MHT CET 2023 Physics Paper: 9 May, Shift 1

The coil of an a.c. generator has 100 turns, each of cross-sectional area $2\text{ m}^2$. It is rotating at constant angular speed $30\text{ rad/s}$, in a uniform magnetic field of $2 \times 10^{-2}\text{ T}$. If the total resistance of the circuit is $600\ \Omega$ then maximum power dissipated in the circuit is

In an $AC$ circuit, the current is $i = 5\sin\left(100t - \frac{\pi}{2}\right)\text{ A}$ and voltage is $e = 200\sin(100t)$ volt. Power consumption in the circuit is $(\cos 90^\circ = 0)$

A capacitor, an inductor and an electric bulb are connected in series to an a.c. supply of variable frequency. As the frequency of the supply is increased gradually, then the electric bulb is found to

For an electron moving in the $n$th Bohr orbit the deBroglie wavelength of an electron is

If an electron in a hydrogen atom jumps from an orbit of level $n = 3$ to orbit of level $n = 2$, then the emitted radiation frequency is (where R = Rydberg's constant, C = Velocity of light)

The ratio of wavelengths for transition of electrons from $2$nd orbit to $1$st orbit of Helium $\left(\text{He}^{+}\right)$ and Lithium $\left(\text{Li}^{++}\right)$ is (Atomic number of Helium $= 2$, Atomic number of Lithium $= 3$)

The ratio of potential difference that must be applied across parallel and series combination of two capacitors $C_1$ and $C_2$ with their capacitance in the ratio $1 : 2$ so that energy stored in these two cases becomes same is

The potential energy of charged parallel plate capacitor is $v_0$. If a slab of dielectric constant $K$ is inserted between the plates, then the new potential energy will be

The capacitance of a parallel plate capacitor is $2.5\ \mu\text{F}$. When it is half filled with a dielectric as shown in figure, its capacitance becomes $5\ \mu\text{F}$. The dielectric constant of the dielectric is

A galvanometer of resistance $G$ is shunted with a resistance of $10\%$ of $G$. The part of the total current that flows through the galvanometer is

In a meter bridge experiment null point is obtained at $l\text{ cm}$ from the left end. If the meter bridge wire is replaced by a wire of same material but twice the area of across-section, then the null point is obtained at a distance

From a metallic surface photoelectric emission is observed for frequencies $v_1$ and $v_2\ (v_1 > v_2)$ of the incident light. The maximum values of the kinetic energy of the photoelectrons emitted in the two cases are in the ratio $1 : x$. Hence the threshold frequency of the metallic surface is

The magnetic flux through a loop of resistance $10\ \Omega$ varying according to the relation $\phi = 6t^{2} + 7t + 1$, where $\phi$ is in milliweber, time is in second at time $t = 1\text{ s}$ the induced e.m.f. is

A conducting wire of length $2500\text{ m}$ is kept in east-west direction, at a height of $10\text{ m}$ from the ground. If it falls freely on the ground then the current induced in the wire is (Resistance of wire $= 25\sqrt{2}\ \Omega$, acceleration due to gravity $g = 10\text{ m/s}^{2},\ B_H = 2 \times 10^{-5}\text{ T}$)

An electron (mass $m$) is accelerated through a potential difference of '$V$' and then it enters in a magnetic field of induction '$B$' normal to the lines. The radius of the circular path is ($e =$ electronic charge)

Self inductance of solenoid is

A solid metallic sphere has a charge $+3Q$. Concentric with this sphere is a conducting spherical shell having charge $-Q$. The radius of the sphere is '$A$' and that of the spherical shell is '$B$'. $(B > A)$. The electric field at a distance '$R$' $(A < R < B)$ from the centre is ( $\varepsilon_0 =$ permittivity of vacuum)

Water is flowing through a horizontal pipe in stream line flow. At the narrowest part of the pipe

A body weighs $300\text{ N}$ on the surface of the earth. How much will it weigh at a distance $\frac{R}{2}$ below the surface of earth? ( $R \rightarrow$ Radius of earth)

A thin rod of length '$L$' is bent in the form of a circle. Its mass is '$M$'. What force will act on mass '$m$' placed at the centre of this circle?

( $G =$ constant of gravitation)

A seconds pendulum is placed in a space laboratory orbiting round the earth at a height '$3R$' from the earth's surface. The time period of the pendulum will be ( $R =$ radius of earth)

According to kinetic theory of gases, which one of the following statements is wrong?

The materials suitable for making electromagnets should have

A long straight wire carrying a current of $25\text{ A}$ rests on the table. Another wire PQ of length $1\text{ m}$ and mass $2.5\text{ g}$ carries the same current but in the opposite direction. The wire PQ is free to slide up and down. To what height will wire PQ rise? ($\mu_0 = 4\pi \times 10^{-7}$ SI unit)

A rubber ball filled with water, having a small hole is used as the bob of a simple pendulum. The time period of such a pendulum

The maximum velocity of a particle performing S.H.M. is '$V$'. If the periodic time is made $\left(\frac{1}{3}\right)$rd and the amplitude is doubled, then the new maximum velocity of the particle will be

The angle of prism is $A$ and one of its refracting surface is silvered. Light rays falling at an angle of incidence '$2A$' on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index of the material of the prism is

A square lamina of side '$b$' has same mass as a disc of radius '$R$' the moment of inertia of the two objects about an axis perpendicular to the plane and passing through the centre is equal. The ratio $\frac{b}{R}$ is

Two discs of same mass and same thickness (t) are made from two different materials of densities '$d_1$' and '$d_2$ ' respectively. The ratio of the moment of inertia $I_1$ to $I_2$ of two discs about an axis passing through the centre and perpendicular to the plane of disc is

A solid sphere rolls without slipping on an inclined plane at an angle $\theta$. The ratio of total kinetic energy to its rotational kinetic energy is

For an intrinsic semiconductor $(n_h$ and $n_e$ are the number of holes per unit volume and number of electrons per unit volume respectively)

To get the truth table shown, from the following logic circuit, the Gate G should be

A $5.0\text{ V}$ stabilized power supply is required to be designed using a $12\text{ V}$ DC power supply as input source. The maximum power rating of zener diode is $2.0\text{ W}$. The minimum value of resistance $R_\text{s}$ in $\Omega$ connected in series with zener diode will be

The excess of pressure in a first soap bubble is three times that of other soap bubble. Then the ratio of the volume of first bubble to other is

The radii of two soap bubbles are $r_1$ and $r_2$. In isothermal condition they combine with each other to form a single bubble. The radius of resultant bubble is

A jar '$P$' is filled with gas having pressure, volume and temperature $P, V, T$ respectively. Another gas jar $Q$ filled with a gas having pressure $2P$, volume $\frac{V}{4}$ and temperature $2T$. The ratio of the number of molecules in jar $P$ to those in jar $Q$ is

For a gas having '$X$' degrees of freedom, '$\gamma$' is ($\gamma =$ ratio of specific heats $= C_P/C_V$)

In a thermodynamic process, there is no exchange of heat between the system and surroundings. Then the thermodynamic process is

A gas at N.T.P. is suddenly compressed to $\left(\frac{1}{4}\right)$th of its original volume. The final pressure in (Given $\gamma =$ ratio of sp. heats $= \frac{3}{2}$) atmosphere is ( $P =$ original pressure)

Two uniform brass rods $A$ and $B$ of length '$l$' and '$2l$' and their radii '$2r$' and '$r$' respectively are heated to same temperature. The ratio of the increase in the volume of $\text{rod A}$ to that of $\text{rod B}$ is

When both source and listener are approaching each other the observed frequency of sound is given by $(V_L$ and $V_S$ is the velocity of listener and source respectively, $n_0 =$ radiated frequency)

A closed organ pipe of length '$L_1$' and an open organ pipe contain diatomic gases of densities '$\rho_1$ ' and '$\rho_2$' respectively. The compressibilities of the gases are same in both pipes, which are vibrating in their first overtone with same frequency. The length of the open organ pipe is (Neglect end correction)

Equation of simple harmonic progressive wave is given by $y = \frac{1}{\sqrt{a}}\sin\omega t \pm \frac{1}{\sqrt{b}}\cos\omega t$ then the resultant amplitude of the wave is $(\cos 90^\circ = 0)$

When a string of length '$l$' is divided into three segments of length $l_1, l_2$ and $l_3$. The fundamental frequencies of three segments are $n_1, n_2$ and $n_3$ respectively. The original fundamental frequency '$n$' of the string is

In a diffraction pattern due to single slit of width '$a$', the first minimum is observed at an angle of $30^\circ$ when the light of wavelength $5400\text{ \AA}$ is incident on the slit. The first secondary maximum is observed at an angle of $\left(\sin 30^\circ = \frac{1}{2}\right)$

In a single slit experiment, the width of the slit is doubled. Which one of the following statements is correct?

A beam of unpolarized light passes through a tourmaline crystal A and then it passes through a second tourmaline crystal B oriented so that its principal plane is parallel to that of A. The intensity of emergent light is $I_0$. Now B is rotated by $45^\circ$ about the ray. The emergent light will have intensity $\left(\cos 45^\circ = \frac{1}{\sqrt{2}}\right)$

The rays of different colours fail to converge at a point after passing through a thick converging lens. This defect is called

A stone is projected vertically upwards with speed '$v$'. Another stone of same mass is projected at an angle of $60^\circ$ with the vertical with the same speed '$v$'. The ratio of their potential energies at the highest points of their journey is $\left[\sin 30^\circ = \cos 60^\circ = 0.5, \cos 30^\circ = \sin 60^\circ = \frac{\sqrt{3}}{2}\right]$