List of top Questions asked in MHT CET- 2021

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

The area of the parallelogram with vertices \( A(1, 2, 3) \), \( B(1, 3, a) \), \( C(3, 8, 6) \) and \( D(3, 7, 3) \) is \( \sqrt{265} \) sq. units, then \( a = \)

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

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

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 \( A = \)

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

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 \( f = \)

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

If \[ \lim_{x \to 5} \frac{x^k - 5^k}{x - 5} = 500 \], then the value of \( k \), where \( k \in \mathbb{N} \) is

If the half life period of a substance is 5 years, then the total amount of the substance left after 15 years, when initial amount is 64 gms 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

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 \(\frac{dy}{dx} =\)

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

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

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

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

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

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 $p =$

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

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