Practice Questions

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.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

Q21.A magnetic needle of magnetic moment 6 .7 × 10-2 A m2 and moment of inertia 7 .5 × 10-6 kg m2 is performing simple harmonic oscillations in a magnetic field of 0 . 01 T. Time taken for 10 complete oscillations is: (1) 8 . 76 s (2) 6 . 65 s (3) 8 . 89 s (4) 6 . 98 s JEE Main 2017 (02 Apr) JEE Main Previous Year Paper

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.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.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

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)

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

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.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.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.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.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

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.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

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

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

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 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

Q31.Excess of NaOH (aq) was added to 100 mL of FeCl3 (aq) resulting into 2. 14 g of Fe (OH)3 . The molarity of FeCl3(aq) is: (Given the molar mass of Fe = 56 g mol−1 and molar mass of Cl = 35 .5 g mol−1 ) (1) 0. 3 M (2) 0. 2 M (3) 0. 6 M (4) 1. 8 M JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper

Q31.What quantity (in mL ) of a 45% acid solution of a mono-protic strong acid must be mixed with a 20% solution of the same acid to produce 800 mL of a 29. 875% acid solution? (1) 316 (2) 320 (3) 325 (4) 330