MHT CET 2021 20th September Evening Shift

An inductive coil has a resistance of \(100 ~\Omega\). When an a.c. signal of frequency \(1000 \mathrm{~Hz}\) is applied to the coil the voltage leads the current by \(45^{\circ}\). The inductance of the coil is $$\left(\tan 45^{\circ}=1\ri...

In an ideal step down transformer, out of the following quantities, which quantity increases in the secondary coil?

A series LCR circuit with resistance (R) \(500 ~\mathrm{ohm}\) is connected to an a.c. source of \(250 \mathrm{~V}\). When only the capacitance is removed, the current lags behind the voltage by \(60^{\circ}\). When only the inductance is r...

A sample of radioactive element contains \(8 \times 10^{16}\) active nuclei. The halt-life of the element is 15 days. The number of nuclei decayed after 60 days is

The P.E. 'U' of a moving particle of mass 'm' varies with 'x'-axis as shown in figure. The deBroglie wavelength or the particle in the regions \(0 \leq x \leq 1\) and \(x > 1\) are \(\lambda_1\) and \(\lambda_2\) respectively. II the total ...

The gyromagnetic ratio of an electron in an hydrogen atom, according to Bohr model is

In the arrangement of the capacitors as shown in figure, each capacitor is of 6 \(\mu\)F, then equivalent capacity between points A and B is

A parallel plate air capacitor is charged upto 100 V. A plate 2 mm thick is inserted between the plates. Then to maintain the same potential difference, the distance between the plates is increased by 1.6 mm. The dielectric constant of the ...

Two masses '\(m_{\mathrm{a}}\)' and '\(\mathrm{m}_{\mathrm{b}}\)' moving with velocities '\(v_{\mathrm{a}}\)' and '\(v_{\mathrm{b}}\)' opposite directions collide elastically. Alter the collision '\(m_a\)' and '\(m_b\)' move with velocities...

A particle at rest starts moving with a constant angular acceleration of \(4 \mathrm{~rad} / \mathrm{s}^2\) in a circular path. At what time the magnitude of its centripetal acceleration and tangential acceleration will be equal?

A galvanometer has resistance '\(\mathrm{G}\)' \(\Omega\) and '\(\mathrm{I}_{\mathrm{g}}\)' is current flowing through it which produces full scale deflection. '\(\mathrm{S}_1\)' is the value of shunt which converts it into an ammeter of ra...

In potentiometer experiment, null point is obtained at a particular point for a cell on potentiometer wire '\(\mathrm{x}\)' cm long. If length of potentiometer wire is increased by few centimeter without changing the cell, the balancing len...

What is the additional energy that should be supplied to a moving electron to reduce its de Broglie wavelength from \(1 \mathrm{~nm}\) to \(0.5 \mathrm{~nm}\) ?

Photoelectrons are emitted when photons of energy \(4.2 ~\mathrm{eV}\) are incident on a photosensitive metallic sphere of radius \(10 \mathrm{~cm}\) and work function \(2.4 ~\mathrm{eV}\). The number of photoelectrons emitted before the em...

A metal wire of length \(2500 \mathrm{~m}\) is kept in east-west direction, at a height of \(10 \mathrm{~m}\) from the ground. If it falls freely on the ground then the current induced in the wire is (Resistance of wire $$=25 \sqrt{2} \Omeg...

A uniformly charged semicircular arc of radius '\(r\)' has linear charge density \((\lambda)\), is the electric field at its centre? ( \(\in_0=\) permittivity of free space)

A hollow charged metal sphere has radius 'R'. If the potential difference between its surface and a point at a distance '5 R' from the centre is \(\mathrm{V}\), then magnitude of electric field Intensity at a distance '5R' from the centre o...

What should be the radius of water drop so that excess pressure inside it is 72 Nm\(^{-2}\) ? (The surface tension of water 7.2 \(\times\) 10\(^{-2}\) Nm\(^{-1}\))

A body of density \(V\) is dropped from (at rest) height '\(h\)' into a lake of density '\(\delta\)' \((\delta > \rho)\). The maximum depth to which the body sinks before returning to float on the surface is [Neglect all dissipative forces]

The surface energy of a liquid drop is 'U'. It splits up into 512 equal droplets. The surface energy becomes

A body is projected from earth's surface with thrice the escape velocity from the surface of the earth. What will be its velocity when it will escape the gravitational pull?

The depth at which acceleration due to gravity becomes \(\frac{\mathrm{g}}{\mathrm{n}}\) is [ \(\mathrm{R}\) = radius of earth, \(\mathrm{g}=\) acceleration due to gravity, \(\mathrm{n}=\) integer \(]\)

A perfect gas of volume 10 litre n compressed isothermally to a volume of 1 litre. The rms speed of the molecules will

The relation obeyed by a perfect gas during an adiabatic process is \(\mathrm{PV}^{3 / 2}\). The initial temperature of the gas is '\(\mathrm{T}\)'. When the gas is compressed to half of its Initial volume, the final temperature of the gas ...

A black rectangular surface of area '\(\mathrm{A}\)' emits energy '\(\mathrm{E}\)' per second at \(27^{\circ} \mathrm{C}\). If length and breadth is reduced to \((1 / 3)^{\text {rd }}\) of its initial value and temperature is raised to $$32...

A monoatomic gas is suddenly compressed to (1/8)th of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is (\(\gamma=5/3\))

A conducting rod of length \(1 \mathrm{~m}\) has area of cross-section \(10^{-3} \mathrm{~m}^2\). One end is immersed in baiting water \(\left(100^{\circ} \mathrm{C}\right)\) and the other end in Ice \(\left(0^{\circ} \mathrm{C}\right)\). I...

Two stars 'P' and 'Q' emit yellow and blue light respectively. The relation between their temperatures \(\left(\mathrm{T}_{\mathrm{P}}\right.\) and \(\left.\mathrm{T}_{\mathrm{Q}}\right)\) is

A cricket player hit a ball like a projectile but the fielder caught the ball after 2 second. The maximum height reached by a ball is (g = 10 m/s2)

A metal conductor of length \(1 \mathrm{~m}\) rotates vertically about one of its ends at an angular velocity of \(5 \mathrm{~rad} / \mathrm{s}\). If horizontal component of earth's magnetic field is \(0.2 \times 10^{-4} \mathrm{~T}\), then...

Two wires carrying currents \(5 \mathrm{~A}\) and \(2 \mathrm{~A}\) are enclosed in a circular loop as shown in the figure. Another wire carrying a current of \(3 \mathrm{~A}\) is situated outside the loop. The value of $$\oint \overrightar...

The magnetic field at the centre of a current carrying circular coil of area 'A' is 'B'. The magnetic moment of the coil is ( \(\mu_0=\) permeability of free space)

The relation between magnetic moment 'M' of revolving electron and principle quantum number 'n' is

A convex lens of focal length \(\mathrm{T}\) is used to form an image whose size is one fourth that of size of the object. Then the object distance is

Inside a vessel filled with liquid a converging lens is placed as shown in figure. The lens has focal length \(15 \mathrm{~cm}\) when in air and has refractive index \(\frac{3}{2}\). If the liquid has refractive index \(\frac{9}{5}\), the f...

A disc of radius 0.4 metre and mass 1 kg rotates about an axis passing through its centre and perpendicular to its plane. The angular acceleration is 10 rad s\(^{-2}\). The tangential force applied to the rim of the disc is

The ratio of radii of gyration of a circular ring and circular disc of the same mass and radius, about an axis passing through their centres and perpendicular to their planes is

The output of an 'OR' gate is 'one'

In the case of insulators, a band gap and conduction band is respectively

A rectifier is used to

A particle executes S.H.M. of period \(\frac{2 \pi}{\sqrt{3}}\) second along a straight line \(4 \mathrm{~cm}\) long. The displacement of the particle at which the velocity is numerically equal to the acceleration is

A particle is suspended from a vertical spring which is executing S.H.M. of frequency \(5 \mathrm{~Hz}\). The spring is unstretched at the highest point of oscillation. Maximum speed of the particle is $$(\mathrm{g} =10 \mathrm{~m} / \mathr...

A body performs S.H.M. under the action of force '\(\mathrm{F}_1\)' with period '\(\mathrm{T}_1\)' second. If the force is changed to '\(\mathrm{F}_2\)' it performs S.H.M. with period '\(\mathrm{T_2}\)' second. If both forces '$$\mathrm{F_1...

In a single slit diffraction pattern, the distance between the first minimum on the left and the first minimum on the right is \(5 \mathrm{~mm}\). The screen on which the diffraction pattern is obtained is at a distance of $$80 \mathrm{~cm}...

In Young's double slit experiment, with a source of light having wavelength \(6300 \mathop A\limits^o\), the first maxima will occur when the

In Young's double slit experiment, the intensity at a point where the path difference is \(\frac{\lambda}{4}\) [ \(\lambda\) is wavelength of light used] is '\(\mathrm{I}\)'. If '\(\mathrm{I}_0\)' is the maximum intensity then $$\frac{\math...

Which one of the following statements is true?

Two consecutive harmonics of an air column in a pipe closed at one end are of frequencies 150 Hz and 250 Hz. The fundamental frequency of an air column is

An air column in a pipe, which is closed at one end will be in resonance with a vibrating tuning fork of frequency 264 Hz for various lengths. Which one of the following lengths is not possible? (V = 330 m/s)

Beats are produced by waves \(\mathrm{y_1=a\sin2000\pi t}\) and \(\mathrm{y_2=a\sin2008\pi t}\). The number of beats heard per second is