MHT CET 2026 11th April Morning Shift

The difference between the local extreme values of the function $f(x) = 2x^3 - 15x^2 + 36x + 40$ is ......

A wire of length $64$ m is to be bent to form a rectangle such that its area is maximum, then its area is.....

The approximate value of $\sqrt[3]{63}$ is

The equation of the tangent to the curve $y = 3x^3 - 3x^2 + x$ at $x = 1$ is

The area of the shaded region is ... sq.units.

$\int_0^3 \sqrt{9 - x^2} dx = $

The equation of a circle which passes through the points $(2,3)$ and $(4,5)$ and whose center lies on the straight line $y - 4x + 3 = 0$ is

If $-1 + \sqrt{-3} = r e^{i\theta}$, then the value of $\theta$ is

If $[\cdot]$ denotes the greatest integer function, then $\int_1^4 x[x] dx$ is equal to

If $\int_1^a (2x + 1) dx = 5$, then the sum of the values of $a$ is..

The particular solution of the differential equation $xdy + 2ydx = 0$, when $x = 2$ and $y = 1$ is

The differential equation representing the family of curves $x \sin x + y^3 = 4ax$ is

The order and degree of the differential equation $\sqrt{2 + \left(\dfrac{d^2 y}{dx^2}\right)^3} = \left(\dfrac{d^3 y}{dx^3}\right)^{5/2}$ respectively are

If $y = f\left(\dfrac{3 + 2x}{3 - 2x}\right)$, where $f(x) = \tan(\log x)$ and $\dfrac{dy}{dx} = \left(\dfrac{A}{B + C x^2}\right) \cdot \sec^2\left(\log\left(\dfrac{3 + 2x}{3 - 2x}\right)\right)$, then the respective values of A, B and C a...

If $y = \sqrt{x^2 + 8x + 3}$, then the value of $\dfrac{d^2 y}{dx^2}$ at $x = 3$ is

If $y = \sqrt{\tan x + \sqrt{\tan x + \sqrt{\tan x + \cdots \cdots \cdots \infty}}}$, then $\left(\dfrac{dy}{dx}\right)^2$ at $x = \dfrac{\pi}{4}$ is

If $y = \sqrt{x + \sqrt{x^2 + 1}}$, then the value of $\dfrac{dy}{dx}$ is

If $y = \sin(e^{\log 2x})$, then the value of $\dfrac{dy}{dx}$ at $x = \dfrac{\pi}{2}$ is

The domain of the function $f(x) = \sqrt{x - 1} + \sqrt{3 - x}$ is ...

$\int \dfrac{x + 2}{x^2 - 7x + 12} dx$ is equal to

If $\int \dfrac{dx}{\sqrt{2ax - x^2}} = f(g(x)) + c$, where $c$ is constant of integration, then $f(x), g(x)$ are respectively equal to

$\int \dfrac{x}{x + 2} dx$ is equal to

The minimum value of $(\sin^{-1} x)^2 + (\cos^{-1} x)^2$ is............

If $\tan^{-1}(1) + \tan^{-1}(3) + \tan^{-1}(5) + \tan^{-1}\left(\dfrac{1}{4}\right) = \pi + \tan^{-1}\left(\dfrac{\alpha}{2}\right)$, then the value of $\alpha$ is...

The value of $\lim_{x \to 3} \dfrac{[x] - 3}{x - 3}$, where $[\cdot]$ denotes the greatest integer function, is.....

Let the function $f(x)$ be defined as:$f(x) = \begin{cases} \left[\tan\left(\dfrac{\pi}{4} + x\right)\right]^{\dfrac{1}{x}}, & x \neq 0 \\ k, & x = 0 \end{cases}$If $f(x)$ is continuous at $x = 0$, then the value of $k$ is...

The point at which the maximum value of $x + y$ subject to constraints $x + 2y \leq 70$ and $2x + y \leq 95, x \geq 0, y \geq 0$ is.

If $A = \{1, 2, 3, 4, 5\}$, then which of the following statements is not true?

If the truth value of the compound statement $[(p \vee q) \wedge (q \rightarrow r) \wedge (\sim r)] \rightarrow (p \wedge q)$ is False then the truth values of $p \rightarrow q$ and $q \rightarrow p$ are respectively......

The statement pattern $(p \vee q) \rightarrow \sim r$ is logically equivalent to

If $A = \dfrac{1}{2}\begin{bmatrix} -1 & -\sqrt{3} \\ \sqrt{3} & -1 \end{bmatrix}$ then $A^{-1} - A^2$ is not

If $A = \begin{bmatrix} 2i & i^3 \\ i^2 & 1 \end{bmatrix}$, then $A^{-1}$ is equal to

There are $5$ boys and $3$ girls seated in a row for a photograph. The number of ways in which a photograph can be taken if the girls occupy only odd places is...

Let $X \sim B(n, p)$. If $E(X) = 2$ and $\text{Var}(X) = 1$, then the probability of getting at most one success is .....

If the following function is probability density function of r.v. X$f(x) = kx^2(1-x)$, for $0 < x < 1 = 0$, otherwise, then the value of $k$ is

Two cards are drawn at random from a standard pack of $52$ cards. Then the probability that the draw consists of exactly one face card and exactly one ace card is...

In $\triangle ABC$, with usual notations, if $\cos A = \dfrac{1}{2}, a = 3, \angle B = \dfrac{\pi^c}{6}$, then the values of $b$ and $c$ are.....

The equation of a line passing through the point of the intersection of the lines $x - y + 1 = 0$ and $2x + 3y - 8 = 0$ and having x intercept $3$ is

If the equation $x^2 - ky^2 - 4x + 6y - 5 = 0$ represents a pair of straight lines, then their point of intersection is

If the points $(1, 1, \mu)$ and $(-3, 0, 1)$ are equidistant from the plane $\vec{r} \cdot (3\hat{i} + 4\hat{j} - 12\hat{k}) + 13 = 0$, then the value of $\mu$ are

If the lines $\dfrac{x-1}{2} = \dfrac{y+1}{3} = \dfrac{z-1}{4}$ and $\dfrac{x-2}{1} = \dfrac{y+m}{2} = \dfrac{z-2}{1}$ intersect each other, then the value of $m$ is....

If the lines $L_1: \dfrac{x-1}{-3} = \dfrac{y-2}{2k} = \dfrac{z-3}{2}, L_2: \dfrac{x-1}{3k} = \dfrac{y-5}{1} = \dfrac{z-6}{-5}$ are perpendicular to each other, then the equation of a plane containing the line $L_1$ and parallel to the line...

A plane meets the coordinate axes at points A, B and C, such that the centroid of a triangle ABC is $\left(2, -\dfrac{2}{3}, \dfrac{1}{2}\right)$. The perpendicular distance from the origin to this plane is...

The principal solutions of $\text{cosec}(\theta) = -2$ are...

The value of the expression $\tan(x - 9\pi)$ is equal to:

The vector $\bar{a} + 3\bar{b}$ is perpendicular to $7\bar{a} - 5\bar{b}$ and the vector $\bar{a} - 4\bar{b}$ is perpendicular to $7\bar{a} - 2\bar{b}$. Then the angle between $\bar{a}$ and $\bar{b}$ is

If $7\hat{j} + 10\hat{k}, -\hat{i} + 6\hat{j} + 6\hat{k}$ and $-4\hat{i} + 9\hat{j} + 6\hat{k}$ are the position vectors of the vertices A, B and C repectively of $\triangle ABC$. Then the position vector of the point where the bisector of ...

If $a, b, c$ are distinct non-negative numbers and the vectors $a\hat{i} + a\hat{j} + c\hat{k}, \hat{i} + \hat{k}, c\hat{i} + c\hat{j} + b\hat{k}$ lie in the same plane, then the value of $c$ is...

Let $A(2,3,0)$, $B(0,3,2)$ and $C(4,0,3)$ be vertices of a triangle, then the area of the triangle is

If D and E are the midpoints of the sides BA and BC of triangle ABC, then $\overline{AE} + \overline{DC} = $