List of top Mathematics Questions asked in CBSE CLASS XII

Edge of a variable cube increases at the rate of 5 cm/s. The rate at which the surface area of the cube increases when the edge is 2 cm long is :
If $f(x) = 3x - b$, $x>1$ ; $f(x) = 11$, $x = 1$ ; $f(x) = -3x - 2b$, $x<1$ is continuous at $x = 1$, then the values of $a$ and $b$ are :
Show that the derivative of \( \tan^{-1} (\sec x + \tan x) \) with respect to \( x \) is equal to \( \frac{1}{2} \) for \( \left( -\frac{\pi}{2}<x<\frac{\pi}{2} \right) \).
Find the dimensions of a rectangle of perimeter 12 cm which will generate maximum volume when swept along a circular rotation keeping the shorter side fixed as the axis.
Solve the differential equation \((x^2 + y^2) \, dx + xy \, dy = 0\), \(y(1) = 1\).
The matrix $A = \begin{pmatrix} \sqrt{3} & 0 & 0 \\ 0 & \sqrt{2} & 0 \\ 0 & 0 & \sqrt{5} \end{pmatrix}$ is a/an :
(a) Find \[ \int \frac{x}{(x - 1)(x^2 + 4)} \, dx \]
If \[ \begin{bmatrix} 3 & -1 \\ 0 & 1 \\ 2 & -3 \end{bmatrix} A = \begin{bmatrix} 2 & -5 \\ -17 \end{bmatrix} \] then find matrix \( A \).
In a Linear Programming Program (LPP) for objective function \( Z = 14x - 10y \) subject to the constraints: \[ x + y \leq 8, \quad 3x - 2y \geq -6, \quad x, y \geq 0 \] shade the feasible region and mark the corner points in a neatly drawn graph.
\[ \int \frac{e^{9 \log x} - e^{8 \log x}}{e^{6 \log x}} \, dx \] is equal to :
If \( f(x) = -2x^8 \), then the correct statement is :
\[ \int \frac{a^x}{\sqrt{1 - a^2 x}} \, dx \] is equal to :
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 \( \hat{i} + 15 \hat{j} + 6 \hat{k} \) and the other is along the vector \( 2 \hat{i} + 10 \hat{j} + 6 \hat{k} \), then the value of \( \lambda \) is :
If \( R \) be a relation defined as \( a \, R \, b \) iff \( |a - b|>0 \), \( a, b \in \mathbb{R} \), then \( R \) is :
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 :

Show that the line passing through the points A $(0, -1, -1)$ and B $(4, 5, 1)$ intersects the line joining points C $(3, 9, 4)$ and D $(-4, 4, 4)$.

Using integration, find the area of the ellipse \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \quad \text{bounded between the lines} \quad x = -\frac{a}{2} \quad \text{to} \quad x = \frac{a}{2}. \]
Bag I contains 4 white and 5 black balls. Bag II contains 6 white and 7 black balls. A ball drawn randomly from Bag I is transferred to Bag II and then a ball is drawn randomly from Bag II. Find the probability that the ball drawn is white.
Find the value of $x$, if \[ \begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{bmatrix} \begin{bmatrix} 1 \\ x \\ 2 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix} \]
Let $|\vec{a}| = 5 \text{ and } -2 \leq \lambda \leq 1$. Then, the range of $|\lambda \vec{a}|$ is:
The order and degree of the differential equation \[ \left[ \left( \frac{d^2 y}{dx^2} \right)^2 - 1 \right]^2 = \frac{dy}{dx} \text{ are, respectively:} \]
If \[ A = \begin{bmatrix} 0 & 0 & -5 \\ 0 & 3 & 0 \\ 4.3 & 0 & 0 \end{bmatrix}, \text{ then A is a:} \]

The graph shown below depicts:

If $f(x) = x^x$, find the critical point:

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?