List of top Questions asked in MHT CET

Two concentric circular coils having radii $r_1$ and $r_2$ $(r_2 \ll r_1)$ are placed co-axially with centres coinciding. The mutual induction of the arrangement is (Both coils have single turn, $\mu_0$ = permeability of free space)

If the potential difference used to accelerate electrons is doubled, by what factor does the de-Broglie wavelength associated with the electrons change?

A solid sphere of mass $M$ and radius $R$ is rotating about its diameter. A disc of same mass and radius is also rotating about an axis passing through its centre and perpendicular to the plane but angular speed is twice that of the sphere. The ratio of kinetic energy of disc to that of sphere is

The figure shows two diagrams in which diode and resistance are connected. Out of the following statements which one is TRUE?

Two progressive waves $Y_1=\sin 2\pi\left(\dfrac{t}{4}-\dfrac{x}{4}\right)$ and $Y_2=\sin 2\pi\left(\dfrac{t}{4}+\dfrac{x}{4}\right)$ superpose to form a standing wave. $Y_1$ and $Y_2$ are in SI system. Amplitude of the particle at $x=0.5\,\text{m$ is}
$\left[\sin 45^\circ=\cos 45^\circ=\dfrac{1}{\sqrt{2}}\right]$

Earth revolves round the sun in a circular orbit of radius $R$. The angular momentum of the revolving earth is directly proportional to

Let the two forces have equal magnitude $A$. If the magnitude of the resultant is $\dfrac{2A{3}$, then the angle between those two forces is}

A graph of magnetic flux $\phi$ versus current $(I)$ is shown for four inductors A, B, C, D. Smaller value of self inductance is for inductor

The equation of a normal to the curve \[ x = 4\sec\theta,\qquad y = 4\tan^2\theta \] at \( \theta = \frac{\pi}{4} \) is

The equation of the curve which passes through the point \( (1,0) \) and has tangent with slope \[ 1+\frac{y}{x}+\left(\frac{y}{x}\right)^2 \] is

If the function \[ f(x)= \begin{cases} \dfrac{1-\sin2x+\cos2x}{1+\sin2x+\cos2x}, & x\neq \dfrac{\pi}{2}
k, & x=\dfrac{\pi}{2} \end{cases} \] is continuous at \( x=\dfrac{\pi}{2} \), then \( k \) is

Two spheres $S_1$ and $S_2$ have radii $R$ and $3R$, temperature $T$ K and $\dfrac{T{\sqrt{3}}$ K respectively. If they are coated with a material of same emissivity, rate of radiation of $S_1$ is $E$ then rate of radiation of $S_2$ is}

In the experiment to determine the internal resistance of a cell ($E_1$) using potentiometer, the resistance drawn from the resistance box is $R$. The potential difference across the balancing length of the wire is equal to the terminal potential difference $(V)$ of the cell. The value of internal resistance $(r)$ of the cell is

Seven capacitors each of capacitance $2\,\mu F$ are to be connected to obtain equivalent capacitance of $\dfrac{10{11}\,\mu F$. Which of the following combination is possible?}

If \( x^2 + y^2 = 1 \), then find \( \dfrac{d^2x}{dy^2} \).

The general solution of the differential equation \[ \sec^2 x \tan y\,dx + \sec^2 y \tan x\,dy = 0 \] is

If \( \sec\theta = \dfrac{13}{12} \) and \( \theta \) lies in the fourth quadrant, then find \[ \tan\theta \times \csc\theta \times \sin\theta \times \cos\theta \]

The acute angle included between the lines \[ x\sin\theta - y\cos\theta = 5 \] and \[ x\sin\alpha - y\cos\alpha + 11 = 0 \] is

Water at \(100^\circ\text{C}\) cools in 15 minutes to \(75^\circ\text{C}\) in a room temperature of \(25^\circ\text{C}\). Then the temperature of water after 30 minutes is

If \[ A=\begin{bmatrix} 1 & 2 & i\\ 1 & 1 & 1\\ 1 & 1 & 0 \end{bmatrix}, \] then \( [\operatorname{adj}(\operatorname{adj}A)]^{-1} \) is

The length of the latus rectum of the parabola whose focus is at \( (1,-2) \) and directrix is the line \( x + y + 3 = 0 \) is

If \( A=\begin{bmatrix}2 & 3 \\ 1 & 2\end{bmatrix} \) and \( B=\begin{bmatrix}2 & -3 \\-1 & 2\end{bmatrix} \), then \( (B^{-1}A^{-1})^{-1} \) is

If \( \log_{10}\!\left(\dfrac{x^3-y^3}{x^3+y^3}\right)=2 \), then find \( \dfrac{dx}{dy} \).

The integrating factor of the differential equation \[ \frac{dy}{dx} + \frac{1}{x}y = x^3 - 3 \] is

The distance of the point \( (3,4,5) \) from the point of intersection of the line \[ \frac{x-3}{1} = \frac{y-4}{2} = \frac{z-5}{2} \] and the plane \( x+y+z=2 \) is