List of top Mathematics Questions asked in CBSE CLASS XII

For two vectors $\vec a$ and $\vec b$
Assertion (A): $|\vec a\times \vec b|^2+(\vec a\cdot \vec b)^2=|\vec a|^2|\vec b|^2$
Reason (R): $|\vec a\times \vec b|=|\vec a||\vec b|\sin\theta$, where $\theta$ is the angle between them.

Assertion (A): A line can have direction cosines $\langle 1,1,1\rangle$.
Reason (R): $\cos\theta=1$ is possible for $\theta=0^\circ$.

If $e^{x+y}+y=3x$, then $\dfrac{dy}{dx}$ is

If \[ \begin{vmatrix} -1 & -2 & 5 \\ -2 & a & 4 \\ 0 & 4 & 2a \end{vmatrix} = -86 \] then the sum of all possible values of \( a \) is

For a square matrix $A$, $(3A)^{-1}$ is

If \[ A = \begin{bmatrix} \frac{1}{2}\cos x & -\sin x \\ \sin x & \frac{1}{2}\cos x \end{bmatrix} \] and \(A + A^T = I\), then the value of \(x \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\) is

If \[ A = \begin{bmatrix} 1 & a & b \\ -1 & 2 & c \\ 0 & 5 & 3 \end{bmatrix} \] is a symmetric matrix, then the value of \(3a + b + c\) is

If $A$ and $B$ are square matrices of same order, then which of the following statements is/are always true?
(i) $(A+B)(A-B)=A^2-B^2$
(ii) $AB=BA$
(iii) $(A+B)^2=A^2+AB+BA+B^2$
(iv) $AB=0 \Rightarrow A=0$ or $B=0$

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

For two events $A$ and $B$ such that $P(A)>0$ and $P(B)=1$, $P(A^c/B^c)$ is

In a linear programming problem, the linear function which has to be maximized or minimized is called

Direction cosines of line $x=y=1-z$ are

Vector of magnitude 3 making equal angles with $x$ and $y$ axes and perpendicular to $z$ axis is

If $|\vec a|=5$ and $-2\le \lambda \le 1$, then the sum of the greatest and the smallest value of $|\lambda \vec a|$ is

The integrating factor of the differential equation $2x\frac{dy}{dx}-y=3$ is

The general solution of the differential equation $xdy-ydx=0$ is

Which of the following expressions will give the area of region bounded by the curve $y=x^2$ and line $y=16$?

For $f(x)=x+\dfrac{1}{x}$ $(x\neq0)$

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

Let \[ A = \begin{pmatrix} 1 & 4 \\ -2 & 1 \end{pmatrix} \quad \text{and} \quad C = \begin{pmatrix} 3 & 4 & 2 \\ 12 & 16 & 8 \\ -6 & -8 & -4 \end{pmatrix}. \] Then, find the matrix $B$ if $AB = C$.

Find: \[ \int \frac{2x}{(x^2 + 3)(x^2 - 5)} \, dx \]

Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]