List of top Questions asked in CBSE CLASS XII

The phase difference between electric field \( \vec{E} \) and magnetic field \( \vec{B} \) in an electromagnetic wave propagating along the z-axis is:
Figure shows the variation of inductive reactance \( X_L \) of two ideal inductors of inductance \( L_1 \) and \( L_2 \) with angular frequency \( \omega \). The value of \( \frac{L_1}{L_2} \) is: 
variation of inductive reactance
A circular loop A of radius \( R \) carries a current \( I \). Another circular loop B of radius \( r = \frac{R}{20} \) is placed concentrically in the plane of A. The magnetic flux linked with loop B is proportional to:
A galvanometer of resistance 100 \( \Omega \) is converted into an ammeter of range (0 – 1 A) using a resistance of 0.1 \( \Omega \). The ammeter will show full-scale deflection for a current of about:
The magnetic susceptibility for a diamagnetic material is:
A straight wire is kept horizontally along the east-west direction. If a steady current flows in the wire from east to west, the magnetic field at a point above the wire will point towards:
The radius \( r_n \) of the \( n^{th} \) orbit in the Bohr model of the hydrogen atom varies with \( n \) as:
The quantum nature of light explains the observations on the photoelectric effect as:
Two charges \(+q\) each are kept \(2a\) distance apart. A third charge \(-2q\) is placed midway between them. The potential energy of the system is:

Fit a straight-line trend by the method of least squares for the following data:

\[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \textbf{Year} & 2004 & 2005 & 2006 & 2007 & 2008 & 2009 & 2010 \\ \hline \textbf{Profit (₹ 000)} & 114 & 130 & 126 & 144 & 138 & 156 & 164 \\ \hline \end{array} \]
Tabulate the trend values of the years and compute the expected sales trend for the year 2002.
Determine the equation of the straight-line trend.
If \( R_1 \) is the feasible region, then find the maximum value of the objective function \( z = 5x + 2y \).
If \( R_2 \) is the feasible region, then what are the other two non-trivial constraints?
If \( R_1 \) is the feasible region, then what are the other two non-trivial constraints?
What are the two trivial constraints?
Determine the values of \( x \) and \( y \).
Find the inverse of matrix \( A \).
Write the system of linear equations, obtained in (i) above, in matrix form \( AX = B \).
Write the system of linear equations in \( x \) and \( y \) formed from the given situation.
A river near a small town floods and overflows twice in every 10 years on an average. Assuming that the Poisson distribution is appropriate, what is the mean expectation? Also, calculate the probability of 3 or less overflows and floods in a 10-year interval.
[Given \( e^{-2} = 0.13534 \)]
Determine the probability that the student studied for at most 2 hours.
Determine the probability that the student studied for at least 2 hours.
Find the value of \( k \).
Find the intervals in which the following function \( f(x) \) is strictly increasing or strictly decreasing: \[ f(x) = 20 - 9x + 6x^2 - x^3. \]