MHT CET 2026 20th April Evening Shift

An aeroplane at an altitude of 1 km is flying horizontally at 600 km / hr, passes directly over an observer. Then the rate at which it is approaching the observer when it is 1250 meters away from him is........

The line $x + y = 0$ touches the curve $y^2 = ax^3 + b$ at $(1, -1)$ then values of $a$ and $b$ respectively are ...........

The function $f(x) = x(x + 3)e^{-\left(\frac{1}{2}\right)x}$ satisfies all the conditions of Rolle's theorem in $[-3, 0]$, then $c =$

The area in square units of the region bounded by the curve $y = \sqrt{16 - x^2}$ and lines $x = 0, x = 4$ above the X-axis is

The equation of a circle whose center lies on $x + 2y = 0$ and touching the lines $3x - 4y + 8 = 0$ and $3x - 4y - 28 = 0$ is

If $i = \sqrt{-1}$ then $\left[i^{18} + \left(\dfrac{1}{i}\right)^{25}\right]^3 =$

The value of the integral $\int\limits_{1/e}^{e}\dfrac{|\log x|}{x^2}dx$ is

If $\int\limits_{-\pi/2}^{\pi/2}(\sin^2 x + \sin^3 x)dx = k$, then the value of $k$

If $I_n = \int\limits_0^{\pi/4}\tan^n x\ dx, n \in N$ then $I_{n+2} + I_n$ is equal to

The general solution of the differential equation $\dfrac{dy}{dx} + \dfrac{y}{x} = x^2 + 5$ is ....

The order and degree of the differential equation $\sqrt{1 + \dfrac{1}{\left(\frac{dy}{dx}\right)^2}} = \left(\dfrac{d^2y}{dx^2}\right)^{\frac{3}{2}}$, respectively are

If $y = \cos^2\left[\cot^{-1}\left(\sqrt{\dfrac{1 - x}{1 + x}}\right)\right]$ then $\dfrac{dy}{dx} = $ ........

If $\sqrt{\dfrac{x}{y}} + \sqrt{\dfrac{y}{x}} = 6$, then $\dfrac{dy}{dx} =$

If $x = 4t^3 + 3, y = 3t^4 + 4$ and $\dfrac{\frac{d^2x}{dy^2}}{\left(\frac{dx}{dy}\right)^n}$ is constant then the value of $n$ is

If $x = a\sin^3 t$ and $y = a\cos^3 t$, then the value of $\dfrac{d^2y}{dx^2}$ at $t = \dfrac{\pi}{3}$ is equal to

If $P$ be any point on the ellipse $16x^2 + 25y^2 = 400$ with foci $S$ and $S'$ and area of $\triangle PSS'$ is 9 square units, then the abscissa of point $P$ is...........

The statement having truth value 'T' from the following is

If $f(x) = \dfrac{2x - 1}{x + 5}$, $x \neq -5$ then $f^{-1}(x)$ is equal to

If $f(x), g(x)$ be twice differentiable functions, satisfying $f''(x) = g''(x), f'(1) = 2g'(1) = 4$ and $f(2) = 3g(2) = 9$ then $f(x) - g(x)$ at $x = 4$ is equal to

If $\int f(x)dx = g(x) + c$ then $\int f^{-1}(x)dx =$

$\int\dfrac{\log x}{(1 + \log x)^2}dx =$

$\int\dfrac{1}{\sqrt{2x - x^2}}dx =$

$\int(x^{21} + x^6 + x^3)(2x^{18} + 7x^3 + 14)^{\frac{1}{3}}\ dx =$

If $3\sin^{-1}\left(\dfrac{2x}{1 + x^2}\right) - 4\cos^{-1}\left(\dfrac{1 - x^2}{1 + x^2}\right) + 2\tan^{-1}\left(\dfrac{2x}{1 - x^2}\right) = \dfrac{\pi}{3}$ then $x = ?$

If $2\sin^{-1}x - 3\cos^{-1}x = 4$, then $2\sin^{-1}x + 3\cos^{-1}x =$

The value of $\lim\limits_{n \to \infty}\left[\dfrac{1}{1 - n^2} + \dfrac{2}{1 - n^2} + \ldots + \dfrac{n}{1 - n^2}\right]^3$ is

If the function $f(x)$ defined by $f(x) = \begin{cases} ax + 1 & \text{if } x \leq 3 \\ bx + 3 & \text{if } x > 3 \end{cases}$ is continuous at $x = 3$, then $(a - b) =$ ..........

The LPP maximize $z = 2x + 5y$ subject to $x + 3y \leq 6$, $2x + 6y \leq 18$, $x \geq 0$, $y \geq 0$ has

If $\sim p \vee q$ is false then which of the following is correct?

The contrapositive of $\sim q \rightarrow p$ is equivalent to

If $A = \begin{bmatrix} 1 & -5 \\ -2 & 4 \end{bmatrix}$, then $A^{-1} =$

Let $A = \begin{bmatrix} 3 & 1 & 2 \\ 1 & 2 & 0 \\ 1 & 1 & 4 \end{bmatrix}$ and $pC_{11} + 4C_{21} - 5C_{32} = -2$, where $C_{ij}$ denotes the cofactor of an element $a_{ij}$ of matrix $A$, then the value of $p$ is :

The number of permutations of the letters of the word INSTITUTION are .......

Four cards are drawn successively with replacement from well shuffled deck of 52 cards, then the probability that only two cards are club cards is ...........

For the following probability distribution of a random variable $X$, the Expected value and Variance of $X$ are respectively$X = x\(1\)2\(3\)P(X = x)\(1/5\)2/5$$2/5$

A fair die is rolled indefinitely. Player A wins if two consecutive rolls show 3 or 5, and player B wins if two consecutive rolls show 1 or 2 or 4 or 6. The probability that player A wins in the long run is

The angles of $\triangle ABC$ are in A.P. and $b : c = \sqrt{3} : \sqrt{2}$ then $\angle A =$

With the usual notations, if the lengths of the sides of the triangle are 3 units, 5 units and 7 units, then the largest angle of the triangle is

A straight line makes equal negative intercepts on the coordinate axes. If the perpendicular distance from the origin to the line is 4 units, then the equation of the line is ......

If the angle made by the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ with X-axis are $\alpha$ and $\beta$, then $\tan(\alpha + \beta)$ is

If the perpendicular distance of the plane passing through the point $Q(1, 0, -1)$ and containing the line $\vec{r} = (\hat{i} - 3\hat{j} + \hat{k}) + \lambda(2\hat{i} - 2\hat{j} + \hat{k})$ from origin is $\dfrac{p}{\sqrt{53}}$ then $p = $...

If the line joining points $(2, 1, 4)$ and $(a - 1, 4, -1)$ is parallel to the line joining points $(0, 2, b - 1)$ and $(5, 3, -2)$ then the values of $b$ and $a$ are respectively

Lines $\vec{r} = \vec{a} + \lambda\vec{b}$ and $\vec{r} = \vec{b} + \mu\vec{a}$ intersect at point $(2, 4, -4)$. If $|\vec{a} - \vec{b}| = 4$, then $\vec{a} \cdot \vec{b} =$

The Cartesian equations of the line passing through $A(0, 1, 1)$ and parallel to the X-axis are ....

If $x + y = \dfrac{\pi}{4}$, then $(1 + \tan x)(1 + \tan y) =$

Let $\vec{a} = 2\hat{i} + \hat{k}, \vec{b} = \hat{i} + \hat{j} + \hat{k}$, and $\vec{c} = 4\hat{i} - 3\hat{j} + 7\hat{k}$. If $\vec{r}$ is a vector such that $\vec{r} \times \vec{b} = \vec{c} \times \vec{b}$ and $\vec{r} \cdot \vec{a} = 0$,...

If $\vec{u} = \hat{i} + 2\hat{j} - 2\hat{k}, \vec{v} = 2\hat{i} + \hat{k}$ and $\vec{w}$ is unit vector then the maximum value of scalar triple product $[\vec{u}\ \vec{v}\ \vec{w}]$ is

If $\vec{a}, \vec{b}, \vec{c}$ are three non-coplanar vectors and $\vec{p}, \vec{q}, \vec{r}$ are defined as $\vec{p} = \dfrac{\vec{b} \times \vec{c}}{[\vec{a}\ \vec{b}\ \vec{c}]}, \vec{q} = \dfrac{\vec{c} \times \vec{a}}{[\vec{a}\ \vec{b}\...

The volume of the parallelopiped whose coterminous edges are $2\hat{i} + \hat{j} - \hat{k}, 3\hat{i} - \hat{j} - \hat{k}, \hat{j} + 3\hat{k}$ is

Given the following expressionA) $(\vec{a} \times \vec{b}) \cdot \vec{c}$B) $\vec{a} \times (\vec{b} \cdot \vec{c})$C) $\vec{a} \cdot (\vec{b} \cdot \vec{c})$D) $|\vec{a}|(\vec{b} \cdot \vec{c})$E) $(\vec{a} \cdot \vec{b}) \times (\vec{b} \...