List of top Questions asked in MHT CET- 2025

When source of sound moves towards a stationary observer, the apparent frequency heard by him

The formula for the physical quantity is \(P = \frac{x^3 y}{z^2}\) and the percentage error in the determination of physical quantities \(x, y, z\) are \(0.6%, 3%\) and \(1.3%\) respectively. The percentage error in the measurement of \(P\) is

Four particles each of mass \(M\) are placed at the corners of a square of side \(L\). The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

Consider the three statements $\text{p} : \forall \text{n} \in \mathbb{N}, 10\text{n} - 3$ is a prime number, when n is not divisible by 3.
$\text{q} : \frac{2}{\sqrt{3}}, \frac{-2}{\sqrt{3}}, \frac{-1}{\sqrt{3}}$ are the direction cosines of a directed line.
$\text{r} : \sin x$ is an increasing function in the interval $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$.

In a triangle $ABC$, with usual notations, if $\frac{b+c}{11} = \frac{c+a}{12} = \frac{a+b}{13}$ Then $\cos \text{A} : \cos \text{B} : \cos \text{C}$ is

If \(\vec{F} = (5\hat{i} - 10\hat{j})\) and \(\vec{r} = (4\hat{i} - 3\hat{j})\), then the torque acting on the object will be

The time period of a simple pendulum inside a stationary lift is \(\sqrt{3}\) second. When the lift moves upwards with an acceleration \(g/3\), the time period will be ( \(g =\) acceleration due to gravity)

Two particles of equal mass '\(m\)' move in a circle of radius '\(r\)' under the action of their mutual gravitational attraction. The speed of each particle will be ( \(\text{G} =\) Universal gravitational constant)

If $A = \begin{bmatrix} \cos \theta & \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$, where $A_{21}, A_{22}, A_{23}$ are cofactors of $a_{21}, a_{22}, a_{23}$ respectively, then the value of $a_{21}\text{A}_{21} + \text{a}_{22}\text{A}_{22} + \text{a}_{23}\text{A}_{23} =$

A stone of mass \(1\text{ kg}\) tied to a light inextensible string of length \(L = \frac{5}{3}\text{ m}\) is rotating in a circular path of radius \(L\) in a vertical plane. If the ratio of maximum tension in the string to the minimum tension in the string is 3 , the speed of the stone at the highest point of the circle is ( \(g =\) acceleration due to gravity)

If $f(x)$ is continuous at point $x = 0$ where $f(x) = \begin{cases} \frac{3\sin x + 5\tan x}{\text{a}^x - 1} & , x<0 \\ \frac{2}{\log 2} & , x = 0 \\ \frac{8x + 2x\cos x}{\text{b}^x - 1} & , x>0 \end{cases}$ then the values of a and b, respectively, are ________

$\int \frac{\sin 2x}{(a+b\cos x)^2} dx =$

If $x + \log_{15}(5 + 3^x) = x \log_{15} 5 + \log_{15} 24$, then $x =$ ________

The modulus of the square root of the conjugate of $-7 + 24\sqrt{-1}$ is __________

If $m_1$ and $m_2$ are the slopes of the lines represented by $ax^2 + 2hxy + by^2 = 0$ satisfying the condition $16\text{h}^2 = 25\text{ab}$, then

The smallest angle of the triangle whose sides are $6 + \sqrt{12}, \sqrt{48}, \sqrt{24}$ is

If the directed line makes an angle $45^\circ$ and $60^\circ$ with the X and Y -axes respectively, then the obtuse angle $\theta$ made by the line with the Z -axis is

The derivative of $\tan^{-1} \left(\sqrt{1+x^2}-1\right)$ is

In the mean value theorem, $f'(c) = \frac{f(b)-f(a)}{b-a}$, if $\text{a} = 0$, $\text{b} = \frac{1}{2}$ and $f(x) = x(x - 1)(x - 2)$, then the value of $c$ is

The angle between the curves $xy = 6$ and $x^2y = 12$ is

An ellipse has OB as semi-minor axis, S and S' are foci and angle SBS' is a right angle. Then the eccentricity of the ellipse is

By dropping a stone in a quiet lake, a wave in the form of circle is generated. The radius of the circular wave increases at the rate of $2.1 \text{ cm/sec}$. Then the rate of increase of the enclosed circular region, when the radius of the circular wave is $10 \text{ cm}$ , is (Given $\pi = \frac{22}{7}$ )

$f(x) = (\cos x + \text{i}\sin x) \cdot (\cos 3x + \text{i}\sin 3x) \cdots [\cos(2\text{n} - 1)x + \text{i}\sin(2\text{n} - 1)x] \text{n} \in \mathbb{N}$ Then $f''(x) = $ ________, (Where $\text{i} = \sqrt{-1}$ )

If the angle $\theta$ between the line $\frac{x+1}{1} = \frac{y-1}{2} = \frac{z-2}{2}$ and the plane $2x - y + \sqrt{\lambda}z + 4 = 0$ is such that $\sin \theta = \frac{1}{3}$, then $\lambda + 1 =$

If the lines $\frac{3-x}{2} = \frac{5y-2}{3\lambda+1} = 5 - z$ and $\frac{x+2}{-1} = \frac{1-3y}{7} = \frac{4-z}{2\mu}$ are at right angles, then $7\lambda - 10\mu =$