Practice Questions

Q17.The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation: K(x) = Ko + λx(λ = a constant ) The capacitance C, of the capacitor, would be related to its vacuum capacitance Co for the relation : (1) C = λd (2) C = λ ln(1+Koλd Co) d⋅ln(1+Koλd Co) (3) C = λd (4) C = λ ln(1+λd/Ko d.ln(1+Ko/λd Co) Co)

Q17.The gap between the plates of a parallel plate capacitor of area A and distance between plates d, is filled with a dielectric whose relative permittivity varies linearly from ϵ1 at one plate to ϵ2 at the other. The capacitance of the capacitor is JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper (1) ϵ0(∈2−∈1)A (2) ϵ0(∈2+∈1)A [d ln(∈2/∈1)] 2d (3) ϵ0(∈1+∈2)A (4) ϵ0A d [dln(∈2/∈1)]

Q18.In the circuit shown, current (in A) through 50 V and 30 V batteries are, respectively: (1) 2.5 and 3 (2) 3.5 and 2 (3) 4.5 and 1 (4) 3 and 2.5

Q18.The circuit shown here has two batteries of 8.0 V and 16.0 V and three resistors 3Ω, 9Ω and 9Ω and a capacitor of 5.0μF. How much is the current I in the circuit in steady state? JEE Main 2014 (12 Apr Online) JEE Main Previous Year Paper (1) 1.6 A (2) 0.67 A (3) 2.5 A (4) 0.25 A

Q18. Four bulbs B1 , B2 , B3 and B4 of 100 W each are connected to 220 V main as shown in the figure. The reading in an ideal ammeter will be (1) 0. 90 A (2) 1. 35 A (3) 0. 45 A (4) 1. 80 A

Q18.In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of 1 kW. The voltage of the electric mains is 220 V. The minimum capacity of the main fuse of the building will be: JEE Main 2014 (06 Apr) JEE Main Previous Year Paper (1) 8 A (2) 10 A (3) 12 A (4) 14 A

Q19.The mid points of two small magnetic dipoles of length d in end-on positions, are separated by a distance x (x ≫d). The magnitude of force between them is proportional to x−n where n is : JEE Main 2014 (09 Apr Online) JEE Main Previous Year Paper (1) 3 (2) 4 (3) 2 (4) 1

Q19.In the circuit diagrams (A, B, C and D) shown below, R is a high resistance and S is a resistance of the order of galvanometer resistance G. The correct circuit, corresponding to the half deflection method for finding the resistance and figure of merit of the galvanometer, is the circuit labelled as: (a) (b) JEE Main 2014 (11 Apr Online) JEE Main Previous Year Paper (C) (d) (1) Circuit A with G = (R−S)RS (2) Circuit B with G = S (3) Circuit C with G = S (4) Circuit D with G = (R−SRS )

Q19.In the experiment of calibration of voltmeter, a standard cell of e.m.f. 1.1 volt is balanced against 440 cm of potential wire. The potential difference across the ends of resistance is found to balance against 220 cm of the wire. The corresponding reading of voltmeter is 0.5 volt. The error in the reading of volmeter will be: (1) −0.15 volt (2) 0.15 volt (3) 0.5 volt (4) −0.05 volt

Q19.The coercivity of a small magnet, where the ferromagnet gets demagnetised is 3 × 103 A/m . The current required to be passed in a solenoid of length 10 cm and number of turns 100, so that the magnet gets demagnetised when inside the solenoid is (1) 30 mA (2) 60 mA (3) 3 A (4) 6 A

Q20.A positive charge ' q ' of mass ' m ' is moving along the +x axis. We wish to apply a uniform magnetic field B for time Δt so that the charge reverses its direction crossing the y axis at a distance d. Then: (1) B = mvqd and Δt = πdv (2) B = 2qdmv and Δt = πd2v (3) B = 2mvqd and Δt = πd2v (4) B = 2mvqd and Δt = πdv

Q20.A square frame of side 10 cm and a long straight wire carrying current 1 A are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of 10 m s−1 (see figure). The e.m.f induced at the time the left arm of the frame is at x = 10 cm from the wire is (1) 0.75 μV (2) 1 μV (3) 2 μV (4) 0.5 μV JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper Q21. → The figure shows a circular area of tthe radius R where a uniform magnetic field B is going into the plane of the paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field E(r)? (1) (2) (3) (4)

Q20.A conductor lies along the z-axis at −1.5 ≤z < 1.5 m and carries a fixed current of 10.0 A in −ˆaz direction → (see figure). For a field B = 3.0 × 10−4 e−0.2x ˆay T, find the power required to move the conductor at constant speed to x = 2.0 m, y = 0 m in 5 × 10−3 s. Assume parallel motion along the x-axis. (1) 1.57 W (2) 2.97 W (3) 14.85 W (4) 29.7 W

Q20.Three identical bars A, B and C are made of different magnetic materials. When kept in a uniform magnetic field, the field lines around them look as follows: Make the correspondence of these bars with their material being diamagnetic ( D), ferromagnetic (F) and paramagnetic (P) : (1) A ↔D, B ↔P, C ↔F (2) A ↔F, B ↔D, C ↔P (3) A ↔P, B ↔F, C ↔D (4) A ↔F, B ↔P, C ↔D JEE Main 2014 (11 Apr Online) JEE Main Previous Year Paper

Q21.In the circuit shown here, the point ' C ' is kept connected to point A '' till the current flowing through the circuit becomes constant. Afterward, suddenly, point ' C ' is disconnected from point A '' and connected to point ' B' at time t = 0. Ratio of the voltage across resistance and the inductor at t = RL will be equal to : (1) e (2) 1 1−e (3) - 1 (4) 1−e e

Q21.Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field B1 , at its centre when a current I passes through it. The ratio B1 : B2 is: (1) 1:1 (2) 1 : 3 (3) 1 : 9 (4) 9 : 1

Q21.Three straight parallel current carrying conductors are shown in the figure. The force experienced by the middle conductor of length 25 cm is: (1) 3 × 10−4 N toward right (2) 6 × 10−4 N toward right (3) 9 × 10−4 N toward right (4) Zero

Q22.A coil of circular cross-section having 1000 turns and 4 cm2 face area is placed with its axis parallel to a magnetic field which decreases by 10−2 Wb m−2 in 0.01 s. The e.m.f. induced in the coil is: (1) 400mV (2) 200mV (3) 4mV (4) 0.4mV

Q22.Match List I (Wavelength range of electromagnetic spectrum) with List II (Method of production of these waves) and select the correct option from the options given below the lists. List I List II 700 nm to (a) (i) Vibration of atoms and molecules. 1 mm 1 nm to Inner shell electrons in atoms moving from one (b) (ii) 400 nm energy level to a lower level. (c) < 10−3 nm (iii) Radioactive decay of the nucleus. (d) 1 mm to 0. 1 m (iv) Magnetron valve. (1) (a) - (iii), (b) - (iv), (c) - (i), (d) - (ii) (2) (a) - (i), (b) - (ii), (c) - (iii), (d) - (iv) (3) (a) - (iv), (b) - (iii), (c) - (ii), (d) - (i) (4) (a) - (ii), (b) - (iii), (c) - (iv), (d) - (i)

Q22.A sinusoidal voltage V(t) = 100 sin(500t) is applied across a pure inductance of L = 0.02H. The current through the coil is: (1) 10 cos(500t) (2) −10 cos(500t) (3) 10 sin(500t) (4) −10 sin(500t)

Q23.A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly: (1) 1.34 V/m (2) 2.68 V/m (3) 4.02 V/m (4) 5.36 V/m

Q23.The diameter of the objective lens of the microscope makes an angle β at the focus of the microscope. Further, the medium between the object and the lens is the oil of the refractive index n. Then the resolving power of the microscope. JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper (1) Increases with decreasing value of β (2) Increases with increasing value of n sin 2β (3) Increases with increasing value of 1 (4) Increases with decreasing value of n nsin2β

Q23.An electromagnetic wave of frequency 1 × 1014 hertz is propagating along z-axis. The amplitude of electric field is 4 V/m. If ε0 = 8.8 × 10−12C2/N−m2 , then average energy density of electric field will be: (1) 35.2 × 10−10 J/m3 (2) 35.2 × 10−11 J/m3 (3) 35.2 × 10−12 J/m3 (4) 35.2 × 10−13 J/m3

Q23.Match List - I (Electromagnetic wave type) with List - II (Its association/application) and select the correct option from the choices given below the lists : JEE Main 2014 (06 Apr) JEE Main Previous Year Paper List - I List - II (a) Infrared waves (i) To treat muscular strain (b) Radio waves (ii) For broadcasting (c) X - rays (iii) To detect fracture of bones (d) Ultraviolet rays (iv) Absorbed by the ozone layer of the atmosphere (1) (a) (b) (c) (d) (2) (a) (b) (c) (d) (iv) (iii) (ii) (i) (i) (ii) (iv) (iii) (3) (a) (b) (c) (d) (4) (a) (b) (c) (d) (iii) (ii) (i) (iv) (i) (ii) (iii) (iv)

Q24.A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is θiC and Brewster's angle of incidence is θiB , such that sinθiC = η = 1.28 . The relative refractive index of the two sinθiB media is (1) 0.4 (2) 0.2 (3) 0.9 (4) 0.8