List of top Mathematics Questions asked in MHT CET

In $\triangle ABC$, if $2a^2 = b^2 + c^2$, then the value of $\frac{\cos 3A}{\cos A} + 2$ is

The value of $\tan^{-1}(\sqrt{3}) + \sec^{-1}(-2) - \sin^{-1}\left(-\frac{1}{2}\right)$ is

Evaluate the integral: \(\int \frac{2x}{x^2 - 5x + 4} \, dx\)

Evaluate the integral: \(\int \frac{\sin x}{\sin 4x} \, dx\)

For the curve \(y = 3x^3 - 3x^2 + 1\) at \(x = 1\), find the equation of the tangent.

A plane is formed by the axes whose centroid is \(\left(2, -\frac{2}{3}, \frac{1}{2}\right)\). Find the distance of the plane from the origin.

Evaluate: \(\int_0^3 \sqrt{9 - x^2} \, dx\).

If \(\tan^{-1}(-1) + \tan^{-1}(5) + \tan^{-1}(3) + \tan^{-1}\left(\frac{1}{4}\right) = \pi + \tan^{-1}\left(\frac{\alpha}{2}\right)\), find \(\alpha\).

Given \(\int_1^a (2x + 1) \, dx = 5\), find the sum of all values of \(a\).

Determine the shortest distance between the lines \( \dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{4} \) and \( \dfrac{x-2}{3} = \dfrac{y-4}{4} = \dfrac{z-5}{5} \).

Evaluate the integral: \[ \int_{3}^{5} |x-4|\,dx \]

The projection of the line segment joining P(2, -1, 0) and Q(3, 2, -1) on the line whose direction ratios are 1, 2, 2 is

The equation of the curve passing through $(2, \frac{9}{2})$ and having the slope $(1 - \frac{1}{x^2})$ at $(x, y)$ is

Four defective oranges are accidentally mixed with sixteen good ones. Three oranges are drawn from the mixed lot. The probability distribution of defective oranges is

The general solution of the differential equation $\frac{\text{d}y}{\text{d}x} + \sin \left( \frac{x+y}{2} \right) = \sin \left( \frac{x-y}{2} \right)$ is

The value of the integral $\int_1^2 \frac{x \text{ d}x}{(x+2)(x+3)}$ is

In a box containing 100 apples, 10 are defective. The probability that in a sample of 6 apples, 3 are defective is

Three urns respectively contain 2 white and 3 black, 3 white and 2 black and 1 white and 4 black balls. If one ball is drawn from each um, then the probability that the selection contains 1 black and 2 white balls is

$\int \text{e}^{2x} \frac{(\sin 2x \cos 2x-1)}{\sin^2 2x} \text{d}x =$

If four digit numbers are formed by using the digits 1, 2, 3, 4, 5, 6, 7 without repetition, then out of these numbers, the numbers exactly divisible by 25 are

An open tank with a square bottom is to contain 4000 cubic cm . of liquid. The dimensions of the tank so that the surface area of the tank is minimum, is

If the lengths of three vectors $\bar{a}, \bar{b}$ and $\bar{c}$ are 5, 12, 13 units respectively, and each one is perpendicular to the sum of the other two, then $|\bar{a} + \bar{b} + \bar{c}| = ..............$

$\int \sec^{\frac{2}{3}} x \cdot \csc^{\frac{4}{3}} x dx =$

If $f(x) = \begin{cases} \frac{1-\cos 4x}{x^2} & , \text{if } x<0 \\ a & , \text{if } x = 0 \\ \frac{(16+\sqrt{x})^{\frac{1}{2}}-4}{\sqrt{x}} & , \text{if } x>0 \end{cases}$ is continuous at $x = 0$, then a =}