List of top Mathematics Questions asked in CBSE CLASS XII

If \[ A = \begin{bmatrix} 1 & 2 & 3 \\ -4 & 3 & 7 \end{bmatrix}, \quad B = \begin{bmatrix} 4 & 3 \\ -1 & 2 \\ 0 & 5 \end{bmatrix}, \] then the correct statement is:

If \( P(A \cup B) = 0.9 \) and} \( P(A \cap B) = 0.4 \), then \( P(A) + P(B) \) is:

Find: \[ I = \int (\sqrt{\tan x} + \sqrt{\cot x}) dx. \]

Find:$\displaystyle \int \dfrac{dx}{\sin x + \sin 2x}$

Evaluate:
$\displaystyle \int_{0}^{3} x \cos(\pi x) \, dx$

For the given graph of a Linear Programming
For the given graph of a Linear Programming Problem, write all the constraints satisfying the given feasible region.
Check the differentiability of the function f(x) = |x| at x = 0.
Find $ k $ so that the function \[ f(x) = \begin{cases} \frac{x^2 - 2x - 3}{x + 1} & \text{if } x \neq -1 \\ k & \text{if } x = -1 \end{cases} \] is continuous at $ x = -1 $.
A cylindrical water container has developed a leak at the bottom. The water is leaking at the rate of 5 cm$^3$/s from the leak. If the radius of the container is 15 cm, find the rate at which the height of water is decreasing inside the container, when the height of water is 2 meters.
Find: \[ \int \frac{\sqrt{x}}{1 + \sqrt{x^{3/2}}} \, dx \]
If $ \int e^{-3 \log x} \, dx = f(x) + C $, then $ f(x) $ is:
The solution of the differential equation $ \frac{dy}{dx} = -\frac{x}{y} $ represents family of:
If \[ A = \begin{bmatrix} 2 & -2 \\ -2 & 2 \end{bmatrix} \quad \text{and} \quad A^2 = kA, \quad \text{then find the value of k.} \]
Domain of $ \sin^{-1}(2x^2 - 3) $ is:
If A and B are invertible matrices of order $3 \times 3$ such that $\text{det} = 4$ and $\text{det}([AB]^{-1}) = \frac{1}{20}$, then $\text{det}$ is equal to:
The coordinates of the foot of the perpendicular drawn from the point $A(-2, 3, 5)$ on the y-axis are:
Evaluate: \[ I = \int_0^{\frac{\pi}{4}} \frac{\sin x \cos x}{\cos^4 x + \sin^4 x} \, dx \]
Find: \[ J = \int \frac{\sqrt{x^2 + 1} \left[ \log(x^2 + 1) - 2 \log x \right]}{x^2} \, dx \]
Solve the following Linear Programming Problem graphically:
Minimise \( Z = 3x + 5y \)
subject to the constraints: \[ x + 2y \geq 10, \quad x + y \geq 6, \quad 3x + y \geq 8, \quad x, y \geq 0. \]
Find the local maxima and local minima of the function \[ f(x) = \frac{8}{3} x^3 - 12x^2 + 18x + 5. \]
Consider the experiment of tossing a coin. If the coin shows head, toss it again; but if it shows a tail, then throw a die. Find the conditional probability of the event A: `the die shows a number greater than 3' given that B: `there is at least one tail'.
Find: \[ \int \frac{\cos x \, dx}{1 + \cos x + \sin x}. \]

Probability Distribution of Random Variable X

X1232λ3λ4λ
P(X)\(\frac{11}{30}\)\(\frac{1}{15}\)\(\frac{10}{30}\)\(\frac{3\lambda}{10}\)\(\frac{1}{15}\)\(\frac{1}{10}\)

(i) Calculate \( \lambda \), if \( E(X) = 3.2 \)
(ii) Find P(X > 1).

Using matrices and determinants, find the value(s) of $k$ for which the pair of equations \[ 5x - ky = 2; \quad 7x - 5y = 3 \] has a unique solution.
The integrating factor of the differential equation \[ \frac{dy}{dx} + y \tan x - \sec x = 0 \quad \text{is:} \]