List of top Questions asked in MHT CET

If $A = \begin{bmatrix} 1 & 2 & 3 \\ 1 & 1 & a \\ 2 & 4 & 7 \end{bmatrix}$ and $B = \begin{bmatrix} 13 & 2 & b \\ -3 & -1 & 2 \\ -2 & 0 & 1 \end{bmatrix}$ where matrix $B$ is the inverse of matrix $A$, then the values of $a$ and $b$ are

The differential equation of the family of parabolas with focus at the origin and the $X$-axis as its axis, is

If $A = (-2, 2, 3)$, $B = (3, 2, 2)$, $C = (4, -3, 5)$, and $D = (7, -5, -1)$, then the projection of $\vec{AB}$ on $\vec{CD}$ is

The probability distribution of a discrete random variable $X$ is given as

Find the value of $P(2 < X < 6)$.

$\int \cos^3 x \cdot e^{\log(\sin x)} , dx = $

The value of $\sin^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ is

If $A = \begin{bmatrix} 2 & -2 \\ 2 & -3 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$, then $(B^{-1}A^{-1})^{-1} = $

If one of the lines given by $kx^2 + xy - y^2 = 0$ bisects the angle between the co-ordinate axes, then the values of $k$ are

If $p$ : It is raining and $q$ : It is pleasant, then the symbolic form of "It is neither raining nor pleasant" is

If $\int \frac{dx}{32 - 2x^2} = A \log|4 - x| + B \log|4 + x| + c$, then the values of $A$ and $B$ are respectively

If $|\vec{a}| = 4$, $|\vec{b}| = 5$, then the values of $k$ for which $\vec{a} + k\vec{b}$ is perpendicular to $\vec{a} - k\vec{b}$ are

Equation of the chord of the circle $x^2 + y^2 - 4x - 10y + 25 = 0$ having mid-point $(1, 2)$ is

If $A$ and $B$ are the foot of the perpendicular drawn from the point $Q(a, b, c)$ to the planes $YZ$ and $ZX$ respectively, then the equation of the plane through the points $A$, $B$, and the origin $O$ is

The area bounded by the lines $y = x$, $x = -1$, $x = 2$ and the $X$-axis is

$\int_{0}^{\pi / 2} \log\left(\frac{4+3\sin x}{4+3\cos x}\right) dx = $

If the function $$f(x) = \begin{array}{cc} 3ax + b, & \text{for } x < 1 \\ 11, & \text{for } x = 1 \\ 5ax - 2b, & \text{for } x > 1 \end{array}$$ is continuous at $x = 1$, then the values of $a$ and $b$ are

If the vectors $\vec{a} = 2\hat{i} + p\hat{j} + 4\hat{k}$ and $\vec{b} = 6\hat{i} - 9\hat{j} + q\hat{k}$ are collinear, then $p$ and $q$ are

If $\mathrm{P(A)} = \frac{3}{10}$, $\mathrm{P(B)} = \frac{2}{5}$, and $\mathrm{P(A \cup B)} = \frac{3}{5}$, then $\mathrm{P(A / B) \times P(B / A)} = $

If $y = \log_{10} x + \log_x 10 + \log_x x + \log_{10} 10$, then $\frac{dy}{dx} = $

If $y = \tan^{-1}\left[\frac{\log\left(\frac{e}{x^2}\right)}{\log(ex^2)}\right] + \tan^{-1}\left[\frac{3 + 2\log x}{1 - 6\log x}\right]$, then $\frac{d^2y}{dx^2} = $

If $\vec{a} = \hat{i} + \hat{j} + \hat{k}$, $\vec{c} = \hat{j} - \hat{k}$, $\vec{a} \times \vec{b} = \vec{c}$ and $\vec{a} \cdot \vec{b} = 1$, then $\vec{b} = $

The square roots of the complex number $(-5 - 12i)$ are

Equation of the plane passing through the point $(1, 2, 3)$ and parallel to the plane $2x + 3y - 4z = 0$ is

The general solution of the differential equation $(2y - 1) \, dx - (2x + 3) \, dy = 0$ is

The negation of $p \wedge (q \rightarrow r)$ is