List of top Questions asked in CBSE CLASS XII

If $\begin{vmatrix} 3x & x+2 \\ 3(x-1) & x-2 \end{vmatrix} = \begin{vmatrix} 1 & 5 \\ 3 & 3 \end{vmatrix}$, then the value of $x$ is :

The value of $\sin^{-1}\left(\sin\frac{3\pi}{5}\right)$ is :

If $f(x) = \begin{cases} \dfrac{|x|}{x}, & x \neq 0 \\ 0, & x = 0 \end{cases}$, then which of the following statements is not correct ?

If $A = \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$ satisfies $A^{\prime} + A = I$, then the value of $\theta$ is :

Three students A, B and C go to a book-store to buy art books, story books and puzzle solving books. A buys one of each type of book for a total of ₹21. B buys 4 art books, 3 story books and 2 puzzle solving books for ₹60. C buys 6 art books, 2 story books and 3 puzzle solving books and pays ₹10 more than B. Use matrix method to find the cost of each type of book.

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 $.