List of top Mathematics Questions asked in MHT CET

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

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

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

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

For the probability distribution given by following

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

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

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

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)

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 $|\vec{x}| =$

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

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?

Evaluate the indefinite integral $$\int \frac{dx}{\cos x \sqrt{\cos 2x}}$$

If the function defined by $f(x) = K(x - x^2)$ if $0 < x < 1$ and $f(x) = 0$ otherwise, is the probability density function (p.d.f.) of a random variable X, then the value of $P\left(X < \frac{1}{2}\right)$ is

If the slopes of the lines given by the equation $ax^2 + 2hxy + by^2 = 0$ are in the ratio $5 : 3$, then the ratio $h^2 : ab =$

For all real $x$, the minimum value of the function $f(x) = \frac{1 - x + x^2}{1 + x + x^2}$ is

The equation of the tangent to the curve $y = \sqrt{2} \sin\left(2x + \frac{\pi}{4}\right)$ at $x = \frac{\pi}{4}$ is

If $\vec{a} = 2\hat{\text{i}} - \hat{\text{j}} + \hat{\text{k}}$, $\vec{b} = \hat{\text{i}} + 2\hat{\text{j}} - 3\hat{\text{k}}$ and $\vec{c} = 3\hat{\text{i}} + \lambda\hat{\text{j}} + 5\hat{\text{k}}$ are coplanar, then $\lambda$ is the root of the equation

The domain of the function $\log_{10}(x^2 - 5x + 6)$ is

The general solution of the differential equation $\cos(x + y) \frac{dy}{dx} = 1$ is