List of top Mathematics Questions asked in MHT CET

If \( y = \tan^{-1} \left\{ \frac{a \cos x - b \sin x}{b \cos x + a \sin x} \right\} \), then \( \frac{dy}{dx} = \)

If \( y = \tan^{-1} \left( \frac{a \cos x - b \sin x}{b \cos x + a \sin x} \right) \), then \( \frac{dy}{dx} = \)

With usual notations, perimeter of a triangle \( ABC \) is 6 times the arithmetic mean of sine of its angles. If \( a = 1 \), then measure of angle \( A = \)

Let \( A = \{10, 11, 12, 14, 26\} \) and let \( f : A \to \mathbb{N} \) be such that \( f(a) = \) highest prime factor of \( a \), where \( a \in A \), then range of \( f = \)

If \( \theta + \phi = \alpha \) and \( \tan \theta = k \tan \phi \) (where \( k > 1 \)), then the value of \( \sin(\theta - \phi) \) is

If \( m \) is order and \( n \) is degree of the differential equation \[ \left( \frac{d^2y}{dx^2} \right)^5 + 4 \left( \frac{\frac{d^2y}{dx^2}}{\frac{d^3y}{dx^3}} \right) + \left( \frac{d^3y}{dx^3} \right) = x^2 \] then

If \( p \to (\sim p \lor q) \) is false, then the truth values of \( p \) and \( q \) are, respectively

If \[ \int \frac{5 \tan x}{\tan x - 2} dx = x + a \log | \sin x - 2 \cos x | + c \], then \( a = \) (Where \( c \) is constant of integration)

For a set of five true or false questions, no student has written the all correct answers and no two students have given the same sequence of answers. The maximum number of students in the class for this to be possible is

The general solution of the differential equation. \[ \left( \frac{y}{x} \right) \cos \left( \frac{y}{x} \right) dx - \left[ \left( \frac{x}{y} \right) \sin \left( \frac{y}{x} \right) + \cos \left( \frac{y}{x} \right) \right] dy = 0 \] is

A bakerman sells 5 types of cakes. Profit due to sale of each type of cake is respectively ₹ 2.5, ₹ 3, ₹ 1.5, ₹ 1 and ₹ 2. The demands for these cakes are 20%, 5%, 10%, 50% and 15% respectively, then the expected profit per cake is

The logical statement \((p \to q) \land (q \to \sim p)\) is equivalent to

The number of solutions of \( \cos 2\theta = \sin \theta \) in \( (0, 2\pi) \) are

The area bounded by the parabola \( y^2 = x \), the straight line \( y = 4 \) and \( Y \) axis is

If \( y = \tan^{-1} \left[ \frac{1}{1+x+x^2} \right] + \tan^{-1} \left[ \frac{1}{x^2+3x+3} \right] \), \( x > 0 \), then \(\frac{dy}{dx} =\)

If \( \sin^{-1}\left(\frac{3}{5}\right) + \cos^{-1}\left(\frac{12}{13}\right) = \sin^{-1}\alpha \), then \( \alpha = \)

If \( z(2 - i) = (3 + i) \), then \( z^{38} = \), (where \( z = x + iy \))

The function \( f(x) = \log(1 + x) - \frac{2x}{2+x} \) is increasing on

The equation of a line passing through $(3, -1, 2)$ and perpendicular to the lines $\bar{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda (2\hat{i} - 2\hat{j} + \hat{k})$ and $\bar{r} = (2\hat{i} + \hat{j} - 3\hat{k}) + \mu (\hat{i} - 2\hat{j} + 2\hat{k})$ is

Let $f(x)$ be a function defined as: $$f(x) = \begin{cases} \frac{\sqrt{1 + px} - \sqrt{1 - px}}{x}, & \text{if } -1 \leq x < 0 \\ \frac{2x + 1}{x - 2}, & \text{if } 0 \leq x \leq 1 \end{cases}$$ If $f(x)$ is continuous in the interval $[-1, 1]$, then $p =$

If \( y = 2 \sin x + 3 \cos x \) and \( y + A \frac{d^2 y}{dx^2} = B \), then the values of \( A, B \) are respectively

If \( A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{bmatrix} \), then \( A^{-1} = \)

The equation of circle with centre at \( (2, -3) \) and the circumference \( 10\pi \) units is

The coordinates of the point $P \equiv (1,2,3)$ and $O \equiv (0,0,0)$ are given. The direction cosines of $\overline{OP}$ are

Evaluate the definite integral: $$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\cos x}{1 + e^x}\ dx$$