List of top Mathematics Questions asked in CBSE CLASS XII

For an LPP with constraints

\[ \begin{aligned} 2x + y &\le 70 \\ x + y &\le 40 \\ x, y &\ge 0, \end{aligned} \]

shade the feasible region on the graph and write the coordinates of its corner points.

If \(2y^3 + y = 2x\), then show \(\dfrac{d^2y}{dx^2} = \dfrac{-48y}{(6y^2 + 1)^3}\).

Determine \(a\) and \(b\) if \(f(x)\) is a continuous function, where

\[ f(x) = \begin{cases} 2, & x \le 3 \\ ax + b, & 3 < x < 5 \\ 5, & x \ge 5 \end{cases} \]

Solve the matrix equation for \(x\) and \(y\).

\[ \begin{bmatrix} x^2 \\ y^2 \end{bmatrix} - 3\begin{bmatrix} x \\ 3y \end{bmatrix} = \begin{bmatrix} -2 \\ -20 \end{bmatrix} \]

Assertion (A) : Let \(R\) be a relation on set \(A\) of all books in a school library given by \(R = \{(x, y) : x, y \in A,\ x \text{ and } y \text{ have the same number of pages}\}\) and \(S\) is a relation on set \(A\) from the same library such that \(S = \{(p, q) : p \text{ and } q \text{ are Mathematics books}\}\). Also, \(R\cap S \neq \phi\). Then, \(R\cap S\) is an equivalence relation.

Reason (R) : The intersection of two equivalence relations on a set is an equivalence relation on the set.

If \(A\) and \(B\) are independent events such that \(P(A) = 0{\cdot}45\) and \(P(A\cup B) = 0{\cdot}5\), then \(P(B)\) is equal to :

If two events \(A\) and \(B\) are independent, then which of the following statements is not correct ?

Assertion (A) : Points \(A(6, -7, 0)\), \(B(16, -19, -4)\) and \(C(1, -1, 2)\) are collinear.

Reason (R) : Three points \(A\), \(B\) and \(C\) are collinear, when point \(C\) is the mid-point of line segment joining points \(A\) and \(B\).

If \(\displaystyle\int_{0}^{4}\frac{1}{x+\sqrt{x}}\,dx = k\log 3\), then the value of \(k\) is :

If vectors \(\vec{a} = 3\hat{i} - 2\hat{j} + 4\hat{k}\) and \(\vec{b} = \lambda\hat{i} + \hat{j}\) are perpendicular to each other, then the value of \(\lambda\) is :

If \(y = \log \sqrt{\tan x}\), then the value of \(\frac{dy}{dx}\) at \(x = \frac{\pi}{4}\) is :

\( \displaystyle\int \left[ \dfrac{1}{\log x} - \dfrac{1}{(\log x)^{2}} \right] dx \) is equal to :

The values of \( x \) for which the rate of increase of \( f(x) = x^{3} - 5x^{2} + 6x - 7 \) is thrice the rate of increase of \( x \), are :

If \( \displaystyle\int_{0}^{1} (9x^{2} - 4x - 2k)\,dx = 0 \), then the value of \( k \) is :

If \( A \) and \( B \) are square matrices of order 3 such that \( |A| = 4 \) and \( |B| = 7 \), then \( |2AB| \) is :

Differential of \( \cos^{-1}(e^{x}) \) with respect to \( x \) is :

If \( A = \begin{bmatrix} 1 & -2 & 3 \\ 3 & 2 & -1 \end{bmatrix} \), \( B = \begin{bmatrix} 2 & 3 \\ -1 & 2 \\ 4 & -5 \end{bmatrix} \) and \( C = [C_{ij}] = AB \), then \( C_{12} \) is :

For \( f(x) = -|x+1| + 5 \), which of the following statements is true ?

\( \left[ \tan^{-1}\sqrt{3} - \sec^{-1}(-2) \right] \) is equal to :

If \(A\) is a square matrix, then which of the following is not true ?

The value of \(\sin^{-1}\left(\sin\frac{3\pi}{5}\right)\) is :

If \(\begin{vmatrix} 3x & x+2 \\ 3(x-1) & x-2 \end{vmatrix} = \begin{vmatrix} 1 & 5 \\ 3 & 3 \end{vmatrix}\), then the value of \(x\) is :

If \(f(x) = \begin{cases} \dfrac{|x|}{x}, & x \neq 0 \\ 0, & x = 0 \end{cases}\), then which of the following statements is not correct ?

If \(A = \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}\) satisfies \(A^{\prime} + A = I\), then the value of \(\theta\) is :