List of top Questions asked in MHT CET- 2025

The differential equation whose solution represents the family \(x^2 y=4 \mathrm{e}^x+\mathrm{c}\), where c is an arbitrary constant, is

\[ \int \frac{d x}{2+\cos x}= \]

\[ \int_{-2}^2\left|x^2-x-2\right| \mathrm{d} x= \]

If X is a binomial variable with range \(\{0,1,2,3,4\}\) and \(\mathrm{P}(\mathrm{X}=3)=3 \mathrm{P}(\mathrm{X}=4)\) then the parameter ' \(p\) ' of the binomial distribution is

Identify the structural formula of phloroglucinol.

The logically equivalent statement of \((\sim \mathrm{p} \wedge \mathrm{q}) \vee(\sim \mathrm{p} \wedge \sim \mathrm{q}) \vee(\mathrm{p} \wedge \sim \mathrm{q})\) is

\[ \int \frac{x \mathrm{~d} x}{(x-1)(x-2)}= \]

Which transition series includes elements Co and Mo respectively?

If two sides of a triangle are \(\sqrt{3}-2\) and \(\sqrt{3}+2\) units and their included angle is \(60^{\circ}\), then the third side of the triangle is

\[ \text { Identify the bond line formula of Neopentane. } \]

Match column I (process) with column II (application)

A gas having \(\gamma=\frac{5}{2}\) and volume 360 c.c. is suddenly compressed to 90 c.c. If the initial pressure of the gas is P , then the final pressure will be

The outer surface of star in the form of a sphere radiates heat as a black body at temperature ' T '. The total radiant energy per unit area, normal to the direction of incidence, received at a distance ' \(R\) ' from the centre of a star of radius ' \(r\) ' is \((R>r)(\sigma=\) Stefan's constant \()\)

An organ pipe closed at one end has fundamental frequency of 1500 Hz . The maximum number of overtones generated by this pipe which a normal person can hear is (Normal man can hear the frequency up to 19.5 kHz , Neglect end correction)

The ratio of the total energy of the \(2^{\text {nd }}\) orbit electron for the hydrogen atom (\(^1\mathrm{H}\)) to that of a helium ion (\(\mathrm{He}^+\)) is :

A radioactive element having half-life 30 min . is undergoing beta decay. The fraction of radioactive element remains undecayed after 90 min . will be

A black body has maximum wavelength ' \(\lambda_{\mathrm{m}}\) ' at temperature 2000 K . Its maximum wavelength at 3000 K will be

A wire of length ' \(L\) ' carries a current ' \(I\) '. If the wire is turned into a square coil of single turn, the maximum magnitude of the torque in a given magnetic field \((\overrightarrow{\mathrm{B}})\) is

A vessel completely filled with water has two holes ' P ' and ' Q ' at depths ' 2 h ' and ' 8 h ' from the top respectively. Hole ' P ' is square of side ' \(a\) ' and hole ' \(Q\) ' is a circle of radius ' \(r\) '. The water flowing out per second from both the holes is same, then side ' \(a\) ' of hole ' \(P\) ' is

A photosensitive surface has work function \(\phi\). If photon of energy \(3 \phi\) falls on this surface, the electron comes out with maximum velocity of \(4 \times 10^6 \mathrm{~m} / \mathrm{s}\) When photon energy is increased to \(7 \phi\) then maximum velocity of photoelectron will be

A student studies for X number of hours during a randomly selected school day. The probability that X can take the values, has the following form, where k is some constant.

\[ \mathrm{P}(\mathrm{X}=x)= \begin{cases}0.2, & \text { if } x=0 \\ \mathrm{k} x, & \text { if } x=1 \text { or } 2 \\ \mathrm{k}(6-x), & \text { if } x=3 \text { or } 4 \\ 0, & \text { otherwise }\end{cases} \]

The probability that the student studies for at most two hours is

If \(\mathrm{X} \sim \mathrm{B}(35, \mathrm{p})\) such that \(7 \mathrm{P}(\mathrm{X}=0)=\mathrm{P}(\mathrm{X}=1)\) then the value of \(\frac{\mathrm{P}(\mathrm{X}=15)}{\mathrm{P}(\mathrm{X}=20)}\) is equal to

The value of \(\tan \left[2 \tan ^{-1} \frac{1}{5}-\frac{\pi}{4}\right]\) is