List of top Questions asked in MHT CET

The order of the differential equation whose solution is $y = a \cos x + b \sin x + c e^{-x}$ is

The velocity of a particle at time $t$ is given by the relation $v = 6t - \frac{t^2}{6}$. If its displacement $S$ is zero at $t = 0$, then the distance travelled in $3\ \text{sec}$ is

$f(x) = \log|\sin x|$, where $x \in (0, \pi)$ is strictly increasing on

If the angle between two lines is $\frac{\pi}{4}$ and the slope of one of the lines is $\frac{1}{2}$, then the slope of the other line is

The length of perpendicular drawn from the point $2\hat{i} - \hat{j} + 5\hat{k}$ to the line $\vec{r} = (11\hat{i} - 2\hat{j} - 8\hat{k}) + \lambda(10\hat{i} - 4\hat{j} - 11\hat{k})$ is

The arithmetic mean of marks in Mathematics for four divisions A, B, C and D were 80, 75, 70 and 72 respectively. Their standard deviations were 12, 6, 8 and 10 respectively. Then, which division has more uniformity.

If $u = \cos^3 x$ and $v = \sin^3 x$, then $\left(\frac{dv}{du}\right)_{x = \frac{\pi}{4}}$ is equal to

The particular solution of the differential equation $\frac{dy}{dx} = \frac{x+y+1}{x+y-1}$ when $x = \frac{2}{3}$ and $y = \frac{1}{3}$ is

If $a\sin\theta = b\cos\theta$, where $a, b \neq 0$, then $a\cos 2\theta + b\sin 2\theta = $

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

If $\vec{a} = 4\hat{i} + 13\hat{j} - 18\hat{k}$, $\vec{b} = \hat{i} - 2\hat{j} + 3\hat{k}$, and $\vec{c} = 2\hat{i} + 3\hat{j} - 4\hat{k}$ are three vectors such that $\vec{a} = x\vec{b} + y\vec{c}$, then $x + y = $

If the probability distribution function of a random variable $X$ is given as

Then $F(0)$ is equal to

If $f(x) = \frac{x}{2x+1}$ and $g(x) = \frac{x}{x+1}$, then $(f \circ g)(x) = $

The difference between the maximum values of $^{6}\mathrm{C}_r$ and $^{n}\mathrm{C}_r$ is 16, then $n = $

If the lines represented by $ax^2 - bxy - y^2 = 0$ make angles $\alpha$ and $\beta$ with the positive direction of the $X$-axis, then $\tan(\alpha + \beta) = $

$\lim_{x \rightarrow 1} \frac{ab^x - a^x b}{x^2 - 1} = $

The maximum area of the rectangle that can be inscribed in a circle of radius $r$ is

If the population grows at the rate of $8\%$ per year, then the time taken for the population to be doubled is (Given $\log 2 = 0.6912$)

$\int_{0}^{4} x[x] , dx = $
(where $[x]$ denotes the greatest integer function not greater than $x$)

Which from following polymers is used to manufacture tyres?

Which among following is an example of cyclic amide?

The conductivity of $0.04\ \mathrm{M}\ \mathrm{BaCl_2}$ solution is $0.0112\ \Omega^{-1}\ \mathrm{cm^{-1}}$ at $25^\circ\text{C}$. What is its molar conductivity?

Identify the conjugate acid-base pair in the following reaction:
$$\mathrm{HCl(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + Cl^-(aq)}$$

For the reaction $\mathrm{A + B \rightarrow \text{product}}$, the rate of reaction is $3.6 \times 10^{-2}\ \mathrm{mol\ dm^{-3}\ sec^{-1}}$. When $[\mathrm{A}] = 0.2\ \mathrm{mol\ dm^{-3}}$ and $[\mathrm{B}] = 0.1\ \mathrm{mol\ dm^{-3}}$, find the rate constant of the reaction if it is second order with respective to both reactants.

Which of the following polymers is used to obtain shopping bags?