MHT CET 2025 Physics Paper: 25 Apr, Shift 2

In an $LR$ circuit, the value of $L$ is $\left(\frac{0.3}{\pi}\right)$ henry and the value of R is $40\ \Omega$, If in the circuit, 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

In an a.c. circuit, a resistance ' $R$ ' is connected in series with an inductance ' $L$ '. If phase angle between voltage and current is $45^\circ$, the value of inductive reactance will be $(\tan 45^\circ = 1)$

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

In hydrogen atom in its ground state, the first Bohr orbit has radius ' $r_1$ '. When the atom is raised to one of its excited states, the electrons orbital velocity becomes one-third. The radius of that orbit is

Seven capacitors each of capacitance $2\ \mu\text{F}$ are to be connected in a configuration to obtain an effective capacitance $\left(\frac{10}{11}\right)\mu\text{F}$. The combination is

Two identical metal plates are given charges $q_1$ and $q_2\ (q_2 < q_1)$ respectively. If they are now brought close together to form a parallel plate capacitor with capacitance ' C ', the potential difference ' $V$ ' between the plates is

Two batteries of e.m.f 4 V and 8 V with internal resistance $1\ \Omega$ and $2\ \Omega$ respectively are connected in a circuit with a resistance of $9\ \Omega$ as shown in the figure. The current and potential difference between the points ' P ' and ' Q ' is $R = 9\ \Omega$

With a resistance ' X ' connected in series with a galvanometer of resistance $100\ \Omega$, it acts as a voltmeter of range $0 - 15\text{ V}$. To double the range, a resistance of $1500\ \Omega$ is to be connected in series with ' X '. The value of ' X ' in ohm is

An electron of mass ' $m$ ' and charge ' $e$ ' initially at rest gets accelerated by a constant electric field ' E '. The rate of change of de-Broglie wavelength of the electron at time ' $t$ ' is

(Ignore relativistic effect)( $h =$ Planck's constant)

If the frequency of incident light in a photoelectric experiment is doubled, then stopping potential will

A copper ring having a cut such as not to form a complete loop is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring as shown in figure. The acceleration of the falling magnet is ( $g =$ acceleration due to gravity)

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

A coil of wire of radius ' $r$ ' has 600 turns and a self-inductance of 108 mH. The self-inductance of a coil with same radius and 500 turns 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

Assuming the drops to be spherical, 27 identical drops of mercury are charged simultaneously to the same potential of 20 volt. If all the charged drops are made to combine to form one big drop, then potential of big drop will be

A horizontal pipeline carries water in a streamline flow. At a point along the pipe, where the cross- sectional area is $10\text{ cm}^2$, the velocity of water is $1\text{ m/s}$ and pressure is 2000 Pa. The pressure of water at another point where the cross-sectional area $5\text{ cm}^2$ is

[Given $\rightarrow$ density of water $= 1000\text{ kg/m}^3$ ]

The depth at which the value of acceleration due to gravity becomes $\left(\frac{1}{n}\right)$ times the value at the surface of the earth is

( $R =$ radius of the earth)

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

The initial average kinetic energy of the molecules was E, when a gas sample is at $27^\circ\text{C}$. When the gas is heated to $327^\circ\text{C}$, then the final average kinetic energy will be

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

A circular coil carrying current ' I ' has a radius ' $r$ ' and ' $n$ ' turns. The magnetic field along the axis of a coil at a distance ' $2\sqrt{2}\, r$ ', from its centre is ( $\mu_0 =$ permeability of free space, $n$ is very small)

In the following figure magnitude of the magnetic field at the point $p$ is

A particle starts oscillating simple harmonically from its mean position with time period ' $T$ '. At time $t = \frac{T}{6}$, the ratio of the potential energy to kinetic energy of the particle is

$\left[\sin 30^\circ = \cos 60^\circ = 0.5, \cos 30^\circ = \sin 60^\circ = \sqrt{3}/2\right]$

Two simple pendulums have first (A) bob of mass ' $M_1$ ' and length ' $L_1$ ', second (B) of mass ' $M_2$ ' and length ' $L_2$ '. $M_1 = M_2$ and $L_1 = 2L_2$. If their total energies are same then the correct statement is

As shown in the figure, $S_1$ and $S_2$ are identical springs with spring constant K each. The oscillation frequency of the mass ' $m$ ' is ' $f$ '. If the spring $S_2$ is removed, the oscillation frequency will become

Two girls are standing at the ends ' $A$ ' and ' $B$ ' of a ground where $AB = b$. The girl at ' B ' starts running in a direction perpendicular to ' $AB$ ' with velocity ' $V_1$ '. The girl at ' A ' starts running simultaneously with velocity ' $V_2$ ' and in shortest distance meets the other girl in time ' $t$ '. The value of ' $t$ ' is

A glass cube of length 21 cm has a small air bubble trapped inside. When viewed normally from the opposite face, its apparent distance is 6 cm. The refractive index of glass and the actual distance of the air bubble from the first surface respectively are

The moment of inertia of a solid sphere of mass ' $m$ ' and radius ' $R$ ' about its diametric axis is ' $I$ '. Its moment of inertia about a tangent in the plane is

A bob of mass ' $m$ ' is tied by a massless string whose other end is wound on a flywheel (disc) of radius ' $R$ ' and mass ' $m$ '. When released from the rest, the bob starts falling vertically downwards. If the bob has covered a vertical distance ' $h$ ', then angular speed of wheel will be (There is no slipping between string and wheel, g - acceleration due to gravity)

Using Bohr's quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule?

( $I =$ moment of inertia of diatomic molecule and $h =$ Planck's constant)

A thin uniform rod of length ' $L$ ' and mass ' $M$ ' is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ' $\omega$ '. Its centre of mass rises to a maximum height of ( $g =$ acceleration due gravity)

A piece of semiconductor is connected in series in an electric circuit. On increasing the temperature, the current in the circuit will

In a common emitter amplifier configuration, the current gain is 62. The collector resistance and input resistance are $5\text{ k}\Omega$ and $500\ \Omega$ respectively. If the input voltage is 0.01 V, the output voltage will be

One of the following values of inputs $\mathrm{A}, \mathrm{B}$ and C respectively gives output $(\mathrm{Y})$ of the following combination of logic gates as ' 1 ' is

When one end of a capillary tube is dipped in water, the height of water column is ' $h$ '. The upward force of 105 dyne due to surface tension is balanced by the force due to the weight of water column. The inner circumference of the capillary tube is

(Surface tension of water $= 7 \times 10^{-2}\text{ N/m}$)

The amount of work done in blowing a soap bubble such that its diameter increases from 'd' to ' $D$ ' is ( $T =$ surface tension of solution)

A balloon is filled at $27^\circ\text{C}$ and 1 atmospheric pressure by volume $500\text{ m}^{3}$ helium gas. At $-3^\circ\text{C}$ and 0.5 atmospheric pressure, the volume of helium gas will be

Heat supplied $dQ =$ increase in internal energy dU is true for

A sample of an ideal gas $\left(\gamma = \frac{5}{3}\right)$ is heated at constant pressure. If 100 J of heat is supplied to the gas, the work done by the gas is

The volume of a metal sphere increases by $0.33\%$ when its temperature is raised by $50^\circ\text{C}$. The coefficient of linear expansion of the metal is

A force F is applied on a square plate of side L. If the percentage error in determining F is $3\%$ and that in L is $2\%$, then the percentage error in determining the pressure is

A tuning fork gives 5 beats per second with 40 cm length of sonometer wire. If the length of the wire is shortened by 1 cm, the number of beats is still the same. The frequency of the fork is

At what speed should a source of sound move so that the observer finds the apparent frequency equal to half the original frequency?

In an open end organ pipe of length ' $L$ ', if the velocity of sound is ' V ', then the fundamental frequency will be (Neglect end correction)

The fundamental frequencies of vibrations of air column in pipe open at both ends and in pipe closed at one end are ' $n_1$ ' and ' $n_2$ ' respectively, then

In a biprism experiment a steady interference pattern is observed on the screen using a light of wavelength $5000\ \text{\AA}$. Without disturbing the set up of the experiment, the source of light is replaced by a source of wavelength $6400\ \text{\AA}$.

The fringe width will

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

In Young's double slit experiment, at two points $P$ and $Q$ on screen, waves from slits $S_1$ and $S_2$ have a path difference of 0 and $\frac{\lambda}{4}$ respectively. The ratio of intensities at point $P$ to that at $Q$ will be $\left(\cos 0^\circ = 1, \cos 45^\circ = \frac{1}{\sqrt{2}}\right)$

A constant force $\vec{F} = 3\hat{i} - 2\hat{j} - \hat{k}$ newton has a displacement $\vec{r} = 2\hat{i} - 3\hat{j} - 3\hat{k}$ metre in 2 second. The work done and the power are respectively