List of top Mathematics Questions asked in CBSE CLASS XII

(b) In a village of 8000 people, 3000 go out of the village to work and 4000 are women. It is noted that 30% of women go out of the village to work. What is the probability that a randomly chosen individual is either a woman or a person working outside the village?
Let \( 2x + 5y - 1 = 0 \) and \( 3x + 2y - 7 = 0 \) represent the equations of two lines on which the ants are moving on the ground. Using matrix method, find a point common to the paths of the ants.
Let \( R \) be a relation defined on a set \( \mathbb{N} \) of natural numbers such that \( R = \{(x, y) : xy \text{ is a square of a natural number}, x, y \in \mathbb{N} \} \). Determine if the relation \( R \) is an equivalence relation.
Show that the function \( f : \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = 4x^3 - 5 \), \( \forall x \in \mathbb{R} \), is one-one and onto.
Assertion (A): The set of values of $\sec^{-1} \left( \frac{\sqrt{3}}{2} \right)$ is a null set.
Reason (R): $\sec^{-1}x$ is defined for $x \in \mathbb{R} - (-1, 1)$.
In a Linear Programming Problem, the objective function $Z = 5x + 4y$ needs to be maximised under constraints $3x + y \leq 6$, $x \leq 1$, $x \geq 0$, $y \geq 0$. Express the LPP on the graph and shade the feasible region, and mark the corner points.
(b) If $2x^2 - 5xy + y^3 = 76$, then find $\frac{dy}{dx}$.
(a) Differentiate $ \left( \frac{5x}{x^5} \right)$ with respect to $x$.
Assertion (A): $f(x) = \begin{cases} x \sin \frac{1}{x}, & x \neq 0 \\ 0, & x = 0 \end{cases}$ is continuous at $x = 0$.
Reason (R): When $x \to 0$, $\sin \frac{1}{x}$ is a finite value between -1 and 1.
If $P(A) = \frac{1}{7}$, $P(B) = \frac{5}{7}$ and $P(A \cap B) = \frac{4}{7}$, then $P(A | B)$ is:
A coin is tossed and a card is selected at random from a well shuffled pack of 52 playing cards. The probability of getting head on the coin and a face card from the pack is:
A student tries to tie ropes, parallel to each other from one end of the wall to the other. If one rope is along the vector $3\hat{i} + 15\hat{j} + 6\hat{k}$ and the other is along the vector $2\hat{i} + 10\hat{j} + \lambda \hat{k}$, then the value of $\lambda$ is:
$\int \frac{e^x}{\sqrt{4 - 2x}} dx$ is equal to:
If $|\mathbf{a} + \mathbf{b}| = |\mathbf{a} - \mathbf{b}|$ for any two vectors, then vectors $\mathbf{a}$ and $\mathbf{b}$ are:
$\int \frac{e^{\log x}}{e^{6 \log x} - e^{5 \log x}} dx$ is equal to:
If $f(x) = -2x^2$, then the correct statement is:
A spherical ball has a variable diameter $\frac{5}{2}(3x + 1)$. The rate of change of its volume w.r.t. $x$, when $x = 1$, is:
If $\begin{bmatrix} 2x-1 & 3x \\ 0 & y^2 - 1 \end{bmatrix}$ is a matrix, then the value of $(x - y)$ is:
If $f: \mathbb{R} \to \mathbb{R}$ is defined as $f(x) = 2x - \sin x$, then $f$ is:
If $f(x) = \begin{cases} ax + b, & x \leq 3 \\ 7, & 5<x \end{cases}$ is continuous in $\mathbb{R}$, then the values of $a$ and $b$ are:
The matrix $A = \begin{bmatrix} \sqrt{5} & 0 & 0 \\ 0 & \sqrt{2} & 0 \\ 0 & 0 & \sqrt{5} \end{bmatrix}$ is an:
Let $A$ be a square matrix of order 3. If $|A| = 5$, then $|adj A|$ is:
If $A$ and $B$ are two square matrices each of order 3 with $|A| = 3$ and $|B| = 5$, then $|2AB|$ is:

The given graph illustrates:

Domain of $f(x) = \cos^{-1} x + \sin x$ is: