List of top Questions asked in CBSE CLASS XII

Find $ \int \frac{3x + 1}{(x - 2)^2 (x + 2)} \, dx $

If $ A = \begin{bmatrix} 1 & 0 \\ -1 & 5 \end{bmatrix} $, then find the value of $ K $ if $ A^2 = 6A + K I_2 $, where $ I_2 $ is the identity matrix.

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 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 $2\hat{i} + 10\hat{j} + \hat{k}$, then the value of $\lambda$ is :

$ \int \frac{e^{-x}}{16 + 9e^{-2x}} \, dx$ is equal to :

If A and B are two events such that $P(B) = \frac{1}{5}$, $P(A | B) = \frac{2}{3}$ and $P(A \cup B) = \frac{3}{5}$, then $P(A)$ is :

If $f(x) = 2x^8$, then the correct statement 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 :

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 :

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.

(a) Find \[ \int \frac{x}{(x - 1)(x^2 + 4)} \, dx \]

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 :

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.

If $ f(x) = -2x^8 $, then the correct statement is :

\[ \int \frac{e^{9 \log x} - e^{8 \log x}}{e^{6 \log x}} \, dx \] is equal to :

\[ \int \frac{a^x}{\sqrt{1 - a^2 x}} \, dx \] 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 :

Explain how the immunity of a person is affected if there is atrophy (degeneration) of the thymus gland at an early stage of life.

Why are restrictions imposed on MTP in India? Up to how many weeks or trimesters, is MTP considered relatively safe for a female, if necessary to perform, by a medical practitioner?

According to the generally accepted definition of the ideal solution there are equal interaction forces acting between molecules belonging to the same or different species. (This is equivalent to the statement that the activity of the components equals the concentration.) Strictly speaking, this concept is valid in ecological systems (isotopic mixtures of an element, hydrocarbons mixtures, etc.). It is still usual to talk about ideal solutions as limiting cases in reality since very dilute solutions behave ideally with respect to the solvent. This law is further supported by the fact that Raoult’s law empirically found for describing the behaviour of the solvent in dilute solutions can be deduced thermodynamically via the assumption of ideal behaviour of the solvent.