List of top Questions asked in MHT CET- 2025

The integrating factor of $x \cdot \frac{dy}{dx} + y \log x = x \cdot e^x x^{-1/2} \log x$ is

If $\vec{c} = 5\vec{a} + 6\vec{b}$ and $3\vec{c} = \vec{a} - 4\vec{b}$ then}

ABCD is a quadrilateral with $\overline{AB} = \overline{a}, \overline{AD} = \overline{b}$ and $\overline{AC} = 2\overline{a} + 3\overline{b}$. If its area is $\alpha$ times the area of the parallelogram with AB, AD as adjacent sides, then the value of $\alpha$ is

A spherical balloon is filled with (4500\pi) cubic meters of helium gas. If a leak causes gas to escape at (72\pi) m(^3)/min, then the rate at which the radius decreases 49 minutes after leakage began is

The solution of $\log(\frac{dy}{dx}) = 2x - 5y, y(0) = 0$ is

If $x \cdot \log_e(\log_e x) - x^2 + y^2 = 4(y > 0)$, then $\frac{dy}{dx}$ at $x = e$ is

If p : switch $S_1$ is closed, q : switch $S_2$ is closed then correct interpretation from the following circuit is

The population ( p ) of the city at time ( t ) is given by ( \frac{dp}{dt} = \frac{p}{2} - 100 ). If initial population is 100 then ( p = )

The area of the region bounded by the parabola ( y^2 = 27x ) and the line ( x = 1 ) is ________ sq.units.

If $( \sin(\alpha + \beta) = 1, \sin(\alpha - \beta) = \frac{1}{2}, \alpha, \beta \in [0, \pi/2] ), then ( \tan(\alpha + 2\beta) \cdot \tan(2\alpha + \beta) = ) $

Two cards are drawn successively with replacement from fair playing 52 cards. let X denote number of kings obtained when two cards are drawn, then ( E(X^2) = )

The equation of plane passing through ( (1, 0, 0) ) and ( (0, 1, 0) ) and making an angle ( 45^\circ ) with the plane ( x + y - 3 = 0 ) is

The distance of the point ( (5, 3, -1) ) from the plane passing through points ( (2, 1, 0), (3, -2, 4) ) and ( (1, -3, 3) ) is

If one of the diameters of the circle, given by the equation ( x^2 + y^2 - 4x + 6y - 12 = 0 ), is a chord of a circle, 'S', whose centre is at ( (-3, 2) ), then the length of radius of 'S' is ________ units.

The eccentric angle of the point ( P(-6, 2) ) of the ellipse ( \frac{x^2}{48} + \frac{y^2}{16} = 1 ) is

Three numbers are chosen at random from numbers 1 to 20. The probability that they are consecutive is

The area of the triangle whose vertices are $( i, \omega, \omega^2 )$ is (Where $\omega$ is a complex cube root of unity other than 1, $i$ is an imaginary number)________ sq.units

The feasible region for the constraints $ x - y \ge 0, x - 5y \le -5, x \ge 0, y \ge 0 $ is shown by the figure:

The function \( f(x) = \sec \left[ \log \left( x + \sqrt{1 + x^2} \right) \right] \) is ________ function

If $x = \tan^{-1} \left\{ \frac{\sqrt{1+t^2}-1}{t} \right\}, y = \cos^{-1} \left\{ \frac{1-t^2}{1+t^2} \right\}$, then $\frac{dy}{dx}$ is equal to

The minimum value of the slope of the tangent to curve $y = x^3 - 3x^2 + 2x + 93$ is

If $f(x) = \begin{cases} \frac{9^x - 2 \cdot 3^x + 1}{\log(1+3x) \cdot \tan 2x} & , \text{if } x \neq 0 \\ a(\log b)^c & , \text{if } x = 0 \end{cases}$ is continuous at $x = 0$, then $a+b+c =$

The area of the triangle formed by the co-ordinate axes and a tangent to the curve $xy = a^2$ at the point $(x_1, y_1)$ is ______ sq. units (where $a, x_1$ and $y_1$ are non-zero)

What is the SI unit of resistivity?