CBSE Class 12 Mathematics — MCQs

If $2\cos^{-1}x = y$, then

Which of the following cannot be the order of a row-matrix?

Which of the following properties is/are true for two matrices of suitable orders? (i) $(A + B)' = A' + B'$ (ii) $(A - B)' = B' - A'$ (iii) $(AB)' = A'B'$ (iv) $(kAB)' = kB'A'$ (k is a scalar)

If $\Delta_1 = \begin{vmatrix}1 & 0 & 0\\0 & 2 & 0\\0 & 0 & 3\end{vmatrix}$ and $\Delta_2 = \begin{vmatrix}0 & 2 & 0\\1 & 0 & 0\\0 & 0 & 6\end{vmatrix}$, then

One of the values of x for which $\begin{vmatrix}\cos x & \sin x\\-\cos x & \sin x\end{vmatrix} = 1$ is

If A and B are skew symmetric matrices of same order, then which of the following matrices is also skew symmetric?

The least value of $f(x) = x^3 - 12x,\ x \in [0, 3]$ is

If $\int \frac{3ax}{b^2 + c^2 x^2}\,dx = A \log |b^2 + c^2 x^2| + K$, then the value of A is

The value of $\int_{-1}^{1} \frac{x^3}{x^2+2|x|+1}\,dx$ is

The area bounded by the curve $y = x|x|$, x-axis and the ordinates $x = -1 \text{ and } x = 1$ is given by

The integrating factor of differential equation $R\left(\frac{dx}{dy}\right) + Px = Q$, where P, Q, R are functions of y, is

The order and degree of the differential equation $\frac{d}{dx}(e^y) = 0$ respectively are

The value of p for which the vectors $\hat{i} + 2\hat{j} + 3\hat{k}$ and $2\hat{i} - p\hat{j} + \hat{k}$ are perpendicular to each other is

The value of m for which the points with position vectors $-\hat{i} - \hat{j} + 2\hat{k}$, $2\hat{i} + m\hat{j} + 5\hat{k}$ and $3\hat{i} + 11\hat{j} + 6\hat{k}$ are collinear, is

If $|\vec{a}| = 8$, $|\vec{b}| = 3$ and $|\vec{a} \times \vec{b}| = 12$, then the value of $|\vec{a} \cdot \vec{b}|$ is

The length of the perpendicular drawn from the point $(2, 5, 7)$ on the line $\frac{x}{1} = \frac{y}{0} = \frac{z}{0}$ is

The feasible region of a linear programming problem with objective function $Z = 5x + 7y$ is shown below. The maximum value of Z - minimum value of Z is

The degree of an objective function of a linear programming problem is