Practice Questions

Q22.A very long solenoid of radius R is carrying current I(t) = kte−αt(k > 0), as a function of time (t ≥0). Counterclockwise current is taken to be positive. A circular conducting coil of radius 2R is placed in the equitorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by: JEE Main 2019 (09 Apr Shift 2) JEE Main Previous Year Paper (1) (2) (3) (4)

Q23.An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is 𝑎 and distance of its centre from the wire is 𝑑 𝑑≫𝑎. If the loop applies a force 𝐹 on the wire then: 2 (1) 𝐹∝𝑎 (2) 𝐹= 0 𝑑 𝑎 (3) 𝐹∝𝑎2 (4) 𝐹∝ 𝑑 𝑑3

Q24.What is the position and nature of image formed by lens combination shown in figure? ( f1, f2 are focal lengths) (1) 40 cm from point B at right; real (2) 203 cm from point B at right, real (3) 70 cm from point B at right; real (4) 70 cm from point B at left; virtual JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper

Q24.A concave mirror has radius of curvature of 40 cm . It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to: (Refractive index of water = 1.33 ) (1) 13.4 cm (2) 8.8 cm (3) 6.7 cm (4) 11.7 cm

Q24.The magnetic field of a plane electromagnetic wave is given by B = B0ˆi[cos(kz −ωt)] + B1ˆjcos(kz + ωt) , where B0 = 3 × 10–5 T and B1 = 2 × 10–6 T . The RMS value of the force experienced by a stationary charge Q = 10–4 C at z = 0 is closest to (1) 0.1 N (2) 0.9 N (3) 3 × 10–2 N (4) 0.6 N

Q24.In figure, the optical fiber is 𝑙= 2 m long and has a diameter of d = 20 μm . If a ray of light is incident on one end of the fiber at angle θ1 = 40° , the number of reflections it makes before emerging from the other end is close to: (refractive index of fiber is 1.31 , sin 40° = 0.64 and sin-1⁡0.49 = 30° .) (1) 55000 (2) 57000 (3) 45000 (4) 66000

Q25.An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm . A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of the lens. The position and size of the final image will be: JEE Main 2019 (08 Apr Shift 1) JEE Main Previous Year Paper (1) 40 cm from the (2) 20 cm from the (3) 40 cm from the (4) 20 cm from the convergent lens, twice convergent mirror, convergent lens, same convergent mirror, the size of the object twice the size of the size of the object same size of the object object

Q25.In a double-slit experiment, green light (5303 A) falls on a double slit having a separation of 19.44μm and a width of 4.05μm. The number of bright fringes between the first and the second diffraction minima is (1) 10 (2) 5 (3) 4 (4) 9

Q25.A thin convex lens L (refractive index = 1.5 ) is placed on a plane mirror M. When a pin is placed at A , such that OA = 18 cm, its real inverted image is formed at A itself, as shown in figure. When liquid of refractive index μl is put between the lens and the mirror, the pin has to be moved to A', such that OA' = 27 cm, to get its inverted real image at A' itself. The value of μl will be (1) 4 (2) √3 3 (3) 3 (4) √2 2

Q26.A particle of mass m moves in a circular orbit in a central potential field U(r) = 12 kr2. If Bohr's quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number n as: (1) rn ∝n2, En ∝ n21 (2) rn ∝√n, En ∝n (3) rn ∝n, En ∝n (4) rn ∝√n, En ∝1n

Q26.Consider a Young's double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength λ such that the first minima occurs directly in front of the slit (S1) ? (1) λ (2) λ (5−√2) 2(√5−2) (3) λ (4) λ 2(5−√2) √5−2

Q26.In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 × 10−12 m, the minimum electron energy required is close to: (1) 100 keV (2) 25 keV (3) 1 keV (4) 500 keV

Q26.A convex lens (of focal length 20 cm ) and a concave mirror, having their principal axes along the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be: (1) 30 cm (2) 25 cm (3) 20 cm (4) 10 cm JEE Main 2019 (08 Apr Shift 2) JEE Main Previous Year Paper

Q28.In Li+ + ,electron in first Bohr orbit is excited to a level by a radiation of wavelength λ.When the ion gets de excited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines are observed. What is the value of λ ? (Given: ℎ= 6.63 × 10-34 J s ; 𝑐= 3 × 108 m s-1 ) (1) 10.8 nm (2) 9.4 nm (3) 11.4 nm (4) 12.3 nm

Q28.An NPN transistor operates as a common emitter amplifier, with a power gain of 60 dB . The input circuit resistance is 100 Ω and the output load resistance is 10 kΩ . The common emitter current gain β is: (1) 6 × 102 (2) 102 (3) 104 (4) 60

Q28.Consider a tank made of glass (refractive index 1.5 ) with a thick bottom. It is filled with a liquid of refractive index 𝜇. A student finds that, irrespective of what the incident angle 𝑖 (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of 𝜇 is: 3 4 (1) (2) √5 3 5 5 (3) (4) √3 √ 3

Q28.An excited He+ ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm in making a transition to the ground state. The quantum number n, corresponding to its initial excited state is 1240 eV (for a photon of wavelength λ, energy E = ) λ ( in nm ) (1) n = 6 (2) n = 5 (3) n = 7 (4) n = 4

Q30.In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the variation dRdl of its resistance R with length l is dRdl ∝ √l1 . Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP? JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper (1) 0.2 m (2) 0.35 m (3) 0.3 m (4) 0.25 m o

Q30.A load of mass M kg is suspended from a steel wire of length 2m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is: (1) 4.0 mm (2) Zero (3) 5.0mm (4) 3.0mm Q31. 8 g of NaOH is dissolved in 18g of H2O. Mole fraction of NaOH in solution and molality (in mol kg−1 ) of the solution respectively are: (1) 0.167, 11.11 (2) 0.167, 22.20 (3) 0.2, 11.11 (4) 0.2, 22.20 JEE Main 2019 (12 Jan Shift 2) JEE Main Previous Year Paper

Q30.The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is 6 V and the load resistance is, RL = 4 kΩ . The series resistance of the circuit is Ri = 1 kΩ . If the battery voltage VB varies from 8 V to 16 V , what are the minimum and maximum values of the current through Zener diode? (1) 0.5 mA; 6 mA (2) 1 mA; 8.5 mA (3) 0.5 mA; 8.5 mA (4) 1.5 mA; 8.5 mA

Q30.In the experimental set up of metre bridge shown in the figure, the null point is obtaine data distance of 40 cm from A. If a 10Ω resistor is connected in series with R1, the null point shifts by 10 cm. The resistance that should be connected in parallel with (R1 + 10)Ω such that the null point shifts back to its initial position is (1) 20Ω (2) 40Ω (3) 60Ω (4) 30Ω Q31. 25 mL of the given HCl solution requires 30 mL of 0.1M sodium carbonate solution. What is the volume of this HCl solution required to titrate 30 mL of 0.2M aqueous NaOH solution? (1) 25 mL (2) 75 mL (3) 50 mL (4) 12.5 mL JEE Main 2019 (11 Jan Shift 2) JEE Main Previous Year Paper

Q2. A man in a car at location Q on a straight highway is moving with speed v . He decides to reach a point P in a field at a distance d from highway (point M ) as shown in the figure.Speed of the car in the field is half to that on the highway. What should be the distance RM, so that the time taken to reach P is minimum? (1) d (2) d √3 2 (3) d (4) d √2

Q4. A particle is moving in a circular path of radius a under the action of an attractive potential U = −k . Its total 2r2 energy is: (1) −32 a2k (2) – 4a2k (3) k (4) Zero 2a2

Q6. A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of 90∘ with respect to each other. The mass of unknown particle is: (1) m (2) m √3 2 (3) 2 m (4) m

Q7. A body of mass m is moving in a circular orbit of radius R about a planet of mass M . At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius R . And the other mass, in a circular 2 orbit of radius 3R 2 . The difference between the final and the initial total energies is (1) + Gm6R (2) −Gm2R (3) −Gm6R (4) Gm2R