MHT CET 2023 Physics Paper: 12 May, Shift 2

Resistor of $2\ \Omega$, inductor of $100\ \mu\text{H}$ and capacitor of $400\text{ pF}$ are connected in series across a source of $e_{\text{rms}} = 0.1$ Volt. At resonance, voltage drop across inductor is

When an inductor '$L$' and a resistor '$R$' in series are connected across a $15\text{ V},\ 50\text{ Hz}$ a.c. supply, a current of $0.3\text{ A}$ flows in the circuit. The current differs in phase from applied voltage by $\left(\frac{\pi}{3}\right)^{c}$. The value of '$R$' is $\left(\sin\frac{\pi}{6} = \cos\frac{\pi}{3} = \frac{1}{2},\ \sin\frac{\pi}{3} = \cos\frac{\pi}{6} = \frac{\sqrt{3}}{2}\right)$

An a.c. source of $15\text{ V},\ 50\text{ Hz}$ is connected across an inductor (L) and resistance (R) in series R.M.S. current of $0.5\text{ A}$ flows in the circuit. The phase difference between applied voltage and current is $\left(\frac{\pi}{3}\right)$ radian. The value of resistance $(R)$ is $\left(\tan 60^\circ = \sqrt{3}\right)$

In Balmer series, wavelength of the $2$nd line is '$\lambda_1$' and for Paschen series, wavelength of the $1$st line is '$\lambda_2$', then the ratio '$\lambda_1$ ' to '$\lambda_2$' is

If the charge on the capacitor is increased by 3 coulombs, the energy stored in it increases by $44\%$. The original charge on the capacitor is

A particle is moving in a circle with uniform speed '$v$'. In moving from a point to another diametrically opposite point

A body of mass '$m$' attached at the end of a string is just completing the loop in a vertical circle. The apparent weight of the body at the lowest point in its path is ( $g$ = gravitational acceleration)

A potentiometer wire of length $4\text{ m}$ and resistance $5\ \Omega$ is connected in series with a resistance of $992\ \Omega$ and a cell of e.m.f. $4\text{ V}$ with internal resistance $3\ \Omega$. The length of $0.75\text{ m}$ on potentiometer wire balances the e.m.f. of

Two resistance $\mathrm{X}$ and $\mathrm{Y}$ are connected in the two gaps of a meterbridge and the null points is obtained at $20\text{ cm}$ from zero end. When the resistance of $20\ \Omega$ is connected in series with the smaller of the two resistance $\mathrm{X}$ and $\mathrm{Y}$, the null point shifts to $40\text{ cm}$ from left end. The value of smaller resistance in ohm is

When an electron is accelerated through a potential '$V$', the de-Broglie wavelength associated with it is '$4\lambda$'. When the accelerating potential is increased to $4\ \mathrm{V}$, its wavelength will be

Graph shows the variation of de-Broglie wavelength $(\lambda)$ versus $\frac{1}{\sqrt{V}}$ where '$V$' is the accelerating potential for four particles A, B, C, D carrying same charge but of masses $\mathrm{m_1, m_2, m_3, m_4}$. Which on represents a particle of largest mass?

An air craft of wing span $40\text{ m}$ flies horizontally in earth's magnetic field $5 \times 10^{-5}\text{ T}$ at a speed of $500\text{ m/s}$. The e.m.f. generated between the tips of the wings of the air craft is

SI units of self inductance is

Inductance per unit length near the middle of a long solenoid is $(\mu_0 =$ permeability of free space, $n =$ number of turns per unit length, $d =$ the diameter of the solenoid)

Select the correct statement from the following.

Two point charges '$q_1$ ' and '$q_2$' are separated by a distance '$d$'. What is the increase in potential energy of the system when '$q_2$' is moved towards '$q_1$' by a distance '$x$'? $(x < d)\ (\frac{1}{4\pi\varepsilon_0} = K$, constant)

Three point charges $+Q, +2q$ and $+q$ are placed at the vertices of a right angled isosceles triangle. The net electrostatic potential energy of the configuration is zero, if $Q$ is equal to

Select the WRONG statement from the following. In a streamline flow

The depth at which acceleration due to gravity becomes $\frac{g}{2n}$ is $(R =$ radius of earth, $g =$ acceleration due to gravity on earth's surface, $n$ is integer)

A simple pendulum is oscillating with frequency '$F$' on the surface of the earth. It is taken to a depth $\frac{R}{3}$ below the surface of earth. ( $R =$ radius of earth). The frequency of oscillation at depth $R/3$ is

A body is projected vertically upwards from earth's surface of radius '$R$' with velocity equal to ${\frac{1}{3}}^{\text{rd}}$ of escape velocity. The maximum height reached by the body is

Compare the rate of loss of heat from a metal sphere at $627^\circ\text{C}$ with the rate of loss of heat from the same sphere at $327^\circ\text{C}$, if the temperature of the surrounding is $27^\circ\text{C}$. (nearly)

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

A ball is projected vertically upwards from ground. It reaches a height '$h$' in time $t_1$, continues its motion and then takes a time $t_2$ to reach ground. The height $h$ in terms of $g, t_1$ and $t_2$ is $(g =$ acceleration due to gravity)

An electron makes a full rotation in a circle of radius $0.8\text{ m}$ in one second. The magnetic field at the centre of the circle is $(\mu_0 = 4\pi \times 10^{-7}$ SI units)

Two concentric circular coils of 10 turns each are situated in the same plane. Their radii are $20\text{ cm}$ and $40\text{ cm}$ and they carry respectively $0.2\text{ A}$ and $0.3\text{ A}$ current in opposite direction. The magnetic field at the centre is ($\mu_0 = 4\pi \times 10^{-7}$ SI units)

A coil of '$n$' turns and radius '$R$' carries a current '$I$'. It is unwound and rewound again to make another coil of radius $\left(\frac{R}{3}\right)$, current remaining the same. The ratio of magnetic moment of the new coil to that of original coil is

Two different radioactive elements with half lives '$\text{T}_1$ ' and '$\text{T}_2$' have undecayed atoms '$\text{N}_1$ ' and '$\text{N}_2$ ' respectively present at a given instant. The ratio of their activities at that instant is

A particle starts from mean position and performs S.H.M. with period 4 second. At what time its kinetic energy is $50\%$ of total energy?

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

In a stationary lift, time period of a simple pendulum is '$T$'. The lift starts accelerating downwards with acceleration $\left(\frac{g}{4}\right)$, then the time period of the pendulum will be

A glass prism deviates the red and violet rays through $9^\circ$ and $11^\circ$ respectively. A second prism of equal angle deviates them through $11^\circ$ and $13^\circ$ respectively. The ratio of dispersive power of second prism to first prism is

An ink mark is made on a piece of paper on which a glass slab of thickness '$t$' is placed. The ink mark appears to be raised up through a distance '$x$' when viewed at nearly normal incidence. If the refractive index of the material of glass slab is '$\mu$' then the thickness of glass slab is given by

A thin wire of length '$L$' and uniform linear mass density '$m$' is bent into a circular coil. The moment of inertia of this coil about tangential axis and in plane of the coil is

In $P$th second, a particle describes angular displacement of '$\beta$' rad. If it starts from rest, the angular acceleration is

In the following digital logic circuit, the output Y will be '1' for inputs

In which figure, the junction diode is forward biased?

Which one of the following statements is WRONG regarding LED?

Eight small drops of mercury each of radius '$r$', coalesce to form a large single drop. The ratio of total surface energy before and after the change is

For polyatomic gases, the ratio of molar specific heat at constant pressure to constant volume is ( $f =$ degrees of freedom)

Select the WRONG statement from the following. For an isothermal process

A monoatomic ideal gas initially at temperature '$T_1$ ' is enclosed in a cylinder fitted with massless, frictionless piston. By releasing the piston suddenly the gas is allowed to expand to adiabatically to a temperature '$T_2$ '. If '$L_1$ ' and '$L_2$' are the lengths of the gas columns before and after expansion respectively, then $\frac{T_2}{T_1}$ is

The volume of a metal block increases by $0.225\%$ when its temperature is increased by $30^\circ\text{C}$. Hence coefficient of linear expansion of the material of metal block is

A spherical metal ball of radius '$r$' falls through viscous liquid with velocity '$\mathrm{V}$'. Another metal ball of same material but of radius $\left(\frac{r}{3}\right)$ falls through same liquid, then its terminal velocity will be

A tuning fork gives 3 beats with $50\text{ cm}$ length of sonometer wire. If the length of the wire is shortened by $1\text{ cm}$, the number of beats is still the same. The frequency of the fork is

End correction at open end for air column in a pipe of length '$l$' is '$e$'. For its second overtone of an open pipe, the wavelength of the wave is

The equation of wave motion is $Y = 5\sin(10\pi t - 0.02\pi x + \pi/3)$ where $x$ is in metre and $t$ in second. The velocity of the wave is

A tuning fork of frequency $220\text{ Hz}$ produces sound waves of wavelength $1.5\text{ m}$ in air at N.T.P. The increase in wavelength when the temperature of air is $27^\circ\text{C}$ is nearly $\left(\sqrt{\frac{300}{273}} = 1.05\right)$

The ratio of intensities of two points on a screen in Young's double slit experiment when waves from the two slits have a path difference of $\frac{\lambda}{4}$ and $\frac{\lambda}{6}$ is

$(\cos 90^\circ = 0, \cos 60^\circ = 0.5)$

In Young's double slit experiment when a glass plate of refractive index 1.44 is introduced in the path of one of the interfering beams, the fringes are displaced by a distance '$y$'. If this plate is replaced by another plate of same thickness but of refractive index 1.66, the fringes will be displaced by a distance

One of the slits in Young's double slit experiment is covered with a transparent sheet of thickness $2.9 \times 10^{-3}\text{ cm}$. The central fringe shifts to a position originally occupied by the $25$th bright fringe. If $\lambda = 5800\ \text{\AA}$, the refractive index of the sheet is