuclear reaction? \[ Z^{X}A \rightarrow Z+1Y^{A} \rightarrow Z-1K^{A-4} \]
Which of the following does not support the wave nature of light?
Six identical conducting rods are joined as shown in the figure. Points A and D are maintained at 200\(^\circ C\) and 20\(^\circ C\) respectively. The temperature of junction B will be
A hydrogen atom is in ground state. Then to get six lines in emission spectrum, wavelength of incident radiation should be
A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 m/s. To give an initial upward acceleration of 20 m/s\(^2\), the amount of gas ejected per second to supply the needed thrust will be (Take \(g = 10 \, \text{m/s}^2\))
The power dissipated in the circuit shown in the figure is 30 Watts. The value of \( R \) is
Four boxes are shown below. The numbers within each box have a specific relationship. What number would replace the question mark?
If '' > 0$ for all $

Let \(f(x)=x+log_{e}​x−xlog_{e}​x,\text{ }x∈(0,∞)\).

  • Column 1 contains information about zeros of \(f(x)\), \(f'(x)\) and \(f''(x)\).
  • Column 2 contains information about the limiting behavior of \(f(x)\), \(f'(x)\) and \(f''(x)\) at infinity.
  • Column 3 contains information about increasing/decreasing nature of \(f(x)\) and \(f'(x)\).
Shown in the figure are circles of diameter 42 cm. What is the total length (in cm) of the path LRMONP as indicated by the red arrows? Assume \(\pi = \frac{22}{7}\).
A forest lies between two parts of a city. How many unique routes are there to go from the west side to point A in the east side without retracing any portion of the route?