List of top Questions asked in MHT CET- 2025

A spherical liquid drop of radius R is divided into 64 equal droplets. If surface tension is \(T\) then the work done in this process will be

A string of length \(L\) is fixed at one end and carries a mass m at the other end. The string makes \(\frac{3}{\pi}\) revolutions per second around the vertical axis through the fixed end. The tension in the string is

When three capacitors of capacitances ' C ', ' 2 C '? and ' 3 C ' are connected in series. The potential difference applied across the combination is ' \(V\) '. The energy stored in the circuit is

In the spectrum of hydrogen atom the ratio of the longest wavelength in the Balmer series to the longest wavelength in the Lyman series is

A particle vibrating simple harmonically has an acceleration of \(16 \mathrm{~cm} / \mathrm{s}^2\), when it is at a distance of 4 cm from the mean position. Its periodic time is

An inductor of 0.5 mH , capacitor of \(20 \mu \mathrm{~F}\) and resistance of \(20 \Omega\) are connected in series with a 220 V a.c. source. If the current is in phase with e.m.f., the maximum current in the circuit is \(\sqrt{x} A\). The value of \(x\) is

Two inductors of 88 mH each are joined in parallel. The current passing through this combination is 4 A . The energy stored in this combination of inductors in joule is

An alternating voltage \(\mathrm{V}=100 \sqrt{2} \sin (50 \mathrm{t})\) is connected to \(2 \mu \mathrm{~F}\) capacitor through a.c. ammeter. The reading of the ammeter is

When the r.m.s. velocity of a gas is denoted by ' V ' and temperature of the gas by T , which of the following relations is TRUE?

' n ' polarising sheets are arranged such that each makes an angle \(45^{\circ}\) with the proceeding sheet. An unpolarised light of intensity I is incident into this arrangement. The output intensity is I/ 64 . The value of \(n\) will be \(\left(\cos 45^{\circ}=1 / \sqrt{2}\right)\)

A gas at \(800^{\circ} \mathrm{C}\) is cooled until both its pressure and volume are halved. The final temperature of the gas will be

A wave is travelling in the negative x direction having displacement 3 cm along Y direction, wavelength \(2 \pi \mathrm{~m}\) and frequency \(\left(\frac{1}{2 \pi}\right) \mathrm{Hz}\) is represented as ( \(t=\) time)

If the shape of the liquid surface is curved, then the

A photon and an electron have equal energy ' \(E\) '. The ratio of wavelength of photon to wavelength of electron is proportional to

A straight wire of mass ' M ' and length 2 m is placed in a magnetic field of 2 T which is acting perpendicular to the length of the wire. When a current of 1 A flows through the wire, the wire experiences an upthrust and leviates in a magnetic field. The mass ' \(M\) ' of the wire is (acceleration due to gravity \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )

Four solid spheres each of mass ' \(m\) ' and radius ' \(r\) ' are arranged as shown in the figure. The moment of inertia of the system about the given axis of rotation \(\mathrm{AA}^1\) is

When forward bias is applied to a p-n junction, then the potential barrier and the width of the depletion region respectively.

If in triangle ABC , with usual notations \(\sin \frac{\mathrm{A}}{2} \cdot \sin \frac{\mathrm{C}}{2}=\sin \frac{\mathrm{B}}{2}\) and 2 s is the perimeter of the triangle, then the value of \(s\) is

If \(\bar{a}, \bar{b}, \bar{c}\) are non coplanar unit vectors such that \(\overline{\mathrm{a}} \times(\overline{\mathrm{b}} \times \overline{\mathrm{c}})=\frac{\overline{\mathrm{b}}+\overline{\mathrm{c}}}{\sqrt{2}}\) then the angle between \(\overline{\mathrm{a}}\) and \(\overline{\mathrm{b}}\) is

The joint equation of the bisector of the angle between the lines \(2 x^2+11 x y+3 y^2=0\) is

A pair of tangents are drawn to the circle \(x^2+y^2+6 x-4 y-12=0\) from a point \(\mathrm{P}(-4,-5)\), then the area enclosed between these tangents and the area of the circle is

\[ \int\limits_0^1 \frac{1}{2+\sqrt{x}} d x= \]

If \(y=\log _3\left(\log _3 x\right)\) then \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) at \(x=3\) is \(\ldots \ldots\)

If a random variable X has the following probability distribution of X

\[ \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \mathrm{X}=x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \mathrm{P}(\mathrm{X}=x) & 0 & \mathrm{k} & 2 \mathrm{k} & 2 \mathrm{k} & 3 \mathrm{k} & \mathrm{k}^2 & 2 \mathrm{k}^2 & 7 \mathrm{k}^2+\mathrm{k} \\ \hline \end{array} \]

Then \(P(x \geq 6)=\)

Let M and N be foots of the perpendiculars drawn from the point \(\mathrm{P}(\mathrm{a}, \mathrm{a}, \mathrm{a})\) on the lines \(x-y=0, \mathrm{z}=1\) and \(x+y=0, \mathrm{z}=-1\) respectively and if \(\angle \mathrm{MPN}=90^{\circ}\) then \(\mathrm{a}^2=\)