List of top Questions asked in MHT CET- 2023

Calculate the edge length of bcc unit cell if radius of metal atom is 227 pm.

Calculate the rate constant of the first order reaction if 80% of the reactant decomposes in 60 minutes.

Which from following polymers is classified fibres depending on inter molecular forces?

Which among the following is haloalkyne?

Let $P(x)$ be a polynomial of degree 2, with $P(2) = -1$, $P'(2) = 0$, $P''(2) = 2$, then $P(1.001)$ is

Let $f(x) = 5 - |x-2|$ and $g(x) = |x + 1|$, $x \in \mathbb{R}$. If $f(x)$ attains maximum value at $\alpha$ and $g(x)$ attains minimum value at $\beta$, then $\lim_{x \to \alpha\beta} \frac{(x-1)(x^2-5x+6)}{x^2-6x+8}$ is equal to}

Which of the following is a structural formula of DDT?

Given a polynomial $P(x) = ax^2 + bx + c$ such that $P''(2)=2$, $P'(2)=0$, and $P(2)=-1$. Find the approximate value of $P(1.001)$ using linear approximation.

The length of the perpendicular drawn from the point $(1, 2, 3)$ to the line $\frac{x-6}{3} = \frac{y-7}{2} = \frac{z-7}{-2}$ is

If $I = \int \frac{dx}{\sin(x-a) \sin(x-b)}$, then $I$ is given by}

A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to retail store. Then the probability that the store will receive at most one defective bulb is

If $a \cos 2\theta + b \sin 2\theta = c$ has $\alpha$ and $\beta$ as its roots, then the value of $\tan \alpha + \tan \beta$ is

A vector parallel to the line of intersection of the planes $\vec{r} \cdot (3\hat{i} - \hat{j} + \hat{k}) = 1$ and $\vec{r} \cdot (\hat{i} + 4\hat{j} - 2\hat{k}) = 2$ is

If $f(x) = \frac{2x-3}{3x-4}, x \neq \frac{4}{3}$, then the value of $f^{-1}(x)$ is

The area bounded by the curve $y = |x - 2|$, $x = 1$, $x = 3$ and X-axis is

$\int \frac{dx}{\cot^2 x - 1} = \frac{1}{A} \log |\sec 2x + \tan 2x| - \frac{x}{B} + c$, (where $c$ is constant of integration), then $A + B =$}

If $f'(x) = \sin(\log x)$ and $y = f\left(\frac{2x+3}{3-2x}\right)$, then $\frac{dy}{dx}$ at $x=1$ is

There are 6 positive and 8 negative numbers. From these four numbers are chosen at random and multiplied. Then the probability, that the product is a negative number, is

The centroid of the triangle formed by the lines $x + 3y = 10$ and $6x^2 + xy - y^2 = 0$ is

The statement $[p \land (q \lor r)] \lor [\sim r \land \sim q \land p]$ is equivalent to}

If the lines $\frac{x-k}{2} = \frac{y+1}{3} = \frac{z-1}{4}$ and $\frac{x-3}{1} = \frac{y-\frac{9}{2{2} = \frac{z}{1}$ intersect, then the value of k is

If $|\vec{a}| = \sqrt{3}$; $|\vec{b}| = 5$; $\vec{b} \cdot \vec{c} = 10$, angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{3}$, $\vec{a}$ is perpendicular to $\vec{b} \times \vec{c}$. Then the value of $|\vec{a} \times (\vec{b} \times \vec{c})|$ is

The value of $\tan^{-1} \left(\frac{1}{8}\right) + \tan^{-1} \left(\frac{1}{2}\right) + \tan^{-1} \left(\frac{1}{5}\right)$ is

In a triangle ABC, $m\angle A$, $m\angle B$, $m\angle C$ are in A.P. and lengths of two larger sides are 10 units, 9 units respectively, then the length (in units) of the third side is

If $\cos^{-1} x - \cos^{-1} \frac{y}{3} = \alpha$, where $-1 \le x \le 1$, $-3 \le y \le 3$, $x \le \frac{y}{3}$, then for all $x, y$, $9x^2 - 6xy \cos \alpha + y^2$ is equal to}