List of top Questions asked in MHT CET- 2025

In a triangle ABC, with usual notations, $\cot\left(\frac{A+B}{2}\right) \cdot \tan\left(\frac{A-B}{2}\right) = $ ______.

In a triangle ABC, with usual notations, $(a + b + c)(a + b - c) = 3ab$, then $\angle C = $ ______.

If $\int \frac{(x^4+1)}{x(x^2+1)^2} \, dx = A \log |x| + \frac{B}{1+x^2} + c$, then $A - B$ is ______.

If $\vec{a}$, $\vec{b}$, $\vec{c}$ are three coplanar vectors such that $|\vec{a}| = 1$, $|\vec{b}| = 2$, $\vec{b} \cdot \vec{c} = 8$, the angle between $\vec{b}$ and $\vec{c}$ is $45^\circ$, then $|\vec{a} \times (\vec{b} \times \vec{c})| = $ ______.

The solution for minimizing the function $z = x + y$ under an L.P.P. with constraints $x + y \ge 2$, $x + 2y \le 8$, $y \le 3$, $x, y \ge 0$ is ______.

The circumcenter of the triangle formed by lines $xy + 2x + 2y + 4 = 0$ and $x + y + 2 = 0$ is ______.

A triangle ABC is formed by A(1, -1, 0), B(3, 5, 3), C(-11, -5, 6). The equation of the internal angle bisector of angle A is ______.

The angle between the tangents drawn from the point (1, 4) to the parabola $y^2 = 4x$, is ______.

If $\vec{a} = \lambda x \hat{i} + y \hat{j} + 4z \hat{k}$, $\vec{b} = x \hat{i} + y \hat{j} + 3y \hat{k}$, and $\vec{c} = -2 \hat{i} - 2z \hat{j} - (\lambda + 1) \hat{k}$ such that $\vec{a} + \vec{b} - \vec{c} = \vec{0}$, then the value of $\lambda$ is ______.

The angle between lines whose direction cosines satisfy the equation $l + m + n = 0$ and $l^2 - m^2 - n^2 = 0$, is ______.

If $y = \alpha \log x + \beta x^2 - x$ has extreme values at $x = -1$ and $x = 1$, then $\alpha$ and $\beta$ are respectively ______.

A manufacturer sells $x$ items at a price of ₹$(6 - \frac{x}{40})$ each. The cost price of $x$ items is ₹$(\frac{x}{5} + 193)$. The maximum profit in ₹ is ______.

The following is p.d.f. of continuous random variable X: $f(x) = \frac{x}{8}$ for $0 < x < 4$. Then $F(0.5)$, $F(1.7)$ and $F(5)$ is respectively ______.

The equation of the tangent to the curve $(1 + x^2)y = 2 - x$, where it crosses the X-axis, is ______.

The mirror image of the point $P(-1, 2, -4)$ in the plane $x - y - 2z + 1 = 0$ is ______.

The cumulative distribution function of a discrete random variable X is given. Then $\frac{P(X \le 0)}{P(X > 0)} = $ ______.

The equation of a curve passing through (1,0) and having slope of tangent at any point (x, y) of the curve as $\frac{y-1}{x^2+x}$ is ______.

$\lim_{x \to \infty} \frac{(2x+1)^{50} + (2x+2)^{50} + (2x+3)^{50} + \dots + (2x+100)^{50}}{(2x)^{50} + (10)^{50}} = $ ______.

$\int_{1/2}^{2} \frac{1}{x} \csc^{101} \left( x - \frac{1}{x} \right) dx = $ ______.

The number of ways in which a team of 11 players can be formed out of 25 players, if 6 out of them are always to be included and 5 of them are always to be excluded, is ______.

A box contains 8 red and $x$ number of green balls. 3 balls are drawn at random, if the probability that 3 balls being red is $\frac{7}{15}$, then number of green balls is ______.

The differential equation which represents the family of curves $y = c_1 e^{c_2 x}$, where $c_1, c_2$ are arbitrary constants is ______.

If $f(x) = \frac{\sin^2 x}{1+\cot x} + \frac{\cos^2 x}{1+\tan x}$, then the value of $f'(\frac{\pi}{6})$ is equal to ______.

$\int \frac{\sqrt{\tan x}{\sin x \cdot \cos x} \, dx = $ ______.

If the plane $\frac{x}{2} + \frac{y}{3} + \frac{z}{6} = 1$ cuts the co-ordinate axes at points A, B, C respectively, then area of the triangle ABC is ______.