List of top Mathematics Questions asked in CBSE CLASS XII

Sketch the curve $ \{(x, y) : 100x^2 + 25y^2 = 2500\} $ and find the area of the region enclosed by it, using integration.

If matrix $ A = \begin{bmatrix} -p & q \\ r & p \end{bmatrix} $ is such that $ A^2 = I $, then :

The probability that it will rain tomorrow in cities A, B and C is $60\%$, $70\%$ and $80\%$ respectively. The probability that it will rain tomorrow in at least one of the cities is:

Find:
Let $A=[a_{ij}]$ be a $2\times2$ matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix $A'$.

If $A = \begin{bmatrix} 3 & 2 & 0 \\ 1 & 4 & 0 \\ 0 & 0 & 5 \end{bmatrix}$, then compute $A^2 - 7A + 10 I$.

The principal value of \[ \sec^{-1}(\sqrt{2})+2\operatorname{cosec}^{-1}(-\sqrt{2}) \] is:

If $A = [a_{ij}]$ is a $2 \times 2$ matrix whose elements are given by $a_{ij} = \frac{|i - 3j|}{2}$, then $A'$ is :

If \[ A(\operatorname{adj}A)= \begin{bmatrix} 2026 & 0 & 0\\ 0 & 2026 & 0\\ 0 & 0 & 2026 \end{bmatrix}, \] then the value of \[ \left|\operatorname{adj}A\right| \] is equal to :

If a matrix B is such that $ B \begin{bmatrix} 1 & 2 & 3 \end{bmatrix} = \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 1 \\ 2 & 0 & 1 \end{bmatrix} $, then the order of matrix B is :

$ \int \frac{dx}{\sqrt{e^{-2x} - 1}} $ is equal to :

Show that $f : \mathbb{R} \to \mathbb{R}$ defined as $f(x) = \frac{x}{\sqrt{1+x^2}}$ is one-one but not onto.

Direction ratios of lines $l_1$ and $l_2$ are $\langle 12, -3, 9 \rangle$ and $\langle 4, q, -p \rangle$ respectively. The values of $p$ and $q$ for which $l_1$ and $l_2$ are parallel are respectively :

If $\begin{bmatrix} 4 \\ 1 \\ 3 \end{bmatrix} A = \begin{bmatrix} -4 & 8 & 4 \\ -1 & 2 & 1 \\ -3 & 6 & 3 \end{bmatrix}$, then order of $A$ must be :

The general solution of the differential equation: $ x^2 dy + y^2 dx = 0 $ is

A relation $ R $ on set $ A = \{1, 2, 3\} $ is defined as $ R = \{(1, 3), (3, 3), (1, 1), (2, 2), (3, 1)\} $ is

$\displaystyle \int \frac{dx}{1+\cos x}$ is equal to

Determine the interval(s) in which $f(x)=5x^{3/2}-3x^{5/2}$, $x>0$ is increasing.

Evaluate $\sin\left[\cos^{-1}\left(\cos\dfrac{7\pi}{6}\right)\right]$.

The value of $\int_{-5}^{-1} \frac{1}{x}\,dx$ is equal to :

If $ A = \begin{bmatrix} 2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0 \end{bmatrix} $, then compute $ A^{2} - 5A + 4I $.

Find the length of the perpendicular drawn from the point $ P(1, 2, 3) $ to the line $ \frac{x - 6}{3} = \frac{y - 7}{2} = \frac{z - 7}{-2} $. Also, find the equation of the perpendicular line joining $ P $ and the foot of the perpendicular.

The probability that a particular item is available in three shops A, B and C is $ \dfrac{4}{5}, \dfrac{3}{4} $ and $ \dfrac{2}{3} $ respectively. If a person visits all the three shops to buy the item, then what is the probability that it will be available in at least one of the shops ?

Using integration, find the area of the region bounded by $ y = 5x + 4 $, $ y = 0 $, $ x = -1 $ and $ x = 1 $.

Solve the following Linear Programming Problem graphically :

Maximize $ Z = 20x + 10y $

subject to constraints

$ x + 2y \leq 28 $

$ 3x + y \leq 24 $

$ x \geq 2 $

$ x, y \geq 0 $

If in a parallelogram PQRS, $ \overrightarrow{PQ} = 2\hat{i} + 3\hat{j} + \hat{k} $ and $ \overrightarrow{QR} = \hat{i} - 2\hat{j} + \hat{k} $, then find the unit vectors parallel to the diagonals $ \overrightarrow{PR} $ and $ \overrightarrow{SQ} $.