Practice Questions

Q13.A particle is executing simple harmonic motion with a time period 𝑇. At time 𝑡= 0, it is at its position of equilibrium. The kinetic energy - time graph of the particle will look like: (1) (2) (3) (4)

Q13.In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r1 and r2 . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5 × 10−4 s, the difference in radii, |r1 −r2| is best-given by (1) 0. 01 cm (2) 0. 05 cm (3) 0. 5 cm (4) 1 cm

Q13.A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to a 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is (1) 2 Hz (2) 14 Hz (3) 1 Hz (4) 12 Hz 2√2

Q14.An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer? (speed of light = 3 × 108 m s-1) (1) 15 . 3 GHz (2) 10 . 1 GHz (3) 12 . 1 GHz (4) 17 . 3 GHz

Q14.Two wires W1 and W2 have the same radius r and respective, densities ρ1 and ρ2 , such that ρ2 = 4ρ1 . They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept under tension T . The point O is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in W1 to W2 is (1) 4 : 1 (2) 1 : 2 (3) 1 : 1 (4) 1 : 3

Q14.A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by, y(x, t) = 0.5 sin( 5π4 x) cos(200πt). What is the speed of the travelling wave moving in the positive x direction? ( x and t are in meter and second, respectively) (1) 120 m s−1 (2) 90 m s−1 (3) 160 m s−1 (4) 180 m s−1 JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper

Q15.An electric dipole has fixed dipole moment →𝑝, which makes angle 𝜃 with respect to 𝑥- axis. When subjected to an electric field →𝐸1 = 𝐸^𝑖, it experiences a torque →𝑇1 = 𝜏^𝑘. When subjected to another electric field →𝐸2 = √3 𝐸1^𝑗 it experiences a torque →𝑇2 = - →𝑇1 . The angle 𝜃 is: (1) 90𝑜 (2) 30𝑜 (3) 45𝑜 (4) 60𝑜

Q15.There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at P , in the region, is found to vary between the limits 589. 0 V to 589. 8 V . What is the potential at a point on the JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper sphere whose radius vector makes an angle of 60° with the direction of the field? (1) 589. 4 V (2) 589. 5 V (3) 589. 2 V (4) 589. 6 V

Q15.Four closed surfaces and corresponding charge distributions are shown below. Let the respective electric fluxes through the surfaces be ϕ1, ϕ2, ϕ3 and ϕ4 . Then: (1) ϕ1 > ϕ2 > ϕ3 > ϕ4 (2) ϕ1 < ϕ2 = ϕ3 > ϕ4 (3) ϕ1 > ϕ3; ϕ2 < ϕ4 (4) ϕ1 = ϕ2 = ϕ3 = ϕ4

Q16.The energy stored in the electric field produced by a metal sphere is 4. 5 J. If the sphere contains 4 μC charge, its radius will be: [Take : 4π∈01 = 9 × 109 N m2 C−2] (1) 32 mm (2) 16 mm (3) 28 mm (4) 20 mm

Q16.A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is: (1) Away from the wire (2) Towards the wire (3) Parallel to the wire along the current (4) Parallel to the wire opposite to the current

Q16.A capacitance of 2 μF is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 𝜇F capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is: (1) 32 (2) 2 (3) 16 (4) 24 JEE Main 2017 (02 Apr) JEE Main Previous Year Paper

Q17.A combination of parallel plate capacitors is maintained at a certain potential difference. When a 3 mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by 2. 4 mm. Find the dielectric constant of the slab. (1) 6 (2) 4 (3) 3 (4) 5

Q17. A 9 V battery with an internal resistance of 0.5 Ω is connected across an infinite network, as shown in the figure. All ammeters A1, A2, A3 and voltmeter V are ideal. Choose the correct statement. (1) Reading of A1 is 18 A . (2) Reading of V is 9 V . (3) Reading of V is 7 V . (4) Reading of A1 is 2 A .

Q17.In the given circuit diagram, when the current reaches a steady-state in the circuit, the charge on the capacitor of capacitance 𝐶 will be: (1) 𝐶𝐸 𝑟1 (2) 𝐶𝐸 𝑟1 + 𝑟 𝑟1 𝑟2 (3) 𝐶𝐸 (4) 𝐶𝐸 𝑟2 + 𝑟 𝑟+ 𝑟2

Q18.A potentiometer PQ is set up to compare two resistances, as shown in the figure. The ammeter A in the circuit reads 1. 0 A when the two-way key K3 is open. The balance point is at a length l1 cm from P when the two- way key K3 is plugged in between 2 and 1 , while the balance point is at a length l2 cm from P when the key K3 is plugged in between 3 and 1 . The ratio of two resistances R1R2 , is found to be (1) l1 (2) l2 l1−l2 l2−l1 (3) l1 (4) l1 l1+l2 l2−l1

Q18.In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance P = 4 Ω and the neutral point N is at 60 cm from A . Now an unknown resistance R is connected in series to P and the new JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper position of the neutral point is at 80 cm from A . The value of unknown resistance R is - (1) 33 5 Ω (2) 6 Ω (3) 20 3 Ω (4) 7 Ω

Q18. In the above circuit the current in each resistance is: (1) 0 A (2) 1 A (3) 0 . 25 A (4) 0 . 5 A

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

Q19.A magnetic dipole in a uniform magnetic field has: (Take zero potential energy when magnetic dipole is perpendicular to magnetic field) JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper (1) Maximum potential energy when the torque is (2) Zero potential energy when the torque is maximum maximum (3) Zero potential energy when the torque is (4) Minimum potential energy when the torque is minimum maximum

Q19.Which of the following statements is false? (1) Kirchhoff's second law represents energy (2) Wheatstone bridge is the most sensitive when all conservation the four resistances are of the same order of magnitude (3) In a balanced Wheatstone bridge if the cell and (4) A rheostat can be used as a potential divider the galvanometer are exchanged, the null point is disturbed

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 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