List of top Questions asked in MHT CET

With usual notations, in a triangle $ABC$, if $\theta$ is any real number, then $a \cos(B - \theta) + b \cos(A + \theta)$ is

The shaded region in the following figure represents a solution set of

If $\tan 3\theta = \cot \theta$, then $\theta =$

In a triangle ABC with usual notations, if a, b, c are in arithmetic progression, then, $\tan \frac{A}{2} \cdot \tan \frac{C}{2} =$}

If $y = \log_e x^3 + 3 \sin^{-1} x + kx^2$ and $y'\left(\frac{1}{2}\right) = 2\sqrt{3}$, then $k =$}

If $f(1) = 1, f'(1) = 3$, then the derivative of $f(f(f(x))) + (f(x))^2$ at $x = 1$ is

In a triangle ABC, with usual notations if $\frac{2\cos A}{a} + \frac{\cos B}{b} + \frac{2\cos C}{c} = \frac{a}{bc} + \frac{b}{ca}$ then $\angle A =$}

If $\tan^{-1}\left(\frac{x}{2}\right) + \tan^{-1}\left(\frac{y}{2}\right) + \tan^{-1}\left(\frac{z}{2}\right) = \frac{\pi}{2}$ then $xy + yz + zx =$}

If the plane $\frac{x}{3} + \frac{y}{2} - \frac{z}{4} = 1$ cuts the co-ordinate axes at points A, B and C, then the area of the triangle ABC is

If $y = x^x + x^{\frac{1}{x}}$, then $\frac{dy}{dx}$ is equal to}

The distance between the lines represented by the equation $4x^2 + 4xy + y^2 - 6x - 3y - 4 = 0$ is

The magnitude of a vector which is orthogonal to the vector $\hat{i} + \hat{j} + \hat{k}$ and is coplanar with the vectors $\hat{i} + \hat{j} + 2\hat{k}$ and $\hat{i} + 2\hat{j} + \hat{k}$ is

If $A + B = \frac{\pi}{2}$ then the maximum value of $\cos A \cdot \cos B$ is

$\int \frac{dx}{2+\cos x} =$}

A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides are

If $\bar{a}$ and $\bar{b}$ are unit vectors and $\theta$ is the angle between them, then $\bar{a} + \bar{b}$ is a unit vector when $\theta$ is

The money invested in a company is compounded continuously. Rs. 400 invested today becomes Rs. 800 in 6 years, then at the end of 33 years, it will become .. ($\sqrt{2} = 1.4142$)

If $\int \frac{2x+3}{(x-1)(x^2+1)} dx = \log_e \left\{ (x - 1)^{\frac{5}{2}} (x^2 + 1)^a \right\} - \frac{1}{2} \tan^{-1} x + A$ where A is an arbitrary constant, then the value of $a$ is

The function defined by $f(x) = \frac{2x+3}{3x+4}, x \neq -\frac{4}{3}$ is

If two numbers $p$ and $q$ are chosen randomly from the set $\{1, 2, 3, 4\}$, one by one, with replacement, then the probability of getting $p^2 \ge 4q$ is

The value of $\int_{-1}^{1} (\sqrt{1 + x + x^2} - \sqrt{1 - x + x^2}) dx$ is

The area of the triangle formed by the lines joining the vertex of the parabola $x^2 = 20y$ to the end of its latus rectum is

$\lim_{x \to 0} \frac{e^{\tan x} - e^x}{\tan x - x} =$}

$\int_{-2}^{2} |x^2 - x - 2| dx =$}

If $f(x) = \begin{cases} mx + 1, & x \le \frac{\pi}{2} \\ \sin x + n, & x > \frac{\pi}{2} \end{cases}$ is continuous at $x = \frac{\pi}{2}, (m, n \in \mathbb{Z})$ then}