Practice Questions

Q17.Two electric bulbs marked 25 W −220 V and 100 W −220 V are connected in series to a 440 V supply. Which of the bulbs will fuse? (1) both (2) 100 W (3) 25 W (4) neither

Q17.The electric potential V (x) in a region around the origin is given by V (x) = 4x2 volts. The electric charge enclosed in a cube of 1 m side with its centre at the origin is (in coulomb) (1) 8ε0 (2) −4ε0 (3) 0 (4) −8ε0 JEE Main 2012 (07 May Online) JEE Main Previous Year Paper

Q18.The resistance of a wire is R. It is bent at the middle by 180∘ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is (1) 2R (2) R/2 (3) R/4 (4) R/8

Q19.The magnetic force acting on charged particle of charge 2μC in magnetic field of 2T acting in y− direction, when the particle velocity is (2^i + 3^j) × 106 ms−1 is (1) 8 N in z-direction (2) 8 N in y-direction (3) 4 N in y-direction (4) 4 N in z-direction

Q19.A proton and a deuteron are both accelerated through the same potential difference and enter in a magnetic field perpendicular to the direction of the field. If the deuteron follows a path of radius R, assuming the neutron and proton masses are nearly equal, the radius of the proton's path will be (1) √2R (2) R √2 (3) R (4) R 2

Q19.In an experiment of potentiometer for measuring the internal resistance of primary cell a balancing length ℓ is obtained on the potentiometer wire when the cell is open circuit. Now the cell is short circuited by a resistance R. If R is to be equal to the internal resistance of the cell the balancing length on the potentiometer wire will be (1) ℓ (2) 2ℓ (3) ℓ/2 (4) ℓ/4 JEE Main 2012 (26 May Online) JEE Main Previous Year Paper

Q19.This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: The possibility of an electric bulb fusing is higher at the time of switching ON. Statement 2: Resistance of an electric bulb when it is not lit up is much smaller than when it is lit up. (1) Statement 1 is true, Statement 2 is false (2) Statement 1 is false, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1. (3) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1. (4) Statement 1 is false, Statement 2 is true.

Q19.Proton, Deuteron and alpha particle of the same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively rp, rd and rα . Which one of the following relations is correct? (1) rα = rp = rd (2) rα = rp < rd (3) rα > rd > rp (4) rα = rd > rp

Q20.A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; it is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to : JEE Main 2012 (Offline) JEE Main Previous Year Paper (1) development of air current when the plate is (2) induction of electrical charge on the plate placed. (3) shielding of magnetic lines of force as aluminium (4) electromagnetic induction in the aluminium plate is a paramagnetic material. giving rise to electromagnetic damping.

Q20.Currents of a 10 ampere and 2 ampere are passed through two parallel thin wires A and B respectively in opposite directions. Wire A is infinitely long and the length of the wire B is 2 m. The force acting on the conductor B, which is situated at 10 cm distance from A will be (1) 8 × 10−5 N (2) 5 × 10−5 N (3) 8π × 10−7 N (4) 4π × 10−7 N

Q21.Magnetic flux through a coil of resistance 10Ω is changed by Δϕ in 0.1 s. The resulting current in the coil varies with time as shown in the figure. Then |Δϕ| is equal to (in weber) (1) 6 (2) 4 (3) 2 (4) 8

Q21.This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: Self inductance of a long solenoid of length L, total πμ0N 2r2 number of turns N and radius r is less than L . Statement 2: The magnetic induction in the solenoid in Statement 1 carrying current I is μ0NIL in the middle of the solenoid but becomes less as we move towards its ends. (1) Statement 1 is true, Statement 2 is false. (2) Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1. (3) Statement 1 is false, Statement 2 is true. (4) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

Q21.This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: A charged particle is moving at right angle to a static magnetic field. During the motion the kinetic energy of the charge remains unchanged. Statement 2: Static magnetic field exert force on a moving charge in the direction perpendicular to the magnetic field. (1) Statement 1 is false, Statement 2 is true. (2) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1. (3) Statement 1 is true, Statement 2 is false. (4) Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

Q22.An object 2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1 cm thick, of refractive index 1.50 is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object be shifted to be in sharp focus on film? (1) 7.2 m (2) 2.4 m (3) 3.2 m (4) 5.6 m

Q22.An electromagnetic wave with frequency ω and wavelength λ travels in the +y direction. Its magnetic field is along +x-axis. The vector equation for the associated electric field (of amplitude E0 ) is JEE Main 2012 (19 May Online) JEE Main Previous Year Paper 2π (1) →E = −E0 cos (ωt + λ y)^x (2) →E = E0 cos (ωt −2πλ y)^x 2π (4) →E = −E0 cos (ωt + (3) →E = E0 cos (ωt −2πλ y)^z λ y)^z

Q22.A resistance R and a capacitance C are connected in series to a battery of negligible internal resistance through a key. The key is closed at t = 0 . If after t sec the voltage across the capacitance was seven times the voltage across R, the value of t is (1) 3RCℓn2 (2) 2RCℓn2 (3) 2RC ln 7 (4) 3RCℓn7

Q22.In an LCR circuit shown in the following figure, what will be the readings of the voltmeter across the resistor and ammeter if an a.c. source of 220 V and 100 Hz is connected to it as shown? JEE Main 2012 (07 May Online) JEE Main Previous Year Paper (1) 800 V, 8 A (2) 110 V, 1.1 A (3) 300 V, 3 A (4) 220 V, 2.2 A

Q23.We wish to make a microscope with the help of two positive lenses both with a focal length of 20 mm each and the object is positioned 25 mm from the objective lens. How far apart the lenses should be so that the final image is formed at infinity? JEE Main 2012 (12 May Online) JEE Main Previous Year Paper (1) 20 mm (2) 100 mm (3) 120 mm (4) 80 mm

Q23.A glass prism of refractive index 1.5 is immersed in water (refractive index 34 ) as shown in figure. A light beam incident normally on the face AB is totally reflected to reach the face BC, if (1) sin θ > 95 (2) sin θ > 32 (3) sin θ > 98 (4) sin θ > 31

Q23.In Young's double slit experiment, one of the slit is wider than other, so that the amplitude of the light from one slit is double of that from other slit. If Im be the maximum intensity, the resultant intensity I when they interfere at phase difference ϕ is given by (1) Im 9 (4 + 5 cos ϕ) (2) lm3 (1 + 2 cos2 ϕ2 ) (3) Im 5 (1 + 4 cos2 ϕ2 ) (4) Im9 (1 + 8 cos2 ϕ2 )

Q24.In a Young's double slit experiment with light of wavelength λ, fringe pattern on the screen has fringe width β. When two thin transparent glass (refractive index μ ) plates of thickness t1 and t2 (t1 > t2) are placed in the path of the two beams respectively, the fringe pattern will shift by a distance (1) β(μ−1 t1 (2) μβ t1 λ t2 λ ( t2 ) (3) β(μ−1 (t1 + t2 ) λ (t1 −t2 (4) (μ −1 λβ )

Q24.A beam of light consisting of red, green and blue colours is incident on a right-angled prism on face AB. The refractive indices of the material for the above red, green and blue colours are 1.39, 1.44 and 1.47 respectively. A person looking on surface AC of the prism will see (1) no light (2) green and blue colours (3) red and green colours (4) red colour only

Q24.Two coherent plane light waves of equal amplitude makes a small angle α(<< 1) with each other. They fall almost normally on a screen. If λ is the wavelength of light waves, the fringe width Δx of interference patterns of the two sets of waves on the screen is (1) 2λ (2) λ α α (3) λ (4) λ (2α) √α

Q25.The maximum number of possible interference maxima for slit separation equal to 1.8λ, where λ is the wavelength of light used, in a Young's double slit experiment is (1) zero (2) 3 (3) infinite (4) 5

Q25.A telescope of aperture 3 × 10−2 m diameter is focused on a window at 80 m distance fitted with a wire mesh of spacing 2 × 10−3 m. Given: λ = 5.5 × 10−7 m, which of the following is true for observing the mesh JEE Main 2012 (26 May Online) JEE Main Previous Year Paper through the telescope? (1) Yes, it is possible with the same aperture size. (2) Possible also with an aperture half the present diameter. (3) No, it is not possible. (4) Given data is not sufficient.