List of top Questions asked in MHT CET- 2025

For $\text{n} \in \mathbb{N}$ if $y = \text{a}x^{\text{n}+1} + \text{b}x^{-\text{n}}$, then $x^2 \frac{\text{d}^2 y}{\text{d}x^2} =$

The feasible region represented by the given constraints $2x + 3y \ge 12, -x + y \le 3, x \le 4, y \ge 3$ is denoted by

The solution of the differential equation $x \frac{\text{d}^2 y}{\text{d}x^2} = 1$ at $x = y = 1$ with $\frac{\text{d}y}{\text{d}x} = 0$ at $x = 1$, is

If the points $\text{A}(2 - x, 2, 2), \text{B}(2, 2 - y, 2), \text{C}(2, 2, 2 - z)$ and $\text{D}(1, 1, 1)$ are coplanar, then the locus of point $\text{P}(x, y, z)$ is

If the sum of the squares of the distance of the point $\text{P}(x, y, z)$ from the co-ordinate axes is 242 , then the distance of the point P from the origin is units.

$\int_1^e \frac{e^x}{x}(1 + x \log x) dx =$

The volume of the tetrahedron whose co-terminus edges are $\bar{a}, \bar{b}, \bar{c}$ is 12 cubic units. If the scalar projection of $\bar{a}$ on $\bar{b} \times \bar{c}$ is 4 , then $|\bar{b} \times \bar{c}| =$

The ratio of the areas bounded by the curves $y = \cos x$ and $y = \cos 2x$ between $x = 0, x = \frac{\pi}{3}$ and X -axis is

In a bank, the principal increases continuously at a rate of $x%$ per year. Then the rate $x$, if Rs.\ 100 doubles itself in 10 years, is ($\log 2 = 0.6931$)

If $4 \sin^{-1} x + \cos^{-1} x = \pi$ then $x =$

The number of common tangents that can be drawn to the circles $x^2 + y^2 - 6x = 0$ and $x^2 + y^2 + 6x + 2y + 1 = 0$ is ________

If a random variable $X$ follows the Binomial distribution $\text{B}(33, \text{p})$ such that $3\text{P}(\text{X} = 0) = \text{P}(\text{X} = 1)$, then the variance of X is

If $y = y(x)$ satisfies $\left(\frac{2+\sin x}{1+y}\right) \frac{dy}{dx} = -\cos x$ such that $y(0) = 2$, then $y\left(\frac{\pi}{2}\right)$ is equal to

The ratios of sides in a triangle ABC are $5 : 12 : 13$ and its area is 270 . Then sides of the triangle are

The value of $\int_1^4 \log[x]\text{d}x$, where $[x]$ is the greatest integer function is equal to

$\int \frac{\text{e}^{2030 \log x} - \text{e}^{2029 \log x}}{\text{e}^{2028 \log x} - \text{e}^{2027 \log x}} \text{d}x = .......$

If a random variable $X$ has the p.d.f. $f(x) = \begin{cases} \frac{k}{x^2+1} & , \text{if } 0<x<\infty \\ 0 & , \text{otherwise} \end{cases}$ then c.d.f. of X is

The order and degree of differential equation of all tangent lines to the parabola $x^2 = 4y$ is respectively.

$\int \frac{\text{d}x}{2\text{e}^{2x}+3\text{e}^x+1} =$

The probability distribution of a discrete random variable X is

If $\text{a} = \text{P}(x<3)$ and $\text{b} = \text{P}(2 \le \text{X}<4)$, then

A plane passes through $(1, -2, 1)$ and is perpendicular to the planes $2x - 2y + z = 0$ and $x - y + 2z = 4$. The distance of the point $(1, 2, 2)$ from this plane is ________ units.

The point of intersection of the diagonals of the rectangle whose sides are contained in the lines $x = 8, x = 10, y = 11$ and $y = 12$ is

If $3 \sin \alpha = 5 \sin \beta$, then $\tan \left( \frac{\alpha+\beta}{2} \right) + \tan \left( \frac{\alpha-\beta}{2} \right) =$

The statement pattern $[(p \rightarrow q)\land \sim q] \rightarrow r$ is a tautology when $r$ is equivalent to

$\lim_{x \to 3} \frac{(84-x)^{\frac{1}{4}} - 3}{x - 3}$ is