List of top Questions asked in MHT CET

What type of peptide is the glycylalanine?

Which among the following is haloalkyne?

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

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

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.

Which of the following is a structural formula of DDT?

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}

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

A 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

$\int \frac{dx}{\cot^2 x - 1} = \frac{1}{A} \log |\sec 2x + \tan 2x| - \frac{x}{B} + c$, (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 area bounded by the curve $y = |x - 2|$, $x = 1$, $x = 3$ and X-axis is

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

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 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}

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}

The differential equation representing the family of curves $y^2 = 2c(x + \sqrt{c})$, where $c$ is a positive parameter, is of}

The p.m.f. of a random variable X is $P(x) = \begin{cases} \frac{2x}{n(n+1)}, & x = 1, 2, 3, ....... n \\ 0, & \text{otherwise} \end{cases}$, then $E(X)$ is

If $f(a) = 2$, $f'(a) = 1$, $g(a) = -1$, $g'(a) = 2$, then as $x$ approaches $a$, $\frac{g(x)f(a)-g(a)f(x)}{(x-a)}$ approaches}