List of top Questions asked in MHT CET- 2025

If the lengths of three vectors $\bar{a}, \bar{b}$ and $\bar{c}$ are 5, 12, 13 units respectively, and each one is perpendicular to the sum of the other two, then $|\bar{a} + \bar{b} + \bar{c}| = ..............$

$\int \sec^{\frac{2}{3}} x \cdot \csc^{\frac{4}{3}} x dx =$

If $f(x) = \begin{cases} \frac{1-\cos 4x}{x^2} & , \text{if } x<0 \\ a & , \text{if } x = 0 \\ \frac{(16+\sqrt{x})^{\frac{1}{2}}-4}{\sqrt{x}} & , \text{if } x>0 \end{cases}$ is continuous at $x = 0$, then a =}

Identify the correct symbolic representation for the circuit provided in the image.

If p : switch $S_1$ is closed, q : switch $S_2$ is closed, r : switch $S_3$ closed, then the symbolic form of the following switching circuit is equivalent to

In a triangle ABC with usual notations, if $3a = b + c$, then $\cot \frac{B}{2} \cdot \cot \frac{C}{2} =$

The normal to the curve $x = 9(1 + \cos \theta), y = 9 \sin \theta$ at $\theta$ always passes through the fixed point}

The derivative of $\tan^{-1} \left( \frac{\sqrt{1+x^2}-1}{x} \right)$ w.r.t. $\tan^{-1} \left( \frac{2x\sqrt{1-x^2}}{1-2x^2} \right)$ at $x = 0$ is

The number of solutions of $\tan^{-1} (x + \frac{2}{x}) - \tan^{-1} (\frac{4}{x}) - \tan^{-1} (x - \frac{2}{x}) = 0$ are

Derivative of $x^{(x^x)}$ is

The circumradius of the triangle formed by the lines $xy + 2x + 2y + 4 = 0$ and $x + y + 2 = 0$ is

The correct constraints for the given feasible region are ..............

The angle between the lines $x - 3y - 4 = 0, 4y - z + 5 = 0$ and $x + 3y - 11 = 0, 2y - z + 6 = 0$ is

If the point $(1, \alpha, \beta)$ lies on the line of the shortest distance between the lines $\frac{x+2}{-3} = \frac{y-2}{4} = \frac{z-5}{2}$ and $\frac{x+2}{-1} = \frac{y+6}{2}, z = 1$, then $\alpha + \beta =$

If $\bar{p} = 2\hat{\text{i}} + \hat{\text{k}}, \bar{q} = \hat{\text{i}} + \hat{\text{j}} + \hat{\text{k}}, \bar{r} = 4\hat{\text{i}} - 3\hat{\text{j}} + 7\hat{\text{k}}$ and a vector $\bar{\text{m}}$ is such that $\bar{\text{m}} \times \bar{q} = \bar{r} \times \bar{q}, \bar{\text{m}} \cdot \bar{p} = 0$, then $\bar{\text{m}} = .......$

If a random variable $X$ has p.d.f. $f(x) = \begin{cases} \frac{ax^2}{2} + bx & , \text{if } 1 \leq x \leq 3 \\ 0 & , \text{otherwise} \end{cases}$ and $f(2) = 2$, then the values of $a$ and $b$ are, respectively}

A wet substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet, hung in the open air, loses half its moisture during the first hour, then $90%$ of the moisture will be lost in .............. hours.

The foci of a hyperbola coincide with the foci of the ellipse $\frac{x^2}{25} + \frac{y^2}{9} = 1$. The equation of the hyperbola with eccentricity 2 is

$\int_0^{\pi/4} (\sqrt{\tan x} + \sqrt{\cot x}) dx =$

If sin A = n sin(A + 2 B), then tan(A + B) =}

The equations of the tangents to the circle $x^2 + y^2 = 36$ which are perpendicular to the line $5x + y = 2$, are

$z = \frac{3+2i \sin \theta}{1-2i \sin \theta}, (i = \sqrt{-1})$ will be purely imaginary if $\theta =$

$\int \frac{x^3}{x^4+5x^2+4} dx =$

The values of $b$ and $c$ for which the identity $f(x + 1) - f(x) = 8x + 3$ is satisfied, where $f(x) = bx^2 + cx + d$, are

The function $f(x) = \sin^4 x + \cos^4 x$ increases if}