MHT CET 2025 Physics Paper: 26 Apr, Shift 1

A resistor of $5\ \Omega$, inductor of self inductance $\left(\frac{2}{\pi^2}\right)\text{H}$ and a capacitor of unknown capacity are connected in series to an a.c. source of $100\text{ V}, 50\text{ Hz}$ supply. When the voltage and current are in phase, the value of capacitance is

In series LCR circuit C $= 2\ \mu\text{F},\ L = 5\text{ mH}$ and $R = 5\ \Omega$. The ratio of energy stored in the inductor to that in capacitor, when maximum current flows through the circuit is

$L, C$ and R are connected in series to an a. c. source. Which one of the following is true? Phase relation between current and voltage is such that

In Paschen series, wavelength of first line is ' $\lambda_1$ ' and for Brackett series, wavelength of first line is ' $\lambda_2$ ' then ratio $\frac{\lambda_1}{\lambda_2}$ is

The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) third to $2$nd energy level and (ii) highest energy level to $3$rd level is

Three capacitors are connected to a battery as shown in figure. The ratio of charge on capacitors $C_3$ and $C_1$ is

The capacity of air filled parallel plate capacitor is $C_0$. One-half of the space between the plates is filled with a dielectric constant ' K ' as shown in figure. The new capacity becomes $C_n$. The ratio $C_n$ to $C_0$ is

When a resistance of $100\ \Omega$ is connected in series with a galvanometer of resistance ' G ', its range is ' $V$ '. To double its range, a resistance of $1000\ \Omega$ is connected in series. The value of ' $G$ ' is

The potentiometer wire is 5 m long and potential difference of 4 V is maintained between the ends. The e.m.f. of the cell which balances against a length of 200 cm of the potentiometer wire is

The wavelength ' $\lambda$ ' of a photon and the deBroglie wavelength of an electron have same value. The ratio of kinetic energy of the electron to the energy of a photon is

( $\mathrm{m} =$ mass of electron, $\mathrm{c} =$ velocity of light, $\mathrm{h} =$ Planck's constant)

Light of incident frequency 3 times the threshold frequency is incident on a photosensitive material. If the incident frequency is made $\left(\frac{1}{4}\right)$th and intensity is tripled then the photoelectric current will

A magnetic field $4 \times 10^{-2}\text{ T}$ acts at right angles to a coil of area $100\text{ cm}^{2}$ with 50 turns. The average e.m.f. induced in the coil is 0.1 V, when it is removed from the field in time ' $t$ '. The value of ' $t$ ' is

When magnetic flux changes from $6.5 \times 10^{-2}\text{ Wb}$ to $11 \times 10^{-2}\text{ Wb}$ and the change in current is 0.03 A, the coefficient of mutual inductance will be

Two circuits A and B are connected to identical d.c. sources each of e.m.f. 10 volt. Self-inductances of circuits A and B are respectively $L_A = 10\text{ H}$ and $L_B = 10\text{ mH}$. The total resistance of each circuit is $40\ \Omega$. The ratio of energy consumed in circuit A and circuit B to build up the current to steady value is

Out of the following statements which is NOT the characteristics of electric lines of force?

Charges of $2\,\mu\text{C}$ and $-3\,\mu\text{C}$ are placed at two points A and B separated by distance of 1 m. The distance of the point from $A$ where net potential is zero is

A body weighs 45 N on the surface of the earth. The gravitational force on a body due to earth at a height equal to half the radius of earth will be

Two black spheres $P \,\&\, Q$ have radii in the ratio $4 : 3$. The wavelength of maximum intensity of radiation are in the ratio $4 : 5$ respectively. The ratio of radiated power by P to Q is

The temperature at which oxygen molecules will have same r.m.s. speed as helium molecules at $57^\circ\text{C}$ is (molecular masses of oxygen and helium are 32 and 4 respectively.)

The work done in turning a magnet of magnetic moment ' $M$ ' by an angle of $90^\circ$ from the meridian is ' $n$ ' times the corresponding Work done to turn it through an angle of $60^\circ$ where the value of ' $n$ ' is $(\cos 90^\circ = 0, \cos 60^\circ = 0.5)$

A bar of iron having magnetic moment $2.4\text{ Am}^2$ weighs 66 g. If the density of the material of the bar is $7700\text{ kg/m}^3$, the intensity of magnetisation in $\text{Am}^{-1}$ is

A boy throws a ball vertically upwards from a bridge with velocity $5\text{ m/s}$. It strikes water surface after 2 s. The height of the bridge is (Take $g = 10\text{ m/s}^2$)

An infinitely long straight conductor carrying current ' $I$ ' is bent into a shape as shown in figure. The radius of the circular loop is ' $r$ '. The magnetic induction at the centre of the loop at point ' O ' is ( $\mu_0 =$ permeability of free space)

The ratio of the frequencies of two simple pendulums is $4 : 3$ at the same place. The ratio of their respective lengths is

At a place, the length of the oscillating simple pendulum is made $\frac{1}{4}$ times keeping amplitude same then the total energy will be

A spring executes S.H.M. with mass 1 kg attached to it. The force constant of the spring is $4\text{ N/m}$. If at any instant its velocity is $20\text{ cm/s}$, the displacement at that instant is (Amplitude of S.H.M. is 0.4 m)

A monochromatic ray of light is incident normally on a thin prism of refracting angle A. The ray is deviated through an angle $(1.15)^\circ$ in passing through the prism. The ray reflected internally from the second face emerges from the first face making an angle of $(6.3)^\circ$ with the incident ray. The refractive index of the prism is

Moment of inertia of a solid sphere about its diameter is 'I'. It is then casted into 27 small spheres of same diameter. The moment of inertia of each small sphere about its diameter is

Moment of inertia of the rod about an axis passing through the centre and perpendicular to its length is ' $I_1$ '. The same rod is bent into a ring and its moment of inertia about the diameter is ' $I_2$ '. Then $I_1/I_2$ is

A rigid body rotates about a fixed axis with variable angular velocity $(\alpha - \beta t)$ at time $t$, where $\alpha$ and $\beta$ are constants. The angle through which it rotates before it comes to rest is

In a common emitter transistor amplifier circuit, the input resistance is $1.8\text{ k}\Omega$ and output is obtained across a load resistance of $9\text{ k}\Omega$. The alternating current gain is 70. Corresponding to an a.c. input voltage of 6 mV, the output voltage will be

Applying forward bias to p-n junction, the potential barrier

The material used for solar cell should have band gap

A capillary tube when immersed vertically in water, the rise of water column is upto height $h_1$ on earth's surface. When this arrangement is taken into a mine of depth 'd', below earth's surface, the height of the water column is $h_2$. If R is the radius of the earth, the ratio $\frac{h_2}{h_1}$ is

Let $R_1, R_2$ and $R_3$ be the radii of three mercury drops. A big mercury drop is formed from them under isothermal conditions. The radius of the resultant drop is

In case of free expansion, which one of the following statements is WRONG?

The heat energy that must be supplied to 14 gram of nitrogen at room temperature to raise its temperature by $48^\circ\text{C}$ at constant pressure is (Molecular weight of nitrogen $= 28, R =$ gas constant, $C_p = \frac{7}{2}R$ for diatomic gas)

An ideal gas expands adiabatically, $(\gamma = 1.5)$. To reduce the r.m.s. velocity of the molecules 4 times, the gas has to be expanded

The difference in length between two rods A and B is 60 cm at all temperatures. If $\alpha_{\text{A}} = 18 \times 10^{-6}/^\circ\text{C}$ and $\alpha_{\text{B}} = 27 \times 10^{-6}/^\circ\text{C}$, then the length of $\text{rod A}$ and $\text{rod B}$ at $0^\circ\text{C}$ is respectively

The error in the measurement of length and mass of a cube is $3\%$ and $4\%$ respectively. The error in the measurement of density will be

If $|\vec{a}| = \sqrt{26}, \ |\vec{b}| = 7$

$|\vec{a} \times \vec{b}| = 35$, find $\vec{a} \cdot \vec{b}$

125 small water drops of same size fall through air with constant velocity $4\text{ cm/s}$. They coalesce to form a big drop. The terminal velocity of the big drop is

A source of sound emits sound wave of frequency ' f ' and moves towards an observer with a velocity $\frac{V}{3}$ where V is the velocity of sound. If the observer moves away from the source with a velocity $\frac{V}{5}$ the apparent frequency heard by him will be

An air column is of length 17 cm. The ratio of frequencies of $5$th overtone if the air column is closed at one end to that open at both ends is (velocity of sound in air $= 340\text{ ms}^{-1}$)

In Sonometer experiment, the frequency of a tuning fork used is 288 Hz. Harmonics will 'NOT' be produced at the frequency

Fundamental frequency of sonometer wire is ' $n$ '. If the tension and length are increased 3 times and diameter is increased twice, the new frequency will be

A single slit diffraction pattern is formed with white light. For what wavelength of light the $4$th secondary maximum in diffraction pattern coincides with the $3$rd secondary maximum in the pattern of light of wavelength ' $\lambda$ '?

In Young's double slit experiment, the distance between the slits is 2 mm and the slits are 1 m away, from the screen. Two interference patterns can be obtained on the screen due to light of wavelength ' $\lambda_1$ ' and ' $\lambda_2$ ' respectively. The separation on the screen between the $3$rd order bright fringes on the two interference patterns is ( $\lambda_2 = 1.5\lambda_1$)

The ratio of the distance of $n$th bright band and $m$th dark band from the central bright band in an interference pattern is