Practice Questions

Q19.A uniform wire of length l and radius r has a resistance of 100 Ω . It is recast into a wire of radius 2r . The resistance of new wire will be- (1) 1600 Ω (2) 100 Ω (3) 200 Ω (4) 400 Ω

Q20.In a certain region static electric and magnetic fields exist. The magnetic field is given by → B = = + B0(ˆi + 2ˆj −4ˆk). If a test charge moving with a velocity →v v0(3ˆi −ˆj 2ˆk) experiences no force in that region, then the electric field in the region, in SI units, is: → → (1) (2) + E = −v0 E = −υ0 B0(ˆi +ˆj 7ˆk) B0(3ˆi −2ˆj −4ˆk) → → (3) (4) E = v0 + E = −v0 + B0(14ˆj 7ˆk) B0(14ˆj 7ˆk)

Q20.When a current of 5 mA is passed through a galvanometer having a coil of resistance 15 Ω, it shows full- scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range 0 - 10 V is: (1) 4.005 × 103 Ω (2) 1.985 × 103 Ω (3) 2.045 × 103 Ω (4) 2.535 × 103 Ω

Q20.The figure shows three circuits I, II and III which are connected to a 3 V battery. If the powers dissipated by the configurations I, II and III are P1, P2 and P3 respectively, then - (1) P2 > P1 > P3 (2) P1> P 2 > P3 (3) P3 > P2 > P1 (4) P1 > P3 > P2

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)

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

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.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 ) →

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)

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

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

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

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

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 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

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 current gain of a common emitter amplifier is 69 . If the emitter current is 7. 0 mA , collector current is : (1) 69 mA (2) 0. 69 mA (3) 6. 9 mA (4) 9. 6 mA

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

Q30.A signal of frequency 20 kHz and peak voltage of 5 Volt is used to modulate a carrier wave of frequency 1. 2 MHz and peak voltage 25 Volts . Choose the correct statement. (1) Modulation index = 5 , side frequency bands are (2) Modulation index = 5 , side frequency bands are at 1400 kHz and 1000 kHz. at 21. 2 kHz and 18. 8 kHz. (3) Modulation index = 0. 2 , side frequency bands (4) Modulation index = 5 , side frequency bands are are at 1220 kHz and 1180 kHz. at 24. 2 kHz and 18. 8 kHz.

Q30.A signal is to be transmitted through a wave of wavelength λ, using a linear antenna. The length l of the antenna and effective power radiated Peff will be given, respectively, as- ( K is a constant of proportionality) (1) λ 8 , Peff = K( λl ) (2) 16λ , Peff = K( λl ) 3 (3) λ 1 (4) λ, Peff = K( λl ) 2 5 , Peff = K( λl ) 2

Q1. In the following I refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity: (1) M−1L−3T3I (2) M−1L−3T3I2 (3) M−1L3T3I (4) ML−3T−3I2

Q1. A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be: (1) 92 ± 1.8 s (2) 92 ± 3 s (3) 92 ± 2 s (4) 92 ± 5.0 s