List of top Questions asked in MHT CET- 2025

A normal is drawn at a point $P(x, y)$ of a curve $y = f(x)$. The normal meets the $X$ axis at $Q$. $l(PQ) = k \cdot$ (k is a constant) Then equation of the curve through $(0, k)$ is

The equation of the plane passing through the line of intersection of the planes $x + y + z = 1$ and $3x + 4y + 5z = 2$ and perpendicular to the XY- plane is

If $f(x) = \frac{(27-2x)^{\frac{1}{3}} - 3}{9 - 3(243+5x)^{\frac{1}{5}}}, x \ne 0$ is continuous at $x = 0$, then the value of $f(0)$ is

$\lim_{x \to 0} \frac{|x|}{|x| + x^2} =$}

The solution of $\frac{dy}{dx} = (x + y)^2$ is

In a game, 3 coins are tossed. A person is paid Rs \( 150 \) if he gets all heads or all tails and he is supposed to pay ₹\( 50 \) if he gets one head or two heads. The amount he can expect to win lose on an average per game in ₹ is

If $A = \begin{bmatrix} 1 & 2 \\ -1 & 4 \end{bmatrix}$ and $A^{-1} = \alpha I + \beta A$, $\beta \in R$ where I is the identity matrix of order 2, then $4(\alpha + \beta) =$}

The principal increases continuously in a newly opened bank at the rate of $10%$ per year. An amount of Rs. 2000 is deposited with this bank. How much will it become after 5 years? ($e^{0.5} = 1.648$)

Which of the following are pairs of equivalent circuits

If two sides of a triangle are \( \sqrt{3} - 1 \) and \( \sqrt{3} + 1 \) units and their included angle is \( 60^\circ \), then the third side of the triangle is

If \( \sin \left(\sin^{-1} \frac{1}{5} + \cos^{-1} x\right) = 1 \), then the value of \( x \) is

A plane passes through \( (2, 1, 2) \) and \( (1, 2, 1) \) and parallel to the line \( 2x = 3y \) and \( z = 1 \), then the plane also passes through the point

If \( a^2 + b^2 + c^2 = r^2 \), then the value of \( \tan^{-1}\left(\frac{ab}{cr}\right) + \tan^{-1\left(\frac{bc}{ar}\right) + \tan^{-1}\left(\frac{ca}{br}\right) = \)}

The value of \( \int_{1/3}^{1} \frac{(x - x^3)^{\frac{1{3}}}{x^4} dx \) is

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

If triangle ABC is a right angled at A and \( \tan \frac{\text{B}}{2}, \tan \frac{\text{C}}{2} \) are roots of the equation \( a x^2 + bx + c = 0, \text{a} \ne 0 \), then

The feasible region for the constraints \( x - 2 \le y, x \ge y - 1, x \ge 2, y \le 4, x, y \ge 0 \), is

Let X be a discrete random variable. The probability distribution of X is given below

and E(X) = 4, then the value of AB is equal to

The perpendicular distance between the lines given by \( (x - 2y + 1)^2 + \text{k(x - 2y + 1) = 0 \) is \( \sqrt{5} \), then k =}

If \( \tan \text{A} = \frac{1}{\sqrt{x(x^2+x+1) \), \( \tan \text{B} = \frac{\sqrt{x}}{\sqrt{x^2+x+1}} \) and \( \tan \text{C} = \sqrt{x^{-1} + x^{-2} + x^{-3}} \) then}

If \( x^{\frac{2}{5}} + y^{\frac{2}{5}} = \text{a}^{\frac{2}{5}} \) then \( \frac{dy}{dx} = \)

The projection of the line segment joining the points \( (2, 1, -3) \) and \( (-1, 0, 2) \) on the line whose direction ratios are \( 3, 2, 6 \) is

The differential equation of all straight lines passing through the point \( (1, -1) \) is

The first derivative of the function \( \left( \cos^{-1}\left(\sin\sqrt{\frac{1+x}{2}}\right) + x^x \right) \) with respect to \( x \) at \( x = 1 \) is

The area enclosed between the curves \( y^2 = 4x \) and \( y = |x| \) is