List of top Questions asked in MHT CET

If the line $\frac{x+1}{2}=\frac{y-m}{3}=\frac{z-4}{6}$ lies in the plane $3x-14y+6z+49=0$, then the value of $m$ is

If $4 \sin ^{-1} x+6 \cos ^{-1} x=3 \pi$, where $-1 \leq x \leq 1$, then $x =$

$\int \frac{x+\sin x}{1+\cos x} d x=$

If $x = a \cos \theta$, $y = b \sin \theta$, then $\left[\frac{d^2 y}{d x^2}\right] = $

If $h(x)=\sqrt{4 f(x)+3 g(x)}$, $f(1)=4$, $g(1)=3$, $f^{\prime}(1)=3$, $g^{\prime}(1)=4$, then $h^{\prime}(1)=$

The slope of the line through the origin which makes an angle of $30^\circ$ with the positive direction of Y-axis measured anticlockwise is :

If $\int \frac{1+x^2}{1+x^4} d x=\frac{1}{\sqrt{2}} \tan ^{-1}\left[\frac{f(x)}{\sqrt{2}}\right]+c$, then $f(x)=$

All the letters of the word 'ABRACADABRA' are arranged in different possible ways. Then the number of such arrangements in which the vowels are together is

The equation of the tangent to the curve $y = 4x e^x$ at $\left(-1, -\frac{4}{e}\right)$ is

The domain of the function $f(x) = \frac{1}{\sqrt{x + |x|}}$ is

The value of $\sin 18^{\circ}$ is

$(2\hat{\mathrm{i}} + 6\hat{\mathrm{j}} + 27\hat{\mathrm{k}}) \times (\hat{\mathrm{i}} + \lambda\hat{\mathrm{j}} + \mu\hat{\mathrm{k}}) = \vec{0}$, then $\lambda$ and $\mu$ are respectively

If $f(x) = [x]$, for $x \in (-1, 2)$, then $f$ is discontinuous at (where $[x]$ represents floor function)

The differential equation of all circles which pass through the origin and whose centre lie on Y-axis is

With usual notations if the angles of a triangle are in the ratio 1 : 2 : 3, then their corresponding sides are in the ratio

The angle between a line with direction ratios 2, 2, 1 and a line joining $(3, 1, 4)$ and $(7, 2, 12)$ is

Rajesh has just bought a VCR from Maharashtra Electronics and the shop offers after sales service contract for Rs. 1000 for the next five years. Considering the experience of VCR users, the following distribution of maintenance expenses for the next five years is formed.

The expected value of maintenance cost is :

The general solution of the differential equation $x + y \frac{d y}{d x} = \sec(x^2 + y^2)$ is

If $A = \begin{bmatrix} 3 & 2 & 4 \\ 1 & 2 & 1 \\ 3 & 2 & 6 \end{bmatrix}$ and $A_{ij}$ are cofactors of the elements $a_{ij}$ of $A$, then $a_{11}A_{11} + a_{12}A_{12} + a_{13}A_{13}$ is equal to

The area of the region bounded by the parabola $x^2 = y$ and the line $y = x$ is

$\lim_{x \to \infty} \left( \sqrt{x^2 + 5x - 7} - x \right) =$

The value of $(1 + i)^5 (1 - i)^7$ is

If inverse of $\begin{bmatrix} 1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6 \end{bmatrix}$ does not exist, then $x =$

If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect, then the value of $k$ is

The parametric equations of a line passing through the points $A(3,4,-7)$ and $B(1,-1,6)$ are