List of top Mathematics Questions asked in CBSE CLASS XII

The order and degree of the differential equation \[ \left( \frac{d^2y}{dx^2} \right)^2 + \left( \frac{dy}{dx} \right)^2 = x \sin \left( \frac{dy}{dx} \right) \] are :

If the sides $AB$ and $AC$ of $\triangle ABC$ are represented by vectors $\hat{i} + \hat{j} + 4 \hat{k}$ and $3 \hat{i} - \hat{j} + 4 \hat{k}$ respectively, then the length of the median through A on BC is :

The function $f$ defined by \[ f(x) = \begin{cases} x, & \text{if } x \leq 1 \\ 5, & \text{if } x>1 \end{cases} \] is not continuous at :

If $f(x) = 2x + \cos x$, then $f(x)$ :

If $f(x) = \begin{cases} 3x - 2, & 0 \leq x \leq 1\\ 2x^2 + ax, & 1<x<2 \end{cases}$ is continuous for $x \in (0, 2)$, then $a$ is equal to :

If $f : \mathbb{N} \rightarrow \mathbb{W}$ is defined as \[ f(n) = \begin{cases} \frac{n}{2}, & \text{if } n \text{ is even} \\ 0, & \text{if } n \text{ is odd} \end{cases} \] then $f$ is :

The matrix \[ \begin{pmatrix} 0 & 1 & -2 \\ -1 & 0 & -7 \\ 2 & 7 & 0 \end{pmatrix} \] is a :

If P is a point on the line segment joining $(3, 6, -1)$ and $(6, 2, -2)$ and the $y$-coordinate of P is 4, then its $z$-coordinate is :

The values of $\lambda$ so that $f(x) = \sin x - \cos x - \lambda x + C$ decreases for all real values of $x$ are :

If $M$ and $N$ are square matrices of order 3 such that $\det(M) = m$ and $MN = mI$, then $\det(N)$ is equal to :

For real $x$, let $f(x) = x^3 + 5x + 1$. Then :

If A and B are square matrices of same order such that AB = BA, then $A^2 + B^2$ is equal to :

The principal value of $\sin^{-1} \left( \sin \left( -\frac{10\pi}{3} \right) \right)$ is :

Find: \[ \int \frac{\sin^{-1} \left( \frac{x}{\sqrt{a + x}} \right)}{ \sqrt{a + x}} \, dx \]

If: \[ \begin{bmatrix} x + y & 3y \\ 3x + 3 & x + 3 \end{bmatrix} \begin{bmatrix} 9 & x + y \\ 4x + y & y \end{bmatrix} \] then \( (x - y) = ? \)

A system of linear equations is represented as \( AX = B \), where \( A \) is the coefficient matrix, \( X \) is the variable matrix, and \( B \) is the constant matrix. Then the system of equations is:

If \( \int_0^1 \frac{e^x}{1+x} \, dx = \alpha \), then \( \int_0^1 \frac{e^x}{(1+x)^2} \, dx \) is equal to:

The order and degree of the differential function \[ \left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^5 = \frac{d^2y}{dx^2} \]

Solve the following linear programming problem graphically: Maximise \( Z = 20x + 30y \) Subject to the constraints: \[ x + y \leq 0, \quad 2x + 3y \geq 100, \quad x \geq 14, \quad y \geq 14. \]

Evaluate: \[ \int_0^{\frac{\pi}{2}} \frac{5 \sin x + 3 \cos x}{\sin x + \cos x} \, dx \]

The unit vector perpendicular to the vectors \( \hat{i} - \hat{j} \) and \( \hat{i} + \hat{j} \) is:

Differentiate: \[ \frac{\tan^{-1}\left(\frac{\sqrt{1 - x^2}}{x}\right)}{x} \quad \text{w.r.t.} \quad \cos^{-1}(2x\sqrt{1 - x^2}), \quad x \in \left(\frac{1}{\sqrt{2}}, 1\right) \]

The area of an expanding rectangle is increasing at the rate of \( 4 \, \text{cm}^2/\text{s} \). The length of the rectangle is always square of its breadth. At what rate is the length of the rectangle increasing at an instant, when breadth \( = 4.5 \, \text{cm} \)?