Practice Questions

Q21.A small circular loop of wire of radius a is located at the centre of a much larger circular wire loop of radius b . The two loops are in the same plane. The outer loop of radius b carries an alternating current I = I0 cos(ωt). The emf induced in the smaller inner loop is nearly: (1) πμ0 I0 a2b ω sin(ωt) (2) πμ02 I0 . a2b ω cos(ωt) I0 b2 (3) πμ0 ω sin(ωt) ω cos(ωt) (4) πμ02 I0 . a2b a

Q21.A uniform magnetic field B of 0 .3 T is along the positive Z -direction. A rectangular loop ( abcd ) of sides 10 cm × 5 cm carries a current I of 12 A . Out of the following different orientations which one corresponds to stable equilibrium? JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper (1) (2) (3) (4)

Q22.A sinusoidal voltage of peak value 283 V and angular frequency 320 s−1 is applied to a series LCR circuit. Given that R = 5 Ω, L = 25 mH and C = 1000 μF . The total impedance and phase difference between the voltage across the source and the current will respectively be- (1) 10 Ω and tan−1( 53 ) (2) 7 Ω and 45o (3) 7 Ω and tan−1( 53 ) (4) 10 Ω and tan−1( 38 ) →

Q22.Magnetic field in a plane electromagnetic wave is given by, → B = B0 sin(kx + ωt)ˆj T. Expression for corresponding electric field will be: (Where c is speed of light) → → (1) (2) E = −B0c sin(kx + ωt)ˆk V m−1 E = B0c sin(kx −ωt)ˆk V m−1 → → (3) (4) B0 E = B0c sin(kx + ωt)ˆk V m−1 E = c sin(kx + ωt)ˆk V m−1

Q22.In a coil of resistance 100 Ω, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is: (1) 275 Wb (2) 200 Wb (3) 225 Wb (4) 250 Wb

Q23.An electron beam is accelerated by a potential difference 𝑉 to hit a metallic target to produce 𝑋- rays. It produces continuous as well as characteristic 𝑋- rays. If 𝜆𝑚𝑖𝑛 is the smallest possible wavelength of 𝑋- ray in the spectrum, the variation of log𝜆𝑚𝑖𝑛 with log𝑉 is correctly represented in : (1) (2) (3) (4)

Q23.The electric field component of a monochromatic radiation is given by E = 2E0 cos kz cos ωt ˆi, Its magnetic → field B is then given by: (1) 2E0 c sin kz sin ωt ˆj (2) 2E0c cos kz cos ωt ˆj (3) 2E0 c sin kz cos ωt ˆj (4) −2E0c sin kz sin ωt ˆj

Q23.Let the refractive index of a denser medium with respect to rarer medium be n12 and its critical angle be θC . At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is 90o . Angle A is given by (1) tan−1(sin θC) (2) 1 tan−1(sin θC) (3) cos−1(sin θC) (4) cos−1(sin1 θC)

Q24.In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is- (1) 20. 0 cm (2) 30. 5 cm (3) 25. 0 cm (4) 27. 5 cm

Q24.A single slit of width b is illuminated by a coherent monochromatic light of wavelength λ. If the second and fourth minima in the diffraction pattern at a distance 1 cm from the slit are at 3 cm and 6 cm respectively from the central maximum, what is the width of the central maximum? (i.e. distance between first minimum on either side of the central maximum) (1) 4. 5 cm (2) 1. 5 cm (3) 6. 0 cm (4) 3. 0 cm

Q24.A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15 cm from a converging lens of magnitude of focal length 20 cm. A beam of parallel light falls on the diverging lens. The final image formed is: (1) Real and at a distance of 6 cm from the (2) Real and at a distance of 40 cm from convergent lens convergent lens (3) Virtual and at a distance of 40 cm from (4) Real and at a distance of 40 cm from the convergent lens divergent lens

Q25.A single slit of width 0. 1 mm is illuminated by a parallel beam of light of wavelength 6000 Å and diffraction bands are observed on a screen 0. 5 m from the slit. The distance of the third dark band from the central bright band is: (1) 9 mm (2) 3 mm (3) 4. 5 mm (4) 1. 5 mm

Q25.In a Young's double slit experiment, slits are separated by 0 . 5 mm, and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is: JEE Main 2017 (02 Apr) JEE Main Previous Year Paper (1) 15 . 6 mm (2) 1 . 56 mm (3) 7 . 8 mm (4) 9 . 75 mm 𝑚

Q25.The maximum velocity of the photoelectrons emitted from the surface is v when light of frequency n falls on a metal surface. If the incident frequency is increased to 3n, the maximum velocity of the ejected photoelectrons will be: (1) more than √3v (2) equal to √3v (3) v (4) less than √3v JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper

Q26.According to Bohr's theory, the time averaged magnetic field at the centre (i.e., nucleus) of a hydrogen atom due to the motion of electrons in the nth orbit is proportional to: ( n = principal quantum number) (1) n−3 (2) n−2 (3) n−4 (4) n−5

Q26.A particle 𝐴 of mass 𝑚 and initial velocity 𝑣 collides with a particle 𝐵 of mass which is at rest. The collision 2 is head on, and elastic. The ratio of the de-Broglie wavelengths 𝜆𝐴 to 𝜆𝐵 after the collision is: (1) 𝜆𝐴 1 (2) 𝜆𝐴 1 𝜆𝐵= 2 𝜆𝐵= 3 (3) 𝜆𝐴 2 (4) 𝜆𝐴 2 𝜆𝐵= 𝜆𝐵= 3

Q26.A laser light of wavelength 660 nm is used to weld Retina detachment. If a laser pulse of width 60 ms and power 0. 5 kW is used, the approximate number of photons in the pulse are (Take Planck's Constant, h = 6.62 × 10−34 J s) JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper (1) 1022 (2) 1019 (3) 1020 (4) 1018

Q27.The acceleration of an electron in the first orbit of the hydrogen atom ( n = 1 ) is : (1) h2 (2) h2 4πm2r3 π2m2r3 (3) h2 (4) h2 8π2m2r3 4π2m2r3

Q27.Two deuterons undergo nuclear fusion to form a Helium nucleus. The energy released in this process is (given binding energy per nucleon for deuteron = 1.1 MeV and for helium = 7.0 MeV ) (1) 23.6 MeV (2) 30.2 MeV (3) 25.8 MeV (4) 32.4 MeV

Q27.Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths 𝑟= 𝜆1 is given by: 𝜆2, 1 4 (1) 𝑟= (2) 𝑟= 3 3 (3) 𝑟= 2 (4) 𝑟= 3 3 4

Q28.The V −I characteristic of a diode is shown in the figure. The ratio of forward to reverse bias resistance is: (1) 100 (2) 106 (3) 10−6 (4) 10

Q28.A radioactive nucleus 𝐴 with a half-life 𝑇, decays into a nucleus 𝐵. At 𝑡= 0, there is no nucleus 𝐵. At some time 𝑡, the ratio of the number of 𝐵 to that of 𝐴 is 0.3. Then, 𝑡 is given by: Consider log𝑒𝑥= log𝑥 𝑇 𝑇 log⁡ 2 (1) 𝑡= (2) 𝑡= log⁡1.3 2 log⁡ 1.3 (3) 𝑡= 𝑇log⁡ 1.3 (4) 𝑡= 𝑇log1.3 log⁡ 2

Q28.Imagine that a reactor converts all the given mass into energy and that it operates at a power level of 109 Watt . The mass of the fuel consumed per hour , in the reactor, will be: (velocity of light, c is 3 × 108 m s−1 ) (1) 6.6 × 10−5 g (2) 0.96 g (3) 4 × 10−2 g (4) 0.8 g

Q29.The conductivity of a semiconductor sample having electron concentration of 5 × 1018 electrons m−3 , hole concentration of 5 × 1019 holes m−3 , electron mobility of 2 .0 m2 V−1 s−1 and hole mobility of 0. 01 m2 V−1 s−1 is (Take charge of an electron as 1 .6 ×10−19 C ) (1) 1 .83 (Ω m)−1 (2) 1 .65 (Ω m)−1 (3) 1 .20 (Ω m)−1 (4) 0 .59 (Ω m)−1

Q29.In a common emitter amplifier circuit using an 𝑛- 𝑝- 𝑛 transistor, the phase difference between the input and the output voltages will be: (1) 180° (2) 45° (3) 90° (4) 135°