List of top Mathematics Questions asked in CBSE CLASS XII

A box contains 4 red, 5 blue and 1 green marble. A child randomly takes out a marble from the box, notes down the colour and puts it back in the box. If the activity is repeated 3 times, what is the probability that at least one marble is red ?

Assertion (A) : If A and B are two square matrices such that AB and BA are defined, then it is not necessary that AB = BA.
Reason (R) : Product of two diagonal matrices of same order is commutative.

The region represented by the system of inequations \(3x + y \ge 3, 2x - y \ge - 5, x, y \ge 0\) is :

In the graph, the feasible region representing the Linear Programming Problem for maximising objective function \(Z = px + qy, p, q > 0\) is shaded. If all points on segment \(AB\) give max (Z), then which of the following is true ?

Three points \(A(0, 1, 1)\), \(B(2, 0, -1)\) and \(C(1, 0, 3)\) form \(\Delta ABC\). The \(ar (\Delta ABC)\) is :

Which of the following is not a Linear Differential Equation ?

\(\int \frac{dx}{\sqrt{25 - 16x^2}}\) is equal to :

Product of the order and degree of differential equation \(1 + \left(\frac{dy}{dx}\right)^3 = \lambda \left(\frac{d^3y}{dx^3}\right)^2\) is :

The greatest integer function, \(f(x) = [x]\), \(0 < x < 3\) is not differentiable at how many points ?

If \(\int_{0}^{1} \frac{dx}{e^x + e^{-x}} = \tan^{-1} e + k\), then the value of \(k\) is :

The area of the region bounded by the curve \(y = x\) and x-axis, between \(x = 0\) and \(x = 2\) is :

If \(A = [a_{ij}]\) is a \(2 \times 2\) matrix whose elements are given by \(a_{ij} = \frac{|i - 3j|}{2}\), then \(A'\) is :

If points (2, 3), (0, 4) and (p, 2) are collinear, then the value of p is :

Differential of \(e^{e^x}\) with respect to x is :

The surface area of a sphere when its volume changes at the same rate as its radius is :

A student selected at random did not qualify the examination. Find the probability that the student was a regular student.

A student selected at random qualified the examination. Find the probability that student is not a dropout.

A student is selected at random from a group of dropout students. What is the probability that the student will not qualify the examination ?

The following graph represents :

On the inauguration day of a new showroom, a lucky draw was organized and some vouchers of Rs 1,000 and Rs 500 were given to the lucky draw winners.

A total of 60 vouchers were given on the day. The number of Rs 1,000 vouchers added to 3 times the number of Rs 500 vouchers, gives 100. Express the given information as a system of linear equations in two variables. Hence, find the number of vouchers of each type by matrix method.

Given that $P = \begin{bmatrix} 2 & -1 \\ 3 & 4 \end{bmatrix}$, $Q = \begin{bmatrix} 5 & 2 \\ 7 & 4 \end{bmatrix}$ and $R = \begin{bmatrix} 2 & 5 \\ 3 & 8 \end{bmatrix}$, find a matrix $S$ such that $PQ - RS$ is a null matrix.}

Represent the equations of lines $l_1$ and $l_2$ in vector form and check whether they are intersecting or not.
$l_1 : \frac{x+3}{-3} = \frac{y-1}{1} = \frac{z-5}{5}$
$l_2 : \frac{x+1}{-1} = \frac{2-y}{-2} = \frac{z-5}{5}$}

Opposite sides of a square are along the lines :
$\vec{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda(2\hat{i} + 3\hat{j} + 6\hat{k})$
$\vec{r} = 3\hat{i} + 3\hat{j} - 5\hat{k} + \mu(2\hat{i} + 3\hat{j} + 6\hat{k})$
Find the area of the square if direction ratios of other pair of opposite sides of the square are given by $\langle -3, 6, p \rangle$. Also, find the value of $p$.}

Solve the following Linear Programming Problem graphically :
Maximise $Z = 600x + 400y$
subject to the constraints
$x + 2y \leq 12$
$4x + 5y \geq 20$
$2x + y \leq 12$
$x, y \geq 0$

Show that $f : \mathbb{R} \to \mathbb{R}$ defined as $f(x) = \frac{x}{\sqrt{1+x^2}}$ is one-one but not onto.}