List of top Questions asked in CBSE CLASS XII

Silicon is doped with a pentavalent element. The energy required to set the additional electron free is about:
Consider a solenoid of length \( l \) and area of cross-section \( A \) with a fixed number of turns. The self-inductance of the solenoid will increase if:
Which one of the following has the highest frequency?
A proton and an alpha particle having equal velocities approach a target nucleus. They come momentarily to rest and then reverse their directions. The ratio of the distance of closest approach of the proton to that of the alpha particle will be:
The current in a coil of \(15 \, mH}\) increases uniformly from zero to \(4 \, A}\) in \(0.004 \, s}\). Calculate the electromotive force (emf) induced in the coil:
A proton is taken from point P1 to point P2, both located in an electric field. The potentials at points P1 and P2 are -5 V and +5 V respectively. Assuming that kinetic energies of the proton at points P1 and P2 are zero, the work done on the proton is:
A circular loop of wire, carrying a current 'I' is lying in the xy-plane with its centre coinciding with the origin. It is subjected to a uniform magnetic field pointing along the +z-axis. The loop will:
A current carrying circular loop of magnetic moment \( \vec{M} \) is suspended in a vertical plane in an external magnetic field \( \vec{B} \) such that its plane is normal to \( \vec{B} \). The work done in rotating this loop by 45° about an axis perpendicular to \( \vec{B} \) is closest to:
Consider a group of charges \( q_1, q_2, q_3, \ldots \) such that \( \sum q \neq 0 \). Then equipotentials at a large distance, due to this group are approximately:
Consider a neutron (mass $m$) of kinetic energy $E$ and a photon of the same energy. Let $\lambda_n$ and $\lambda_p$ be the de Broglie wavelength of the neutron and the wavelength of the photon, respectively. Obtain an expression for $\frac{\lambda_n{\lambda_p}$.}
Which of the following quantity/quantities remains same in primary and secondary coils of an ideal transformer? Current, Voltage, Power, Magnetic flux
Find the probability that exactly two of them are selected.
Find the probability that exactly one of them is selected.
Find \( P(G \cap \overline{H}) \), where \( G \) is the event of Jaspreet's selection and \( \overline{H} \) denotes the event that Rohit is not selected.
What is the probability that at least one of them is selected?
Find the measure of \( \angle VDA \).
Find a unit vector in the direction of \( \overrightarrow{DA} \).
Find a unit vector in the direction of \( \overrightarrow{DA} \).
How far is the star \( V \) from star \( A \)?
What rebate in price of the calculator should the store give to maximise the revenue?
Determine the number of units (\( x \)) that should be sold to maximise the revenue \( R(x) = x \cdot p(x) \). Also verify the result.
If the lines \[ \frac{x - 1}{-3} = \frac{y - 2}{2k} = \frac{z - 3}{2} \] and \[ \frac{x - 1}{3k} = \frac{y - 1}{1} = \frac{z - 6}{-7} \] are perpendicular to each other, find the value of \( k \) and hence write the vector equation of a line perpendicular to these two lines passing through the point \( (3, -4, 7) \).
Find the distance between the line \[ \frac{x}{2} = \frac{2}{y - 6} = \frac{1}{-z - 1} \] and another line parallel to it passing through the point \( (4, 0, -5) \).
Given matrix:
Let \[ A = \begin{bmatrix} 2 & 1 & -3 \\ 3 & 2 & 1 \\ 1 & 2 & -1 \end{bmatrix} \] Find \( A^{-1} \) and hence solve the following system of equations:

System of equations:
\[ 2x + y - 3z = 13, \quad 3x + 2y + z = 4, \quad x + 2y - z = 8 \]
Check whether the relation \( S \) in the set of real numbers \( \mathbb{R} \), defined by:

\[ S = \{(a, b) \mid a - b + \sqrt{2} \text{ is an irrational number} \} \] is reflexive, symmetric, or transitive.