List of top Questions asked in MHT CET- 2025

A black body emits radiation of maximum intensity at wavelength '$\lambda$' at temperature $T$ K. Its corresponding wavelength at temperature $1.5 T$ K will be ______.

In a single slit diffraction experiment, slit width 'a' is illuminated by wavelength '$\lambda$' and the width of central maxima is 'y'. When half the slit is covered and illuminated by $(1.5)\lambda$, the width of the central maximum becomes ______.

To protect the instrument from magnetic field, it is completely surrounded by ______.

An a.c. source of frequency 'f' is connected to a circuit containing an inductance 'L' and resistance 'R' in series. The impedance of this circuit is ______.

Two equally charged small balls placed at a fixed distance experience a force 'F'. A similar uncharged ball after touching one of them is placed at the middle point between the two balls. The force experienced by this ball is ______.

In an $LR$ circuit, the value of $L$ is $(0.3/\pi)$ henry and the value of $R$ is $40 \Omega$. If an alternating e.m.f of 230 V at 50 cycles per second is connected, the impedance of the circuit and current will be respectively ______.

A doctor assumes patient has $d_1, d_2,$ or $d_3$ with equal probability. A test is positive with probability 0.7 for $d_1$, 0.5 for $d_2$, and 0.8 for $d_3$. If the test is positive, what is the probability the patient has $d_2$?

Consider the following three statements:
(A) If $3 + 2 = 7$ then $4 + 3 = 8$.
(B) If $5 + 2 = 7$ then earth is flat.
(C) If both (A) and (B) are true then $5 + 6 = 11$.
Which of the following statements is correct?

A particle P starts from $Z_0 = 1 + 2i$. It moves horizontally away from origin by 5 units, then vertically up by 3 units to $Z_1$. From $Z_1$ it moves $\sqrt{2}$ units in direction $\hat{i} + \hat{j}$, then moves through $\pi/2$ anticlockwise on a circle with centre at origin to reach $Z_2$. Then $Z_2 = \dots$

A coil of 'n' turns and resistance $R \Omega$ is connected in series with a resistance $R/2$. The combination is moved for time 't' second through magnetic flux $\phi_1$ to $\phi_2$. The induced current in the circuit is ______.

$\lim_{x \to 0} \frac{63^x - 9^x - 7^x + 1}{\sqrt{2} - \sqrt{1 + \cos x}} = \dots$

If a circle with centre at $(-1, 1)$ touches the line $x + 2y + 4 = 0$, then the coordinates of the point of contact are \dots

The common principal solution of the equations $\sin \theta = -1/2$ and $\tan \theta = 1/\sqrt{3}$ is \dots}

The slopes of the lines represented by $6x^2 + 2hxy + y^2 = 0$ are in the ratio 2 : 3, then $h = \dots$

If $A = \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix}$ and $A \cdot \text{adj } A = A A^T$, then $5a + b = \dots$

If $\theta$ is an obtuse angle between vectors $\vec{a}$ and $\vec{b}$ such that $|\vec{a}| = 5, |\vec{b}| = 3$ and $|\vec{a} \times \vec{b}| = 5\sqrt{5}$ then $\vec{a} \cdot \vec{b} = \dots$

If the plane $x/2 - y/3 - z/5 = 1$ cuts the co-ordinate axes in points A, B, C respectively, then the area of the triangle ABC is ______.

The probability that a student is not a swimmer is 1/5. The probability that out of 5 students selected at random 4 are swimmers is ______.

The equation of the curve passing through origin and satisfying $(1 + x^2) \frac{dy}{dx} + 2xy = 4x^2$ is ______.

If $y = \tan^{-1} \left[ \frac{12x - 64x^3}{1 - 48x^2} \right]$, then $dy/dx = \dots$

Consider the probability distribution:

Then the value of $P(X > 2)$ is ______.

The rate of increase of population of a city is proportional to population present. In 40 years it increased from 30,000 to 40,000. At time $t$ population is $a(b)^{t/40}$. Then $a$ and $b$ are \dots}

A player tosses two coins. He wins ₹10 if 2 heads appear, ₹5 if one head appears, and ₹2 if no head appears. Then variance of winning amount is ______.

If the lines $x = ay - 1 = z - 2$ and $x = 3y - 2 = bz - 2$ ($ab \neq 0$) are coplanar, then \dots

The order of the differential equation whose general solution is given by $y = (C_1 + C_2) \sin(x + C_3) - C_4 e^{x+C_5}$ is \dots}