List of top Questions asked in UP Board XII

Show the position of focus (f) in ray diagram for convex mirror. At what distance from a convex mirror of focal length 2.0 m should a boy stand so that his image has a height equal to half the original height?
OR
What is wavefront? Explain the refraction of waves with the help of Huygens' principle.

Option 1: What is Gauss's law? The figure shows a cylinder placed in an electric field \(\vec{E}=100\,\hat{i}\ \text{N/C}\). \(\vec{E}\) is positive when \(x>0\) and negative when \(x<0\). Length of the cylinder is \(30\ \text{cm}\) and radius of each plane surface is \(3.5\ \text{cm}\); its centre is at O. Find the electric fluxes \(\phi_1,\ \phi_2\) and \(\phi_3\) linked with each plane and the curved surface respectively. What will be the net charge inside the cylinder?
OR
Option 2: Obtain the formula for the capacitance of a parallel plate capacitor when a dielectric medium is partially filled in between its plates.

Option 1: With the help of the given figure, prove that the magnetic field produced at point P is \(B=\dfrac{\mu_0 i}{2d}\left[1+\dfrac{2}{\pi}\right]\). (The wire is hairpin-shaped: a semicircular arc joined to two long straight parallel segments carrying current \(i\); P is at the centre of the arc and the straight segments are a distance \(d\) apart.)
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Option 2: What is a radial magnetic field? Explain the working of a moving coil galvanometer with a suitable diagram. How can a galvanometer be converted into an ammeter and a voltmeter?

In the figure, the plot of stopping potential versus frequency of light used in an experiment of the photoelectric effect is shown. Find the ratio \( h/e \) and the work function.
(From the graph: the line meets the frequency axis at \( \nu_0 = 1\times10^{15}\ \text{Hz} \), and the stopping potential is \( V = 1.656\ \text{V} \) at \( \nu = 5\times10^{15}\ \text{Hz} \).)
Write the characteristics of nuclear force. How is it different from gravitational and electric (electrostatic) forces?
Explain displacement current and write the formula related to Ampere-Maxwell's law.
Explain total internal reflection. Discuss the working of an optical fibre.
Draw the ray diagram of a compound microscope. Find the expression for its magnifying power.
The energy of a photon is 10 eV. Determine (i) the dynamic mass of the photon, (ii) the frequency of the photon.
(Given: \( h = 6.6\times10^{-34}\ \text{J s} \), \( c = 3\times10^{8}\ \text{m/s} \), \( 1\ \text{eV} = 1.6\times10^{-19}\ \text{J} \).)
In an L-C-R circuit, the inductive reactance of a coil is 400 Ω and the capacitive reactance of a condenser is 100 Ω and \( R = 400\ \Omega \). Find the power factor of the circuit.
What is relaxation time? Find the equation of the relation between drift velocity and relaxation time.

Find the current supplied by the battery in the network shown in the figure. Also calculate the terminal voltage across the cell and the charge on the capacitor.
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What do you mean by electromotive force (EMF) of a cell? In the circuit shown, calculate the terminal voltage of the cell C. The battery B is of negligible internal resistance.
Discuss the working method of a half-wave rectifier using a p-n junction diode.
A circular coil of radius 2.0 cm carries a current of 1.0 A. If the coil has 100 turns, find the intensity of magnetic field at the centre of the coil.

Figure shows a rectangular loop being pulled out of a magnetic field \( B \) with a velocity \( v \) by applying an external force \( F \). Find the amount of magnetic force induced on the loop and show its direction.
Amplitude of intensity of magnetic field of an electromagnetic wave in vacuum is 500 nT. What will be the amplitude of the intensity of electric field of the wave?
Energy of hydrogen atom in ground state is &minus;13&middot;6 eV. What will be the kinetic energy and the potential energy of the electron in the state?
Draw (i &ndash; δ) curve for a triangular prism and show the angle of minimum deviation.
Prove that the energy density inside a charged capacitor is \( \tfrac{1}{2}\varepsilon_0 E^2 \).
Find out equivalent energy of 1&middot;0 gm of a substance.
The unit of \(\dfrac{1}{\mu_0 \varepsilon_0}\) is:
A thin transparent sheet is placed in front of one slit of a Young's double slit. The fringe width will:
Find out the magnetic moment of a rectangular coil of size 20 cm × 10 cm having 10 A current.
Write the unit of self-inductance.
Two resistors \(R\) and \(2R\) are connected in parallel in an electric circuit. The thermal energies developed in \(R\) and \(2R\) are in the ratio: