List of top Mathematics Questions asked in CBSE CLASS XII

The side of an equilateral triangle is increasing at the rate of 3 cm/s. At what rate is its area increasing when the side of the triangle is 15 cm?
The matrix \[ \begin{pmatrix} 0 & 1 & -2 \\ -1 & 0 & -7 \\ 2 & 7 & 0 \end{pmatrix} \] is a :
Amongst all pairs of positive integers with product as 289, find which of the two numbers add up to the least.
Let $f(x) = |x|$, $x \in \mathbb{R}$. Then, which of the following statements is incorrect?
Domain of $f(x) = \cos^{-1} x + \sin x$ is:
If $A$ and $B$ are two square matrices each of order 3 with $|A| = 3$ and $|B| = 5$, then $|2AB|$ is:
The values of $\lambda$ so that $f(x) = \sin x - \cos x - \lambda x + C$ decreases for all real values of $x$ are :
Using integration, find the area of the region bounded by the line \[ y = 5x + 2, \] the \( x \)-axis, and the ordinates \( x = -2 \) and \( x = 2 \).
A vector \( \mathbf{a} \) makes equal angles with all the three axes. If the magnitude of the vector is \( 5\sqrt{3} \) units, then find \( \mathbf{a} \).
If \[ \begin{bmatrix} 2x-1 & 3x \\ 0 & y^2-1 \end{bmatrix} = \begin{bmatrix} x+3 & 12 \\ 0 & 35 \end{bmatrix} \] then the value of \( (x - y) \) is :
Let $A$ be a square matrix of order 3. If $|A| = 5$, then $|adj A|$ is:
Find a point \( P \) on the line \( \frac{x + 5}{1} = \frac{y + 3}{4} = \frac{z - 6}{-9} \) such that its distance from point \( Q(2, 4, -1) \) is 7 units. Also, find the equation of the line joining \( P \) and \( Q \).
Find the distance of the point $(-1, -5, -10)$ from the point of intersection of the lines \[ \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}, \quad \frac{x - 4}{5} = \frac{y - 1}{2} = z. \]
Find the angle at which the given lines are inclined to each other: \[ l_1: \frac{x - 5}{2} = \frac{y + 3}{1} = \frac{z - 1}{-3} \] \[ l_2: \frac{x}{3} = \frac{y - 1}{2} = \frac{z + 5}{-1} \]
Solve the differential equation: \[ x^2y \, dx - (x^3 + y^3) \, dy = 0. \]
If P is a point on the line segment joining $(3, 6, -1)$ and $(6, 2, -2)$ and the $y$-coordinate of P is 4, then its $z$-coordinate is :

The given graph illustrates:

If \( \sqrt{1 - x^2} + \sqrt{1 - y^2} = a(x - y) \), then prove that \( \frac{dy}{dx} = \frac{\sqrt{1 - y^2}}{\sqrt{1 - x^2}} \).
If \[ \left| \frac{2x}{5} \right| = \left| \frac{6 - 5}{4} \right|, \quad \text{then the value of } x \text{ is:} \]
Solve the following Linear Programming Problem using graphical method : Maximize \( Z = 100x + 50y \) subject to the constraints \[ 3x + y \leq 600, \quad x + y \leq 300, \quad y \leq x + 200, \quad x \geq 0, \quad y \geq 0. \]
The integrating factor of the differential equation \( \frac{dy}{dx} + y = \frac{1 + y}{x} \) is:

For a Linear Programming Problem, find min \( Z = 5x + 3y \) (where \( Z \) is the objective function) for the feasible region shaded in the given figure.

A shop selling electronic items sells smartphones of only three reputed companies A, B, and C because chances of their manufacturing a defective smartphone are only 5%, 4%, and 2% respectively. In his inventory, he has 25% smartphones from company A, 35% smartphones from company B, and 40% smartphones from company C.
A person buys a smartphone from this shop

(ii) What is the probability that this defective smartphone was manufactured by company B?

If vector \( \mathbf{a} = 3 \hat{i} + 2 \hat{j} - \hat{k} \) \text{ and } \( \mathbf{b} = \hat{i} - \hat{j} + \hat{k} \),  then which of the following is correct?

(a) Find the point Q on the line \( \frac{2x + 4}{6} = \frac{y + 1}{2} = \frac{-2z + 6}{-4} \) at a distance of \( \frac{\sqrt{5}}{2} \) from the point \( P(1, 2, 3) \).