MHT CET 2021 Physics Paper: 21 Sep, Shift 1

An alternating voltge is represented by $V = 80 \sin(100\pi t) \cos(100\pi t)$ volt. The peak voltage is

In the graphical representation of e.m.f. '$e$' and current '$i$' versus '$\omega t$' for an a.c. circuit, both emf and current reach zero, minimum and maximum value at the same time. The circuit element connected to the source will be

A series combination of resistor 'R' and capacitor 'C' is connected to an a.c. source of angular frequency '$\omega$'. Keeping the voltage same, if the frequency is changed to $\frac{\omega}{3}$ the current becomes half of the original current. Then the ratio of capacitive reactance and resistance at the former frequency is

When an electron in hydrogen atom jumps from third excited state to the ground state, the de- Broglie wavelength associated with the electron becomes

'$\lambda_1$' is the wavelength of series limit of Lyman series, '$\lambda_2$ ' is the wavelength of the first line line of Lyman series and '$\lambda_3$' is the series limit of the Balmer series. Then the relation between $\lambda_1, \lambda_2$ and $\lambda_3$ is

The resultant capacity between points A and B in the given circuit is

An air filled parallel plate capacitor has a capacity $2\text{ pF}$. The sepeartion of the plates is doubled and the interspace between the plates is filled with dielectric material, then the capacity is increased to $6\text{ pF}$. The dielectric constant of the material is

A particle moves in a circular orbit of radius '$r$' under a central attractive force, $F = -\frac{k}{r}$, where $k$ is a constant. The periodic time of its motion is proportional to

In a meter bridge experiment, the balance point is obtained at length $\ell_1\text{ cm}$ from left end when resistances in the left gap and right gap are $5\ \Omega$ and $R\ \Omega$ respectively. When the resistance $R$ is shunted with equal resistance, the new balance point is at $1.6\ell_1$. The resitance $R$ in ohm is

Two wires '$\mathrm{A}$' and '$\mathrm{B}$' of equal length are connected in left and right gap respectively of meter bridge, null point is obtained at $40\text{ cm}$, from the left end. Diameters of the wires '$A$' and '$B$' are in the ratio $3 : 1$ respectively, the ratio of specific resistance of 'A' to that of 'B' is

On a photosensitive surface, if the intensity of incident radiation is increased, the stopping potential

Light of frequency two times the threshold frequency is incident on photosensitive material. If the incident frequency is made $\left(\frac{1}{3}\right)$rd and intensity is doubled, then the photoelectric current will

A wire of length '$L$'; having resistance '$R$' falls from a height '$\ell$' in earth's horizontal magnetic field '$B$'. The current through the wire is ( $g =$ acceleration due to gravity)

A coil of radius '$r$' is placed on another coil (whose radius is '$R$' and current through it is changing) so that their centres coincide. ( $R > r$ ). If both coplanar, then the mutual inductance between them is proportional to

The magnetic potential energy stored in a certain inductor is $25\text{ mJ}$, when the current in the inductor is $50\text{ mA}$. This inductor is of inductance

'$F$' is the force between the two identical charged particles placed at a distance '$Y$' from each other. If the distance between the charges is reduced to half the previous distance then force between them becomes

When the value of acceleration due to gravity '$g$' becomes $\frac{g}{3}$ above surface of height '$h$' then relation between '$h$' and '$R$' is ( $R =$ radius of earth)

A pendulum is oscillating with frequency '$n$' on the surface of the earth. It is taken to a depth $\frac{R}{2}$ below the surface of earth. New frequency of oscillation at depth $\frac{R}{2}$ is

[ $R$ is the radius of earth]

A particle of mass '$m$' is kept at rest at a height $3R$ from the surface of earth, where '$R$' is radius of earth and '$M$' is the mass of earth. The minimum speed with which it should be projected, so that it does not return back is ( $g =$ acceleration due to gravity on the earth's surface)

The temperature difference bewtween two sides of metal plate, $3\text{ cm}$ thick is $15^\circ\text{C}$. Heat is transmitted through plate at the rate of $900\text{ kcal}$ per minute per $\text{m}^2$ at steady state. The thermal conductivity of metal is

A black body has maximum wavelength '$\lambda_{m}$' at temperature $2000\text{ K}$. Its corresponding wavelength at temperature $3000\text{ K}$ will be

A black reactangular surface of area '$a$' emits energy '$E$' per second at $27^\circ\text{C}$. If length and breadth is reduced to $\left(\frac{1}{3}\right)$rd of initial value and temperature is raised to $327^\circ\text{C}$ then energy emitted per second becomes

What is susceptibility of a medium, if its relative permeability is 0.85?

A long solenoid carrying a current produces a magnetic field B along its axis. If the number of turns per $\text{cm}$ is doubled and the current is made $\left(\frac{1}{3}\right)$rd then the new value of the magnetic field will be

A charge moves with velocity '$V$' through electric field $(E)$ as well as magnetic field (B). then the force acting on it is

A bomb is dropped by an aeroplane flying horizontally with a velocity $200\text{ km/hr}$ and at a height of $980\text{ m}$. At the time of dropping a bomb, the distance of the aeroplane from the target on the ground to hit directly is $\left(g = 9.8\text{ m/s}^{2}\right)$

A ray of light is incident at an angle 'I' on one face of thin prism. The ray emerges normally from the other face. Refractive index of the glass prism is '$n$' and angle of prism is '$A$'. The value of '$I$' is

A glass cube of length $24\text{ cm}$ has a small air bubble trapped inside. When viewed normally from one face it is $10\text{ cm}$ below the surface. When viewed normally from the opposite face, its apparent distance is $6\text{ cm}$. The refractive index of glass is

A particle executes linear S.H.M. The mean position of oscillation is at the principal axis of a convex lens of focal length $8\text{ cm}$. the mean position of oscillation is at 14 cm from the lens with amplitude 1 cm. The amplitude of oscillating image of the particle is nearly

The moment of inertia of a circular disc of radius $2\text{ m}$ and mass $1\text{ kg}$ about an axis XY passing through its centre of mass and perpendicular to the plane of the disc is $2\text{ kg m}^2$. The moment of inertia about an axis parallel to the axis $XY$ and passing through the edge of the disc is

The moment of inertia of a body about a given axis is $1.2\text{ kg m}^{2}$. Initially the body is at rest. In order to produce rotational kinetic energy of $1500\text{ J}$, an angular acceleration of $25\text{ rad/s}^{2}$ must be applied about an axis for a time duration of

In a pure silicon, number of electrons and holes per unit volume are $1.6 \times 10^{16}\text{ m}^{-3}$. If silicon is doped with Boron in a way that on doping hole density increases to $4 \times 10^{22}\text{ m}^{-3}$. Then electron density in doped semiconductor will be

For a transistor, $\frac{1}{\alpha_\text{DC}} - \frac{1}{\beta_\text{DC}}$ is equal to [ $\alpha_\text{DC}$ and $\beta_\text{DC}$ are current amplification factors]

The current in the following circuit is

The surface tension of most of the liquid decreases with rise in

Two small drops of mercury each of radius '$R$' coalesce to form a large single drop. The ratio of the total surface energies before and after the change is

The molar specific heats of an ideal gas at constant pressure and volume are denoted by '$C_p$' and '$C_v$' respectively. If $\gamma = \frac{C_p}{C_v}$ and '$R$' is universal gas constant, then $C_v$ is equal to

Which one of the following equations specifies an isobaric process? $[Q =$ heat supplied $\Delta P, \Delta V$ and $\Delta T$ are change in pressure, volume and temperature respectively]

A monoatomic gas at pressure '$P$' having volume '$V$' expands isothermally to a volume $2\,V$ and then adiabatically to a volume $16\,V$. The final pressure of the gas is $\left(\gamma = \frac{5}{3}\right)$

Find the value of $-$ 197$^\circ$C temperature in Kelvin.

The velocity of a small ball of mass '$M$' and density '$\mathrm{d}_1$' when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is '$\mathrm{d}_2$', the viscous force acting on the ball is ( $\mathrm{g} =$ acceleration due to gravity)

In fundamental mode, the time required for the sound wave to reach upto the closed end of pipe filled with air is $t$ second. The frequency of vibration of air column is

A closed organ pipe of length '$L_c$' and an open organ pipe of length '$L_o$' contain different gases of densities '$\rho_1$' and '$\rho_2$' respectively. The compressibility of the gases is the same in both the pipes. The gases are vibrating in their first overtone with the same frequency. What is the length of open organ pipe?

A progressive wave of frequency 50 Hz is travelling with velocity 350 m/s through a medium. The change in phase at a given time interval of 0.01 second is

A simple harmonic progressive wave is given by $Y = Y_0\sin 2\pi\left(nt - \frac{x}{\lambda}\right)$. If the wave velocity is $\left(\frac{1}{8}\right)$th the maximum particle velocity then the wavelength is

In biprism experiment, 21 fringes are observed in a given region using light of wavelength 4800 $\text{\AA}$. If light of wavelength 5600 $\text{\AA}$ is used, the number of fringes in the same region will be

In diffraction experiment, from a single slit, the angular width of central maximum does NOT depend upon

A double slit experiment is immersed in water of refractive index 1.33. The slit separationis 1 $\text{mm}$ and the distance between slit and screen is $1.33\text{ m}$. The slits are illuminated by a light of wavelength $6300\ \text{\AA}$. The fringewidth is

A sphere of mass 25 gram is placed on a vertical spring. It is compressed by $0.2\text{ m}$ using a force $5\text{ N}$. When the spring is released, the sphere will reach a height of $\left(\text{g} = 10\text{ m/s}^2\right)$