MHT CET 2026 Physics Paper: 11 Apr, Shift 1

In an AC circuit $E = 50\sin(500t),\ I = 600\sin\left(500t + \frac{\pi}{3}\right)\text{ mA}$. What is the power dissipated in the circuit? [$\cos 60^\circ = 0.5$]

An inductor of reactance $100\ \Omega$, a capacitor of reactance $50\ \Omega$, and a resistor of resistance $50\ \Omega$ are connected in series with an AC source of $10$ V, $50$ Hz. Average power dissipated by the circuit is ____

In the circuit shown below, the ac source has voltage $V = 30\cos(\omega t)$ volt with $\omega = 2000$ rad/s. What will be the amplitude of the current?

The number of revolutions per second made by an electron in the first Bohr orbit of hydrogen atom is ($h$ = Planck's constant, $m$ is the mass of electron and $r$ is the radius of the orbit.)

The kinetic energy of the electron in an orbit of radius $r$ in hydrogen atom is proportional to ($e$ = electronic charge)

A parallel plate capacitor has plate area $40$ cm$2$ and plates separation $2$ mm. The space between the plates is filled with a dielectric medium of a thickness $1$ mm and dielectric constant $5$. The capacitance of the system is

The position vector of a particle is $\vec{r} = a\cos\omega t\,\hat{i} + a\sin\omega t\,\hat{j}$. Calculate the angle between its position vector and the velocity vector.

($\cos 0 = 1, \cos 90 = 0, \cos 60 = 0.5, \sin 30 = 0.5, \sin 0 = 0$)

In a metre bridge experiment the balance point is obtained if the gaps are closed by $2\ \Omega$ and $3\ \Omega$. A shunt of $X\ \Omega$ is added to $3\ \Omega$ resistor to shift the balancing point by $22.5$ cm. The value of $X$ is

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

Photoelectric emission is observed from a metallic surface for frequencies $v_1$ and $v_2$ of the incident light rays ($v_1 > v_2$). If the maximum values of kinetic energy of the photoelectrons emitted in the two cases are in the ratio of $k : 1$, then what is the threshold frequency of the metallic surface?

The following figure represents two bulbs $B_1$ and $B_2$, resistor R and an inductor L. When the switch S is turned off, which of the following statement is true?

A square loop of area $25$ cm$^{2}$ has a resistance of $10\ \Omega$. The loop is placed in uniform magnetic field of magnitude $40$ T. The plane of the loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in one second will be

A long rectangular conducting loop of width '$l$' mass '$m$' and resistance '$R$' is placed partly in a perpendicular magnetic field '$B$'. With what velocity should it be pushed downwards so that it may continue to fall without any acceleration? ($g$ = acceleration due to gravity)

Three charges $q,\ Q$ and $+4q$ are placed in a straight line of length $d$ at points at distance $0,\ \frac{d}{3},\ \frac{2d}{3}$ respectively. In order to make the net force on $q$ be zero, the value of $Q$ should be

Which of the following statements is NOT TRUE?

a. Work done to move a charge on an equipotential surface is not zero.

b. Equipotential surfaces are the surfaces where the potential is constant.

c. Equipotential surfaces for a uniform electric field are parallel and equidistant from each other. d. Electric field is always perpendicular to an equipotential surface.

Two metal sphere of radius $R$ and $3R$ have same surface charge density $\sigma$. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes $\sigma_1$ and $\sigma_2$, respectively. The ratio $\frac{\sigma_1}{\sigma_2}$ is.

Following figure indicates the electric potential V as a function through 4 regions on x-axis. Which of the following is correct for the electric field E in these regions?

A vessel contains oil (density $= 0.8$ gm$/\text{cm}^{3}$) over mercury (density $= 13.6$ gm$/\text{cm}^{3}$). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in gm$/\text{cm}^{3}$ is

Given below are two statements:

Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.

Statement II: Acceleration due to earth's gravity is same at a height '$h$' and depths '$d$' from earth's surface, if $h = d$.

In the light of above statements, choose the most appropriate answer from the options given below.

Three identical heat conducting rods are connected in series as shown in the figure. The rods on the side have thermal conductivity $2K$ while that in the middle has thermal conductivity $K$. The left end of the combination is maintained at temperature $3T$ and the right end at $T$. The rods are thermally insulated from outside. In steady state, temperature at the left junction is $T_1$ and that at the right junctions is $T_2$. The ratio $T_1/T_2$ is

A wire of length $L$ and diameter $d$ is used in a bulb. The temperature of wire is $T$ and power radiated by the wire is $P$. Its emissivity is ($\sigma$ = Stefan's constant) (Assume that emissivity of wire material is same at all wavelength)

The energy spectrum of a black body exhibits a maximum of wavelength $\lambda_0$. The temperature of the black body is now changed such that the energy is maximum at wavelength $\frac{3\lambda_0}{2}$. The ratio of power radiated by the black body will be

Which of the following figure best represents the variation of magnetic susceptibility ($\chi$) with temperature for a diamagnetic substance?

A car passes three points A, B and C at $3$ m/s, $6$ m/s and $9$ m/s respectively in a straight line with uniform acceleration. If distance $AB = 60$ m then find the distance BC.

A wire of length $L$ is bent in the form of a circular coil and current '$i$' is passed through it. This coil is kept in magnetic field. The torque acting on the coil will be maximum, when the number of turns is ___

Two long parallel wires carrying currents $8$A and $15$A in opposite directions are placed at a distance of $7$ cm from each other. A point P is at equidistant from both the wires such that the lines joining the point P to the wires are perpendicular to each other. The magnetic field at P is ___ $\times 10^{-6}$ T. (Given: $\sqrt{2} = 1.4,\ \mu_0 = 4\pi \times 10^{-7}$ SI unit)

A galvanometer has a current range of $10$ mA and a voltage range of $0.75$ V. To convert this galvanometer into an ammeter of range $10$ A, what is the shunt resistance?

There is a body having mass $m$ and performing SHM with amplitude '$a$'. There is a restoring force $F = -Kx$, where $x$ is the displacement. The total energy of the body depends upon which of the following?

A particle executes simple harmonic motion between $x = -A$ and $x = +A$. If time taken by particle to go from $x = 0$ to $\frac{A}{2}$ is $2$s, then time taken by particle in going from $x = \frac{A}{2}$ to A is

Two massless springs of spring constants $K_1$ and $K_2$ are connected one after the other forming a single chain, suspended vertically and a certain mass is attached to the free end. If $x_1$ and $x_2$ are their respective extensions and 'F' is their stretching force, the total extension produced is

For large magnifying power of a telescope

A wheel is rotating at $600$ rpm about its axis of rotation. When the power is cut off, it comes to rest in half a minute. Its angular retardation expressed in rad$/\text{s}^{2}$ is (retardation is uniform)

A flywheel rotating about a fixed axis has a kinetic energy of $500$ joule, if its angular frequency is $5$ Hz, then calculate the moment of inertia of the wheel about the axis of rotation. ($\pi^2 = 10$)

When the conductivity of a semiconductor is only due to breaking of covalent bonds, the semiconductor is called

In common emitter transistor amplifier, the output resistance is $500$ k$\Omega$ and the current gain $\beta = 50$. If power gain of amplifier is $5 \times 10^{6}$, what is the input resistance?

What does the following combination of gates produce?

A vessel has $6$ gram of hydrogen at pressure $P$ and temperature $500$ K. A small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is $\frac{P}{2}$ and the temperature falls to $300$ K?

An ideal gas undergoes cyclic process ABCDA as shown in given p-V diagram. What is the magnitude of amount of work done by the gas?

Two samples A and B of gas initially at the same pressure and temperature. They are compressed from volume $V$ to $\frac{V}{2}$ (A isothermally and B adiabatically). The relation between pressure of the gas A ($P_A$) and pressure of gas B ($P_B$) is

The period of oscillation of a simple pendulum is given by $T = 2\pi\sqrt{\frac{l}{g}}$ where $l$ is about $80$ cm and is known to have $0.1$ cm accuracy. The period is about $1.5$ s. The time of $50$ oscillations is measured by a stop watch of least count $0.1$ s. The percentage error in $g$ is nearly

Two rain drops of same radius '$r$' falling with same terminal velocity '$V$' merge and form bigger drop of radius '$R$'. The terminal velocity of big drop is

A spherical ball of radius $1$ mm and density $10.5$ g/cc is dropped in glycerine of coefficient of viscosity $9.8$ poise and density $1.5$ g/cc. Viscous force on the ball when it attains constant velocity is $3696 \times 10^{-x}$ N. The value of is

(Given, $g = 9.8$ m$/\text{s}^{2}$ and $\pi = \frac{22}{7}$)

A tuning fork of frequency $n$ produces $x$ beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string, when a slight increase in tension produces lesser beats per second than before?

What is the effect of humidity on sound waves when humidity increases?

A string of length $0.5$ m and mass $10^{-3}$ kg is tightly clamped at its ends. The tension in the string is $0.8$ N. Identical wave pulses are produced at one end at equal intervals of time $\Delta t$. What is the minimum value of $\Delta t$ which allows constructive interference between successive pulses?

A ray of light is incident of the surface of a glass plate at an angle of incidence equal to Brewster's angle $\Phi$. If $\mu$ denotes the refractive index of glass w.r.t. air, then what will be the angle between reflected and refracted rays?

Two polaroid A and B placed in such a way that the pass-axis of polaroid are perpendicular to each other. Now, another polaroid C is placed between A and B bisecting angle between them. If intensity of unpolarised light is $I_0$ then intensity of transmitted light after passing through polaroid B will be

Two light waves amplitudes in the ratio $3 : 1$ produce interference. The ratio of the maximum to minimum intensity is

In a Young's double slit experiment, the intensities at two points, for the path difference $\frac{\lambda}{4}$ and $\frac{\lambda}{3}$ ($\lambda$ being the wavelength of light used) are $I_1$ and $I_2$ respectively. If $I_0$ denotes the intensity produced by each one of the individual slits, then $\frac{I_1 + I_2}{I_0} =$

$\left(\cos 45^\circ = \frac{1}{\sqrt{2}}, \cos 60 = \frac{1}{2}\right)$