MHT CET 2023 Physics Paper: 10 May, Shift 1

In a series LR circuit, $X_L = R$, power factor is $P_1$. If a capacitor of capacitance $C$ with $X_C = X_L$ is added to the circuit the power factor becomes $P_2$. The ratio of $P_1$ to $P_2$ will be

The inductive reactance of a coil is '$X_L$'. If the inductance of a coil is tripled and frequency of a.c. supply is doubled, then the new inductive reactance will be

In the circuit shown the ratio of quality factor and the bandwidth is

The shortest wavelength in the Balmer series of hydrogen atom is equal to the shortest wavelength in the Brackett series of a hydrogen like atom of atomic number $z$. The value of $z$ is

The ratio of longest to shortest wavelength emitted in Paschen series of hydrogen atom is

Two capacitors $C_1 = 3\ \mu\text{F}$ and $C_2 = 2\ \mu\text{F}$ are connected in series across d.c. source of $100\text{ V}$. The ratio of the potential across $C_2$ to $C_1$ is

The mean electrical energy density between plates of a charged air capacitor is (where $q =$ charge on capacitor, $A =$ Area of capacitor plate)

A parallel plate capacitor has plate area '$A$' and separation between plates is '$d$'. It is charged to a potential difference of $V_0$ volt. The charging battery is then disconnected and plates are pulled apart three times the initial distance. The work done to increase the distance between the plates is $(\varepsilon_0 =$ permittivity of free space)

A body of mass 200 gram is tied to a spring of spring constant $12.5\text{ N/m}$, while other end of spring is fixed at point '$O$'. If the body moves about '$O$' in a circular path on a smooth horizontal surface with constant angular speed $5\text{ rad/s}$ then the ratio of extension in the spring to its natural length will be

A voltmeter of resistance $150\ \Omega$ connected across a cell of e.m.f. $3\text{ V}$ reads $2.5\text{ V}$. What is the internal resistance of the cell?

If only $1\%$ of total current is passed through a galvanometer of resistance '$G$' then the resistance of the shunt is

An electron accelerated through a potential difference '$V_1$ ' has a de-Broglie wavelength '$\lambda$'. When the potential is changed to '$V_2$' its de-Broglie wavelength increases by $50\%$. The value of $\left(\frac{V_1}{V_2}\right)$ is

Maximum kinetic energy of photoelectrons is '$E$' when wavelength of incident radiation is '$\lambda$'. If wavelength of incident radiations is reduced to $\frac{\lambda}{3}$ then maximum kinetic energy of photoelectrons becomes four times. Then work function of the metal is

A square loop of area $25\text{ cm}^{2}$ has a resistance of $10\ \Omega$. This loop is placed in a uniform magnetic field of magnitude $40\text{ T}$. The plane of 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

Two conducting circular loops of radii '$R_1$' and '$R_2$' are placed in the same plane with their centres coinciding. If $R_1 > R_2$, the mutual inductance $M$ between them will be directly proportional to

A graph of magnetic flux $(\phi)$ versus current (I) is plotted for four inductors A, B, C, D. Larger value of self inductance is for inductor

An electric dipole consisting of two opposite charges of $2 \times 10^{-6}\text{ C}$ separated by a distance of $3\text{ cm}$ placed in an electric field of $2 \times 10^{5}\text{ N/C}$ then the maximum torque acting on dipole is

Water flows through a horizontal pipe at a speed '$V$'. Internal diameter of the pipe is '$d$'. If the water is coming out at a speed '$V_1$' then the diameter of the nozzle is

There is a second's pendulum on the surface of earth. It is taken to the surface of planet whose mass and radius are twice that of earth. The period of oscillation of second's pendulum on the planet will be

For a satellite orbiting around the earth in a circular orbit, the ratio of potential energy to kinetic energy at same height is

A satellite moves in a stable circular orbit round the earth if (where $V_H, V_c$ and $V_e$ are the horizontal velocity, critical velocity and escape velocity respectively)

Heat energy is incident on the surface at the rate of X J/min. If '$a$' and '$r$' represent coefficient of absorption and reflection respectively then the heat energy transmitted by the surface in '$t$' minutes is

A black body radiates maximum energy at wavelength '$\lambda$' and its emissive power is $E$. Now due to change in temperature of that body, it radiates maximum energy at wavelength $\frac{2\lambda}{3}$. At that temperature emissive power is

The average force applied on the walls of a closed container depends on $T^{x}$ where $T$ is the temperature of an ideal gas. The value of '$x$' is

According to Curie's law in magnetism, the correct relation is ( $\mathrm{M} =$ magnetization in paramagnetic sample, $\mathrm{B} =$ applied magnetic field, $\mathrm{T} =$ absolute temperature of the material, $\mathrm{C} =$ curie's constant)

A body is released from the top of a tower '$H$' metre high. It takes $t$ second to reach the ground. The height of the body $\frac{t}{2}$ second after release is

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

Electron of mass '$m$' and charge '$q$' is travelling with speed '$v$' along a circular path of radius '$R$', at right angles to a uniform magnetic field of intensity '$B$'. If the speed of the electron is halved and the magnetic field is doubled, the resulting path would have radius

The amplitude of a particle executing S.H.M. is $3\text{ cm}$. The displacement at which its kinetic energy will be $25\%$ more than the potential energy is

Which of the following is NOT involved in the formation of secondary rainbow?

A double convex air bubble in water behaves as

A particle of mass '$\mathrm{m}$' is rotating along a circular path of radius '$r$' having angular momentum '$L$'. The centripetal force acting on the particle is given by

If 'I' is moment of inertia of a thin circular disc about an axis passing through the tangent of the disc and in the plane of disc. The moment of inertia of same circular disc about an axis perpendicular to plane and passing through its centre is

Seven identical discs each of mass $M$ and radius $R$ are arranged in a hexagonal plane pattern so as to touch each neighbour disc as shown in the figure. The moment of inertia of the system of seven discs about an axis passing through the centre of central disc and normal to the plane of all discs is

In insulators

To obtain the truth-table shown, from the following logic circuit, the gate G should be

Identify the mismatch out of the following.

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid '$A$' vertically is $5\text{ cm}$. If the tube is dipped in a similar manner in another liquid '$B$' of surface tension and density double the values of liquid '$A$', the height of liquid column raised in liquid '$B$' would be (Assume angle of contact same)

Three liquids have same surface tension and densities $\rho_1, \rho_2$, and $\rho_3\ (\rho_1 > \rho_2 > \rho_3)$. In three identical capillaries rise of liquid is same. The corresponding angles of contact $\theta_1, \theta_2$ and $\theta_3$ are related as

A Carnot engine with efficiency $50\%$ takes heat from a source at $600\text{ K}$. To increase the efficiency to $70\%$, keeping the temperature of the sink same, the new temperature of the source will be

A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is $\left(\frac{C_P}{C_V} = \gamma = \frac{3}{2}\right)\ (R =$ gas constant $)$

A piece of metal at $850\text{ K}$ is dropped into $1\text{ kg}$ water at $300\text{ K}$. If the equilibrium temperature of water is $350\text{ K}$ then the heat capacity of the metal, expressed in $\text{J K}^{-1}$ is $(1\text{ cal} = 4.2\text{ J})$

Consider the Doppler effect in two cases. In the first case, an observer moves towards a stationary source of sound with a speed of $50\text{ m/s}$. In the second case, the observer is at rest and the source moves towards the observer with the same speed of $50\text{ m/s}$. Then the frequency heard by the observer will be

[velocity of sound in air $= 330\text{ m/s}$.]

An open organ pipe having fundamental frequency (n) is in unison with a vibrating string. If the tube is dipped in water so that $75\%$ of the length of the tube is inside the water then the ratio of fundamental frequency of the air column of dipped tube with that of string will be (Neglect end corrections)

In case of a stationary wave pattern which of the following statements is CORRECT?

If the length of stretched string is reduced by $40\%$ and tension is increased by $44\%$ then the ratio of final to initial frequencies of stretched string is

A person is observing a bacteria through a compound microscope. For better observation and to improve its resolving power he should

In Young's double slit experiment the separation between the slits is doubled without changing other setting of the experiment to obtain same fringe width, the distance 'D' of the screen from slit should be made

Two sources of light $0.6\text{ mm}$ apart and screen is placed at a distance of $1.2\text{ m}$ from them. A light of wavelength $6000\ \text{\AA}$ used. Then the phase difference between the two light waves interfering on the screen at a point at a distance $3\text{ mm}$ from central bright band is

If a lighter body of mass '$M_1$' and velocity '$V_1$' and a heavy body (mass $M_2$ and velocity $V_2$) have the same kinetic energy then