List of top Questions asked in MHT CET- 2025

In Young's double slit experiment, the intensity on screen at a point, where path difference is \(\frac{\lambda}{4}\) is \(\frac{K}{4}\). The intensity at a point when path difference is ' \(\lambda\) ' will be \(\left[\cos \frac{\pi}{2}=0, \cos 2 \pi=1\right]\)

A point particle of mass 200 gram is executing S.H.M. of amplitude 0.2 m . When the particle passes through the mean position, its kinetic energy is \(16 \times 10^{-3} \mathrm{~J}\). The equation of motion of this particle is (Initial phase of oscillation \(=0^{\circ}\) )

The vectors \(\bar{a}, \bar{b}\) and \(\bar{c}\) are such that \(|\overline{\mathrm{a}}|=2,|\overline{\mathrm{~b}}|=4,|\overline{\mathrm{c}}|=4\). If the projection of \(\overline{\mathrm{b}}\) on \(\overline{\mathrm{a}}\) is equal to projection of \(\overline{\mathrm{c}}\) on \(\overline{\mathrm{a}}\) and \(\overline{\mathrm{b}}\) is perpendicular to \(\overline{\mathrm{c}}\), then the value of \(|\overline{\mathrm{a}}+\overline{\mathrm{b}}-\overline{\mathrm{c}}|\) is

\[ \begin{array}{r}If\,\,\,\, y=\tan ^{-1}\left(\frac{1}{1+x+x^2}\right)+\tan ^{-1}\left(\frac{1}{x^2+3 x+3}\right) +\tan ^{-1}\left(\frac{1}{x^2+5 x+7}\right) \end{array} \]

then the value of \(y^{\prime}(0)\) is

A fair coin is tossed a fixed number of times. If the probability of getting 5 tails is same as the probability of getting 7 tails, then the probability of getting 3 tails is

\[ \int x^2 \cos x d x= \]

If \(0 \leq x \leq \pi\) and \(81^{\sin ^2 x}+81^{\cos ^2 x}=30\) Then \(x\) takes the value

A manufacturing company produces two items, A and B. Each toy should be processed by two machines, I and II. Machine I can be operated for maximum 10 hours 40 minutes. It takes 20 minutes for an item of A and 15 minutes for B. Machine II can be operated for a total time at 8 hours 20 minutes. It takes 5 minutes for an item A and 8 minutes for B . The profit per item of \(A\) is \(Rs 25\) and per item of \(B\) is ₹ 18 . The formulation of an L.P.P. to maximize the profit (where \(x\) is number of items A and \(y\) is the number of item \(B\) ) is

\[ \int \frac{\mathrm{d} x}{\sin ^2 x \cos ^2 x}= \]

The probability that a non leap year selected at random will contain 52 Saturdays or 53 Sundays is

\[ \int\limits_0^1 x\left|x-\frac{1}{2}\right| \mathrm{d} x= \]

The minimum value of \(a x+b y\) where \(x y=c^2\) is

The solution of the differential equation \((1+x) \frac{\mathrm{d} y}{\mathrm{~d} x}-x y=1-x\) is

\[ \mathop {\lim }\limits_{x \to 0} \frac{\mathrm{e}^{x^2}-\cos 3 x}{\sin x \log (1+2 x)}= \]

Two cylinders A and B fitted with piston contain equal amount of an ideal diatomic gas at temperature T K. The piston of cylinder A is free to move while that of cylinder \(B\) is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise of temperature of the gas in A is \(\mathrm{dT}_{\mathrm{A}}\), then the rise in temperature of the gas in B is \(\left(\gamma=\frac{C_p}{C_v}\right)\)

In an experiment four quantities \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s are measured with percentage \(3 \%, 2 \%, 3 \%\) and \(1 \%\) respectively. Quantity ' \(A\) ' is calculated as follows

\(\mathrm{A}=\frac{\mathrm{pq}^2}{\mathrm{r}^2 \mathrm{~s}^4}\), the percentage error in ' A ' is

In series LCR circuit R \(=18 \Omega\) and impedance is \(30 \Omega\). An rms voltage 210 V is applied across the circuit. The true power consumed in AC circuit is nearly

The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, they produce four beats. The length of open pipe is made half and that of the closed pipe is made two times the original. Now the number of beats produced if the two pipes are vibrating in their fundamental modes simultaneously is

A solid sphere at rests rolls down an inclined plane of vertical height \(h\) without sliding. Its speed on reaching the bottom of plane is ( \(\mathrm{g}=\) acceleration due to gravity)

Graph shows the variation of fringe width ( X ) versus distance of the screen from the plane of the slits (D) in Young's double slit experiment. (keeping other parameters same, \(d=\) distance between the slits). The wavelength of light used can be calculated as

In Young's double slit experiment, in an interference pattern second minimum is observed exactly in front of one slit. The distance between the two coherent sources is ' \(d\) ' and the distance between source and screen is ' \(D\) '. The wavelength of light source used is

When the observer moves towards a stationary source with velocity \(\mathrm{V}_1\), the apparent frequency of emitted note is \(F_1\). When observer moves away from the source with velocity \(\mathrm{V}_1\), the apparent frequency is \(\mathrm{F}_2\). If V is the velocity of sound in air and \(F_1 / F_2=2\) then \(V / V_1\) is equal to

The magnetic moment of electron due to orbital motion is proportional to ( \(\mathrm{n}=\) principal quantum number)

The cumulative distribution function of a discrete random variable X is

\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \mathrm{X}=x & -4 & -2 & 0 & 2 & 4 & 6 & 8 & 10 \\ \hline \mathrm{~F}(\mathrm{X}=x) & 0.1 & 0.3 & 0.5 & 0.65 & 0.75 & 0.85 & 0.90 & 1 \\ \hline \end{array} \]

then \(\frac{P(X \leqslant 0)}{P(X>0)}=\)

If \(\quad \overline{\mathrm{a}}=\lambda x \hat{\mathrm{i}}+y \hat{\mathrm{j}}+4 z \hat{\mathrm{k}}, \quad \overline{\mathrm{b}}=y \hat{\mathrm{i}}+x \hat{\mathrm{j}}+3 y \hat{\mathrm{k}}\), \(\overline{\mathrm{c}}=-z \hat{\mathrm{i}}-2 z \hat{\mathrm{j}}-(\lambda+1) \hat{\mathrm{k}} x\) are the sides of the triangle ABC , where \(x, y, \mathrm{z}\) are not all zero, such that \(\bar{a}+\bar{b}-\bar{c}=\overline{0}\), then value of \(\lambda\) is