List of top Questions asked in MHT CET

In biprism experiment, a source of monochromatic light is used for a certain distance between slit and eyepiece. When the distance between two virtual sources is changed from $d_A$ to $d_B$, then the fringe width is changed from $Z_A$ to $Z_B$. The ratio $Z_A$ to $Z_B$ is

A parallel beam of monochromatic light of wavelength $5\times10^{-7\,\text{m}$ is incident normally on a single narrow slit of width $10^{-3}\,\text{mm}$. At what angle of diffraction, the first minima is observed?}

For a particle performing S.H.M., the displacement–time graph is as shown.

Two identical thin bar magnets are placed mutually at right angles such that the north pole of one touches the south pole of the other. The length of each bar magnet is $\ell$. The magnitude of resultant magnetic moment of the system is
$\left[m = \text{pole strength of the magnet}\right]$

The excess pressure inside a spherical drop of water is three times that of another drop of water. The ratio of their surface area is

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

Relative permeability of an iron is $5500$, then its magnetic susceptibility will be

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)

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}
$\left[\sin 45^\circ=\cos 45^\circ=\dfrac{1}{\sqrt{2}}\right]$

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

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

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

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}

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

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

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

If \( \vec{AB} = 3\hat{i} + 5\hat{j} + 4\hat{k} \), \( \vec{AC} = 5\hat{i} - 5\hat{j} + 2\hat{k} \) represent the sides of triangle \( ABC \), then the length of the median through \( A \) is

If a line in octant OXYZ makes equal angles with the coordinate axes, then

If \( P(A') = 0.6 \), \( P(B) = 0.8 \) and \( P(B|A) = 0.3 \), then find \( P(A|B) \).

A tangent to the curve \( x = at^2,\; y = 2at \) is perpendicular to the X-axis. Then the point of contact is

Given below is the probability distribution of a discrete random variable \( X \):
\[ \begin{array}{c|cccccc} X=x & 1 & 2 & 3 & 4 & 5 & 6
\hline P(X=x) & k & 0 & 2k & 5k & k & 3k \end{array} \] Then find \( P(X \ge 4) \).

If the function \( f \) defined by \[ f(x) = \begin{cases} K(x - x^2), & 0<x<1
0, & \text{otherwise} \end{cases} \] is the p.d.f. of a random variable \( X \), then the value of \( P(X<\tfrac{1}{2}) \) is

If the vectors \( \vec{a} = \hat{i} - 2\hat{j} + \hat{k} \), \( \vec{b} = 2\hat{i} - 5\hat{j} + p\hat{k} \) and \( \vec{c} = 5\hat{i} - 9\hat{j} + 4\hat{k} \) are coplanar, then the value of \( p \) is