List of top Mathematics Questions asked in CBSE CLASS XII

Determine if the lines $\mathbf{r}_1 = ( \hat{i} + \hat{j} - \hat{k} ) + \lambda ( 3\hat{i} - \hat{j} )$ and $\mathbf{r}_2 = ( 4\hat{i} - \hat{k} ) + \mu ( 2\hat{i} + 3\hat{k} )$ intersect with each other.
Vector $\mathbf{r}$ is inclined at equal angles to the three axes $x$, $y$, and $z$. If the magnitude of $\mathbf{r}$ is $5\sqrt{3}$ units, then find $\mathbf{r}$.
If $\mathbf{a}$ and $\mathbf{b}$ are position vectors of point A and point B, respectively, find the position vector of point C on $\overrightarrow{BA}$ such that $BC = 3BA$.
Determine the values of $x$ for which the function $f(x) = \frac{x-4}{x+1}$ is an increasing or a decreasing function.
If $(x)^y = (y)^x$, then find $\frac{dy}{dx}$.
(a) Differentiate $\sqrt{e^{\sqrt{2x}}}$ with respect to $e^{\sqrt{2x}}$ for $x>0$.
Assertion (A): Let $f(x) = e^x$ and $g(x) = \log x$. Then $(f + g)(x) = e^x + \log x$ where the domain of $(f + g)$ is $\mathbb{R}$.
Reason (R): $\text{Dom}(f + g) = \text{Dom}(f) \cap \text{Dom}(g)$.
Find the domain of the function $f(x) = \sin^{-1}(-x^2)$.
A box has 4 green, 8 blue, and 3 red pens. A student picks up a pen at random, checks its color and replaces it in the box. He repeats this process 3 times. The probability that at least one pen picked was red is:
Assertion (A): If $| \mathbf{a} \times \mathbf{b} |^2 + | \mathbf{a} \cdot \mathbf{b} |^2 = 256$ and $| \mathbf{b} | = 8$, then $| \mathbf{a} | = 2$.
Reason (R): $\sin^2 \theta + \cos^2 \theta = 1$ and $| \mathbf{a} \times \mathbf{b} | = | \mathbf{a} | | \mathbf{b} | \sin \theta$ and $ \mathbf{a} \cdot \mathbf{b} = | \mathbf{a} | | \mathbf{b} | \cos \theta$.
The area of the region bounded by the curve $y^2 = x$ between $x = 0$ and $x = 1$ is:

For a Linear Programming Problem (LPP), the given objective function is $Z = x + 2y$. The feasible region PQRS determined by the set of constraints is shown as a shaded region in the graph.

The point $P = ( \frac{3}{13}, \frac{24}{13} )$, $Q = ( \frac{3}{15}, \frac{15}{4} )$, $R = ( \frac{7}{3}, \frac{3}{2} )$, $S = ( \frac{18}{7}, \frac{7}{7} )$. Which of the following statements is correct?

The solution for the differential equation $\log \left( \frac{dy}{dx} \right) = 3x + 4y$ is:

In a Linear Programming Problem (LPP), the objective function $Z = 2x + 5y$ is to be maximized under the following constraints:

\[ x + y \leq 4, \quad 3x + 3y \geq 18, \quad x, y \geq 0. \] Study the graph and select the correct option.

\[ \int \frac{x + 5}{(x + 6)^2} e^x \, dx \] is equal to:
Let $f'(x) = 3(x^2 + 2x) - \frac{4}{x^3} + 5$, $f(1) = 0$. Then, $f(x)$ is:
The order and degree of the following differential equation are, respectively: \[ \frac{d^4y}{dx^4} + 2 \frac{d^2y}{dx^2} + y^2 = 0. \]
If $y = a \cos(\log x) + b \sin(\log x)$, then $x^2y'' + xy'1$ is:
Let $f(x) = |x|$, $x \in \mathbb{R}$. Then, which of the following statements is incorrect?
If $\tan^{-1} (x^2 - y^2) = a$, where $a$ is a constant, then $\frac{dy}{dx}$ is:
\[ \sec^{-1} \left( -\sqrt{2} \right) - \tan^{-1} \left( \frac{1}{\sqrt{3}} \right) \] is equal to:
If \[ f(x) = \begin{cases} \frac{\log(1 + ax) + \log(1 - bx)}{x}, & \text{for } x \neq 0 \\ k, & \text{for } x = 0 \end{cases} \] is continuous at $x = 0$, then the value of $k$ is:

The following graph is a combination of:

Sum of two skew-symmetric matrices of the same order is always a/an:
If \[ A = \begin{pmatrix} -1 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 5 \end{pmatrix} \] then $A$ is a/an: