List of top Questions asked in UP Board XII

The de Broglie wavelengths of a photon and a proton are \(\lambda_1\) and \(\lambda_2\) respectively. Both have same energy \(E\). If mass of proton is \(m\) and speed of light is \(C\), then prove that \(\dfrac{\lambda_1}{\lambda_2} = C\sqrt{\dfrac{2m}{E}}\).

Compute the electric potential energy of the system with the help of the figure given above. The square has side 1 cm with charges \(+1\ \mu C\) and \(+1\ \mu C\) on the two top corners and \(-1\ \mu C\) and \(-1\ \mu C\) on the two bottom corners.
OR
The capacitance of a parallel plate capacitor is 20 pF and distance between the plates is 4 mm. It is charged by a battery of 100 volt and then battery is removed. Now a dielectric slab (K = 4) and 2 mm thickness is placed in between the plates. Find out: (i) the final charge on each plate (ii) the potential difference between the plates.
What is the law of Malus? A plane polarized light of intensity 16 watt/m², is incident on a polaroid in such a way that the vibration of its electric vector makes an angle of 30° from the transmission axis of the polaroid. Find out the intensity of the transmitted light from the polaroid. Write down any one use of polaroid.

Find out from the given circuit shown above: (i) Impedance (ii) power factor (iii) phase difference between current and voltage. The series circuit has \(L = 10\ \text{H}\), \(R = 500\ \Omega\) and \(C = 20\ \mu F\), driven by an AC source \(V = [200\sin 100t]\ \text{Volt}\).
How a galvanometer is converted into an ammeter? The resistance of the coil of a galvanometer is 15 Ω and it gives full scale deflection by a current of 4 mA. How it can be converted into an ammeter in order to measure a current upto 6 A?

A rectangular glass slab ABCD of refractive index \(n_1\) is placed in a liquid of refractive index \(n_2\) (\(n_1 > n_2\)). A ray of light is incident at the surface AB of the slab as shown in the figure. Find out the maximum value of angle \(\alpha\), so that the ray comes out only from the other surface CD.
Work function of a metal surface is 3.2 eV. Find out the kinetic energy of the emitted photoelectrons in Joule, when a photon of 4.0 eV energy is incident on its surface.
What is the phenomenon of radioactivity? How many types are there of radioactive decay?
Explain the difference between conductors and semiconductors on the basis of energy bands in solids.
What will be the effect on the drift velocity of electrons, when the current in a copper wire is passed in a wire, twice of its radius (the same current being maintained)?
What is an equipotential surface?
What are the uses of microwaves?
What is meant by the optical center of a lens?
What are the charge carriers in p-type of semiconductors?
What is the difference between paramagnetic and diamagnetic substances?
Equivalent resistance \( R \) is obtained when \( n \) wires having the same length and same thickness of the same material are joined in parallel. The equivalent resistance on joining them in series will be:
Define and write the formula of mobility.
In which of the following spherical mirrors is the magnification of the image always less than 1?
Coulomb's repulsive force of \( F \) newton acts between two point charges of \( +3\,\mu C \) and \( +8\,\mu C \). If \( -5\,\mu C \) charge is given to both of them, then the force and its nature between them will be:
In the given nuclear reaction, particle W is: \[ {}_{2}^{4}\text{He} + {}_{Z}^{A}X \ \rightarrow\ {}_{Z+2}^{A+3}Y + W \]
A coil of one loop is formed by a wire of length \( L \), and thereafter a coil of 3 loops is formed by the same wire. If the current remains the same in both cases, then the ratio of the magnetic fields at the centre will be:
If the accelerating potential of a moving charged particle of \( \lambda \) de Broglie wavelength is increased by four times, then the de Broglie wavelength will be:
When an impurity is doped in a pure semiconductor, the conductivity of the semiconductor
How can p-type and n-type crystal from pure semiconductor be formed? Find the maximum wavelength of electromagnetic radiation which can create a hole-electron pair in germanium of a band-gap 0.65 eV.
OR
How is the conductivity of a metal and semiconductor changed with raising temperature? Calculate the conductivity of an n-type semiconductor from the following data: Density of conduction electrons = 8×1013 /cm3, Density of holes = 5×1012 /cm3, Mobility of conduction electrons = 2.3×104 cm2/V·s, Mobility of holes = 100 cm2/V·s.
Energy of the \(n^{th}\) state of a hydrogen atom is \(E_n=-\dfrac{13.6}{n^2}\ \text{eV}\). A hydrogen sample is prepared in a particular excited state A. Photons of energy \(2.55\ \text{eV}\) get absorbed by the sample to take some electrons to a particular further excited state B. Find the quantum numbers of states A and B.