List of top Mathematics Questions asked in CBSE CLASS XII

Assertion (A): The principal value of $\cot^{-1}(\sqrt{3})$ is $\frac{\pi}{6}$.
Reason (R): Domain of $\cot^{-1} x$ is $\mathbb{R} - \{-1, 1\}$.

The point which lies in the half-plane $2x + y - 4 \le 0$ is:

If $(\cos x)^y = (\cos y)^x$, then $\frac{dy}{dx}$ is:

The difference of the order and the degree of the differential equation \[ \Big( \frac{d^2 y}{dx^2} \Big)^2 + \Big( \frac{dy}{dx} \Big)^3 + x^4 = 0 \text{ is:} \]

For which value of x, are the determinants \[ \begin{vmatrix} 2x & -3 \\ 5 & x \end{vmatrix} \text{and} \begin{vmatrix} 10 & 1 \\ -3 & 2 \end{vmatrix} \text{ equal?} \]

The value of the cofactor of the element of second row and third column in the matrix \[ \begin{bmatrix} 4 & 3 & 2 \\ 2 & -1 & 0 \\ 1 & 2 & 3 \end{bmatrix} \text{ is:} \]

The vector equation of a line which passes through the point (2, -4, 5) and is parallel to the line $\displaystyle \frac{x+3}{3} = \frac{4-y}{2} = \frac{z+8}{6}$ is:

The value of $\displaystyle \int_{0}^{\pi/6} \sin 3x \, dx$ is:

Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 &  3\\ 2 & 7\end{bmatrix}\)

For what values of x,\(\begin{bmatrix} 1 & 2 & 1 \end{bmatrix}\)\(\begin{bmatrix} 1 & 2 & 0\\ 2 & 0 & 1 \\1&0&2 \end{bmatrix}\)\(\begin{bmatrix} 0 \\2\\x\end{bmatrix}\)=O?

Find the inverse of each of the matrices,if it exists \(\begin{bmatrix} 2 & 1 \\ 7 & 4  \end{bmatrix}\)

Find the inverse of each of the matrices,if it exists. \(\begin{bmatrix} 2 &  3\\ 5 & 7 \end{bmatrix}\)

If A'= \(\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}\)\(\begin{bmatrix}  -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}\) , then verify that 
(i) \((A+B)'=A'+B' \)
(ii) \((A-B)'=A'-B'\)

If (i) A=\(\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}\),then verify that A'A=I
(ii) A= \(\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}\),then verify that A'A=I

Find the vector and the cartesian equations of the lines that pass through the origin and(5,-2,3).

Find the integrals of the function: \(cos\, 2x\, cos\, 4x\, cos\, 6x\)

Integrate the function: \(\frac {4x+1}{\sqrt {2x^2+x-3}}\)

Using Cofactors of elements of third column,evaluate\(△=\begin{bmatrix}1&x&yz\\ 1&y&zx\\ 1&z&xy\end{bmatrix}\)

The traffic police has installed Over Speed Violation Detection (OSVD) system at various locations in a city. These cameras can capture a speeding vehicle from a distance of 300 m and even function in the dark. \vspace{0.3cm} \includegraphics[width=\linewidth]{latex2.png} \vspace{0.3cm} A camera is installed on a pole at the height of 5 m. It detects a car travelling away from the pole at the speed of 20 m/s. At any point, \(x\) m away from the base of the pole, the angle of elevation of the speed camera from the car C is \(\theta\). \vspace{0.3cm} On the basis of the above information, answer the following questions: \begin{enumerate} Express \( \theta \) in terms of the height of the camera installed on the pole and \( x \). Find \( \frac{d\theta}{dx} \). \begin{enumerate} Find the rate of change of angle of elevation with respect to time at an instant when the car is 50 m away from the pole. OR If the rate of change of angle of elevation with respect to time of another car at a distance of 50 m from the base of the pole is \( \frac{3}{101} \) rad/s, then find the speed of the car. \end{enumerate} \end{enumerate}