List of top Questions asked in MHT CET

A random variable $X$ has the following probability distribution:
{|c|c|c|c|c|c|c|} $X = x$ & 1 & 2 & 3 & 4 & 5 & 6 $P(X = x)$ & $k$ & $3k$ & $5k$ & $7k$ & $8k$ & $k$ Then $P(2 \le X < 5) =$

If $A = \begin{bmatrix} k & 2 \\ -2 & -k \end{bmatrix}$, then $A^{-1}$ does not exist if $k =$

If $|\vec{u}| = 2$ and $\vec{u}$ makes angles of $60^\circ$ and $120^\circ$ with the axes $OX$ and $OY$ at the origin, then $\vec{u} =$

The area bounded between the curve $x^2 = y$ and the line $y = 4x$ is

For two events $A$ and $B$, $P(A \cup B) = \frac{5}{6}$, $P(A) = \frac{1}{6}$, $P(B) = \frac{2}{3}$, then $A$ and $B$ are

A rectangle of maximum area is inscribed in an ellipse $\frac{x^2}{25} + \frac{y^2}{16} = 1$, then its dimensions are

The area of the parallelogram whose diagonals are represented by the vectors $\vec{a} = 3\hat{i} - \hat{j} - 2\hat{k}$ and $\vec{b} = -\hat{i} + 3\hat{j} - 3\hat{k}$ is

The value of $\lim_{x \to 0} \frac{\cos(mx) - \cos(nx)}{x^2}$ is

The point on the curve $y^2 = 2(x - 3)$ at which the normal is parallel to the line $y - 2x + 1 = 0$ is

Area of the triangle formed by the lines $y^2 - 9xy + 18x^2 = 0$ and $y = 9$ is

Solution of the differential equation $y' = \frac{x^2+y^2}{xy}$, where $y(1) = -2$ is given by

The value of $\int e^x \left(\frac{x - 1}{x^2}\right) dx =$

The Cartesian equation of a line is $3x + 1 = 6y - 2 = 1 - z$, then its vector equation is

The value of $\int_{-\pi}^{\pi} \frac{x\sin x}{1+\cos^2 x}\,dx =$

If $A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 2 & 3 \\ 1 & 2 & 1 \end{bmatrix}$, then the value of the determinant of $A^{-1}$ is

The position vector of the point of intersection of the medians of a triangle, whose vertices are $A(1, 2, 3)$, $B(1, 0, 3)$ and $C(4, 1, -3)$ is

Bismuth has a half-life period of $5$ days. A sample originally has a mass of $1000\text{ mg}$, then the mass of Bismuth after $30$ days is

If the slope of one of the lines $ax^2 + 2hxy + by^2 = 0$ is twice that of the other, then $h^2 : ab$ is

In $\triangle ABC$, with usual notations, $2ab \sin \frac{1}{2}(A+B-C) =$

The general solution of $\sin^{-1}\left(\frac{dy}{dx}\right) = x + y$ is

$\tan 3A \cdot \tan 2A \cdot \tan A =$

If statements $p$ and $q$ are true and $r$ and $s$ are false, then truth values of $\sim ( p \rightarrow q ) \leftrightarrow ( r \wedge s )$ and $( \sim p \rightarrow q ) \wedge ( r \leftrightarrow s )$ are respectively

The particular solution of the differential equation $y(1+\log x) = \left(\log x^x\right)\frac{dy}{dx}$, when $y(e) = e^2$ is

Let $$\begin{array}{ll} f(x) = |x| + 3, & \text{if } x \le -3 \\ f(x) = -2x, & \text{if } -3 < x < 3 \\ f(x) = 6x - 2, & \text{if } x \ge 3 \end{array}$$ then

The equation of a circle that passes through the origin and cut off intercepts $-2$ and $3$ on the X-axis and Y-axis respectively is