List of top Mathematics Questions asked in CBSE CLASS XII

The number of arbitrary constants in the general solution of the differential equation dy/dx + y = 0 is:
The area (in sq. units) of the region bounded by the curve \( y = x \), x-axis, \( x = 0 \) and \( x = 2 \) is:
If the radius of a circle is increasing at the rate of 0.5 cm/s, then the rate of increase of its circumference is:
The greatest integer function defined by \( f(x) = [x] \), \( 1 < x < 3 \) is not differentiable at \( x = \):
For the function \( f(x) = x^3 \), \( x = 0 \) is a point of:
If X, Y and XY are matrices of order 2 × 3, m × n, and 2 × 5 respectively, then the number of elements in matrix Y is:
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 a unit vector in the direction of \( \overrightarrow{DA} \).
Find the measure of \( \angle VDA \).
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.
Let \( A = \mathbb{R} - \{5\} \) and \( B = \mathbb{R} - \{1\} \). Consider the function \( f : A \to B \), defined by: \[ f(x) = \frac{x - 3}{x - 5} \] Show that \( f \) is one-one and onto.
Sketch the graph of \( y = x|x| \) and hence find the area bounded by this curve, the X-axis, and the ordinates \( x = -2 \) and \( x = 2 \), using integration.
A biased die is twice as likely to show an even number as an odd number. If such a die is thrown twice, find the probability distribution of the number of sixes. Also, find the mean of the distribution.
A card from a well-shuffled deck of 52 playing cards is lost. From the remaining cards of the pack, a card is drawn at random and is found to be a King. Find the probability of the lost card being a King.
Solve the following linear programming problem graphically: Maximise \( Z = 2x + 3y \), subject to the constraints: \( x + y \leq 6, \, x \geq 2, \, y \geq 3, \, x \geq 0, \, y \geq 0. \)