List of top Questions asked in MHT CET

Evaluate the integral: $\int \frac{10^{x/2}}{\sqrt{10^{-x} - 10^x}} dx$

If $3 \sin \theta = 2 \sin 3 \theta$ and $0 < \theta < \pi$, then $\sin \theta =$

Evaluate the integral: $\int_0^{\pi / 2} \frac{\cos x}{3 \cos x + \sin x} dx$

The particular solution of differential equation $(x + y) dy + (x - y) dx = 0$ at $x = y = 1$ is

The maximum value of the objective function $z = 2x + 3y$ subject to the constraints $x + y \le 5$, $2x + y \ge 4$ and $x \ge 0, y \ge 0$ is

The general solution of the differential equation $\frac{dy}{dx} + \frac{y^2+y+1}{x^2+x+1} = 0$ is

Evaluate the trigonometric expression: $\tan \left(\cos^{-1}\left(\frac{4}{5}\right) + \tan^{-1}\left(\frac{2}{3}\right)\right) =$

Function $f(x) = e^{-1/x}$ is strictly increasing for all $x$ where

The general solution of the differential equation $\frac{dx}{dt} = \frac{x \log x}{t}$ is

Evaluate the integral: $\int_{0}^{1} |5x - 3| dx$

The distance between the parallel lines $\frac{x-2}{3}=\frac{y-4}{5}=\frac{z-1}{2}$ and $\frac{x-1}{3}=\frac{y+2}{5}=\frac{z+3}{2}$ is

The equation of line, where length of the perpendicular segment from origin to the line is 4 and the inclination of this perpendicular segment with the positive direction of X-axis is $30^\circ$, is

If $\int \frac{\sin x}{\sin (x-\alpha)} dx = Ax + B \log |\sin (x-\alpha)| + c$, then the value of A and B are respectively (where c is a constant of integration)

S1 : If $-7$ is an integer, then $\sqrt{-7}$ is a complex number
S2 : $-7$ is not an integer or $\sqrt{-7}$ is a complex number
Choose the correct statement from the options given below

For the probability distribution given by following

the value of $\text{Var}(X) =$

Let $\vec{v} = 2\hat{i} + 2\hat{j} - \hat{k}$ and $\vec{w} = \hat{i} + 3\hat{k}$. If $\vec{u}$ is a unit vector, then the maximum value of the scalar triple product $[\vec{u} \,\, \vec{v} \,\, \vec{w}]$ is

The probability distribution of the number of doublets in four throws of a pair of dice is given by

A balloon contains 2.27 L air and has a pressure of $1.013 \times 10^5 \text{ Nm}^{-2}$. The balloon rises to a certain height and expands to volume of 4540 mL. What is the final pressure of air in balloon?

Which among the following is a nonferrous alloy?

Identify product 'B' in following reaction.
$\text{CH}_3\text{Br} + \text{AgNO}_2 \longrightarrow \text{A} \xrightarrow{\text{Sn / HCl}} \text{B}$

If A(3, 2, $-1$), B($-2$, 2, $-3$) and D($-2$, 5, $-4$) are the vertices of a parallelogram, then the area of the parallelogram is

If $\hat{a}$ is a unit vector such that $(\vec{x} - \hat{a}) \cdot (\vec{x} + \hat{a}) = 8$, then $|\vec{x}| =$

The order of reaction for which the units of rate constant are mol dm$^{-3}$ s$^{-1}$ is

Identify the major product when anisole is treated with $\text{Br}_2$ in presence of acetic acid.

What is the IUPAC name of glyoxal?