List of top Questions asked in CBSE CLASS XII

A current flows through a cylindrical conductor of radius \( R \). The current density at a point in the conductor is \( j = \alpha r \) (along its axis), where \( \alpha \) is a constant and \( r \) is the distance from the axis of the conductor. The current flowing through the portion of the conductor from \( r = 0 \) to \( r = \frac{R}{2} \) is proportional to:
Assertion (A): EM waves do not require a medium for their propagation.
Reason (R): EM waves are transverse waves.
Write vector form of Biot–Savart law.

An ideal transformer is designed to convert 50 V into 250 V. It draws 200 W power from an AC source whose instantaneous voltage is given by \( v_i = 20 \sin(100\pi t) \, \text{V} \).

Find:

  • 1. RMS value of input current.
  • 2. Expression for instantaneous output voltage.
  • 3. Expression for instantaneous output current.
Two coils ‘1’ and ‘2’ are placed close to each other as shown in the figure. Find the direction of induced current in coil ‘1’ in each of the following situations, justifying your answers:
Two coils ‘1’ and ‘2’ are placed

(a) Coil ‘2’ is moving towards coil ‘1’.
(b) Coil ‘2’ is moving away from coil ‘1’.
(c) The resistance connected with coil ‘2’ is increased keeping both the coils stationary.
Two small solid metal balls A and B of radii \(R\) and \(2R\) having charge densities 2 and 3 respectively are kept far apart. Find the charge densities on A and B after they are connected by a conducting wire.
A cell of emf \( E \) and internal resistance \( r \) is connected to an external variable resistance \( R \). Plot a graph showing the variation of terminal voltage \( V \) of the cell as a function of current \( I \), supplied by the cell. Explain how the emf of the cell and its internal resistance can be found from it.
Current I (= 1 A) is passing through a copper rod (n = \(8.5 \times 10^{28} \, \text{m}^{-3}\)) of varying cross-sections as shown in the figure. The areas of cross-section at points A and B along its length are \(1.0 \times 10^{-7} \, \text{m}^2\) and \(2.0 \times 10^{-7} \, \text{m}^2\) respectively. Calculate:
Current I (= 1 A) is passing through a copper rod
(I) the ratio of electric fields at points A and B.
(II) the drift velocity of free electrons at point B.
If \( R_s \) and \( R_p \) are the equivalent resistances of \( n \) resistors, each of value \( R \), in series and parallel combinations respectively, then the value of \( (R_s - R_p) \) is:
Diksha Ltd. invited applications for issuing 1,00,000 equity shares of ₹ 10 each at a premium of 10%. The whole amount was payable on application. Applications were received for 3,00,000 equity shares. The company decided to allot the shares on pro-rata basis to all the applicants. The amount refunded by the company was:
Germanium crystal is doped at room temperature with a minute quantity of boron. The charge carriers in the doped semiconductor will be:
A deuteron contains a proton and a neutron and has a mass of 2.013553 u. Calculate the mass defect for it in u and its energy equivalence in MeV.
Given:
\( m_p = 1.007277 \) u, \( m_n = 1.008665 \) u, \( 1 \) u = \( 931.5 \) MeV/\( c^2 \).
_____ are the colours, that represent the four regional confederation in the Deaflympic logo.
State Kirchhoff’s laws. Apply these laws to find the values of current flowing in the three branches of the given circuit.
Kirchhoff’s laws.
A current of 5 A is passing along +X direction through a wire lying along X-axis. Find the magnetic field \( \vec{B} \) at a point \( \vec{r} = (3 \hat{i} + 4 \hat{j}) \, \text{m} \) due to 1 cm element of the wire, centered at the origin.
The frequency of a photon of energy 1.326eV is:
The kinetic energy of an alpha particle is four times the kinetic energy of a proton. The ratio \( \left( \frac{\lambda_\alpha}{\lambda_p} \right) \) of de Broglie wavelengths associated with them will be:
Using the mirror equation and the formula of magnification, deduce that “the virtual image produced by a convex mirror is always diminished in size and is located between the pole and the focus.”
Define the term, ‘distance of closest approach’. A proton of 3.95 MeV energy approaches a target nucleus \( Z = 79 \) in head-on position. Calculate its distance of closest approach.
Calculate the amount of Opening Trade Receivables and Closing Trade Receivables from the following information:
Trade Receivables Turnover Ratio = 5 times
Cost of Revenue from Operations = ₹ 8,00,000
Gross Profit Ratio = 20%
Closing Trade Receivables were ₹ 40,000 more than Opening
Cash Sales = \( \frac{1}{4} \) of Credit Sales
Answer the following giving reasons:
(a) The maximum kinetic energy of the photoelectrons is independent of the intensity of incident radiation.
(b) Photoelectric current increases with the increase in the intensity of the incident radiation.
(c) The stopping potential \( V_0 \) varies linearly with the frequency \( \nu \) of the incident radiation for a given photosensitive surface.
The mass numbers of two nuclei A and B are 27 and 64 respectively. The ratio of their radii \( \left(\frac{r_A}{r_B}\right) \) will be:
Ajanta Ltd. purchased machinery worth Rs 36,00,000 from Sujata Ltd. Ajanta Ltd. paid half the amount to Sujata Ltd. through a bank draft and the balance by issuing 8 debentures of Rs 100 each at a discount of 10.
Pass the necessary journal entries in the books of Ajanta Ltd. for the above transactions.

How do the stories ‘The Last Lesson’ by Alphonse Daudet and ‘Lost Spring’ by Anees Jung illustrate the impact of socio-political factors on education?

A circular coil of wire having 200 turns, each radius 4.0 cm is placed in a horizontal plane. It carries a current of 0.40 A in the clockwise direction. Find the magnitude and direction of the magnetic field at the center of the coil.