Practice Questions

Q22.An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to Q0 and then connected to the L and R as shown below: If a student plots graphs of the square of maximum charge (Q2Max) on the capacitor with time (t) for two different values L1 and L2(L1 > L2) of L then which of the following represents this graph correctly? (plots are schematic and not drawn to scale) JEE Main 2015 (04 Apr) JEE Main Previous Year Paper (1) (2) (3) (4)

Q22.When the current in a coil changes from 5 A to 2 A in 0.1 s, an average voltage of 50 V is produced. The self- inductance of the coil is (1) 1.67 H (2) 6 H (3) 3 H (4) 0.67 H

Q23.An inductor (L = 0.03 H) and a resistor (R = 0.15 kΩ) are connected in series to a battery of 15 V E.M.F. in a circuit shown below. The key K1 has been kept closed for a long time. Then at t = 0, K1 is opened and key K2 is closed simultaneously. At t = 1 ms , the current in the circuit will be : (Take, e5 ≈150) (1) 0. 67 mA (2) 100 mA (3) 67 mA (4) 6. 7 mA

Q23.An electromagnetic wave travelling in the x− direction has frequency of 2 × 1014 H z and electric field amplitude of 27 V m–1 oscillates in Y −direction. From the options given below, which one describes the magnetic field for this wave? (1) → (2) → B(x, t) = × 10−8 B(x, t) = × sin[2π(1.5 × 10−8 x −2 × 1014 (9 T)ˆj (9 10−8T)ˆi sin[1.5 × 10−6 x −2 × 1014t] → → (3) (4) B B −2 × −2 × (x, t) = (9 × (x, t) = (3 × 10−8T)ˆj sin 2π[( 1.5×10−8x ) 1014t] 10−8T)^ksin2π[( 1.5×10−6x ) 1014t]

Q23.For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor C ′ , when joined with the capacitor C present in the circuit, makes the power factor of the circuit unity. The capacitor C ′ , must have been connected in: (1) Parallel with C and has a magnitude 1−ω2LC (2) Series with C and has a magnitude 1−ω2LC ω2L ω2L (3) Series with C and has a magnitude C (4) Parallel with C and has a magnitude C (ω2LC−1) (ω2LC−1)

Q24.A red LED emits light at 0. 1 watt uniformly around it. The amplitude of the electric field of the light at a distance of 1 m from the diode is: (1) 7. 75 V m−1 (2) 1. 73 V m−1 (3) 2. 45 V m−1 (4) 5. 48 V m−1

Q24.For plane electromagnetic waves propagating in the +z-direction, which one of the following combinations → → gives the correct possible direction for E and B field respectively? + (1) (ˆi 2ˆj) and (2ˆi −j) (2) (−2ˆi −3ˆj) and (3ˆi −2ˆj) + + + (3) (2ˆi 3ˆj) and (ˆi 2ˆj) (4) (3ˆi 4ˆj) and (4ˆi −3ˆj)

Q24.A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. If a 50 m tall tower at a distance of 1 km is observed through this telescope in a normal setting, the angle formed by the image of the tower is θ, then θ is close to (1) 30° (2) 15° (3) 1° (4) 86°

Q25.Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is μ , a ray, incident at an angle θ , on the face AB would get transmitted through the face AC of the prism JEE Main 2015 (04 Apr) JEE Main Previous Year Paper provided: sin + θ > (1) θ < cos−1[μ (A sin−1( μ1 ))] (2) sin−1[μ sin(A −sin−1( μ1 ))] sin θ > + (3) θ < sin−1[μ (A −sin−1( μ1 ))] (4) cos−1[μ sin(A sin−1( μ1 ))]

Q25.You are asked to design a shaving mirror assuming that a person keeps it at 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be: (1) 24 cm (2) 30 cm (3) 60 cm (4) −24 cm

Q25.A thin convex lens of focal length f is put on a plane mirror as shown in the figure. When an object is kept at a distance a from the lens-mirror combination, its image is formed at a distance a3 in front of the combination. JEE Main 2015 (11 Apr Online) JEE Main Previous Year Paper The value of a is: (1) 2f (2) 32 f (3) 3f (4) f

Q26.A parallel beam of electrons travelling in x - direction falls on a slit of width d (see figure). If after passing the slit, an electron acquires momentum py in the y - direction then for a majority of electrons passing through the JEE Main 2015 (10 Apr Online) JEE Main Previous Year Paper slit (h is Planck's constant): (1) |py|d < h (2) |py|d > h (3) |py|d ≃h (4) |py|d >> h

Q26.In a Young's double slit experiment with light of wavelength λ, the separation of slits is d and distance of screen is D such that D ≫d ≫λ . If the Fringe width is β , the distance from point of maximum intensity to the point where intensity falls to half of the maximum intensity on either side is: (1) β (2) β 4 3 (3) β (4) β 6 2

Q27.Unpolarized light of intensity I0 is incident on surface of a block of glass at Brewster's angle. In that case, which one of the following statements is true? (1) transmitted light is partially polarized with (2) transmitted light is completely polarized with intensity I0 intensity less than I0 2 2 (3) reflected light is partially polarized with intensity(4) reflected light is completely polarized with I0 intensity less than I0 2 2

Q27.Assuming that the human pupil has a radius of 0. 25 cm and a comfortable viewing distance of 25 cm. The minimum separation between two point objects that the human eye can resolve for the light of wavelength 500 nm is (1) 300 μm (2) 1 μm (3) 30 μm (4) 100 μm

Q27.De-Broglie wavelength of an electron accelerated by a voltage of 50 V is close to (|e| = 1.6 × 10−19 C, me = 9.1 × 10−31 kg, h = 6.6 × 10−34 J s) (1) 0.5 Å (2) 1.2 Å (3) 1.7 Å (4) 2.4 Å

Q28.The de-Broglie wavelength associated with the electron in the n = 4 level is: (1) Half of the de-Broglie wavelength of the electron (2) Four times the de-Broglie wavelength of the in the ground state electron in the ground state (3) 1 th of the de-Broglie wavelength of the electron (4) Two times the de-Broglie wavelength of the 4 in the ground state electron in the ground state

Q28.If one were to apply the Bohr model to a particle of mass ′m′ and charge ′q′ moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the nth level will be: (1) n( hqBπm ) (2) n( 4πmhqB ) (3) n( 2πmhqB ) (4) n( 8πmhqB )

Q28.Match list-I (Fundamental Experiment) with List-II (its conclusion) and select the correct option from the choices given below the list: List-I List-II A Franck-Hertz Experiment (i) Particle nature of light B Photo-electric experiment (ii) Discrete energy levels of the atom C Davison-Germer Experiment (iii) Wave nature of electron (iv) Structure of atom (1) A −(iv) ; B −(iii); C −(ii) (2) A −(i) ; B −(iv); C −(iii) (3) A −(ii) ; B −(iv); C −(iii) (4) A −(ii) ; B −(i); C −(iii)

Q29.In an unbiased p - n junction electrons diffuse from n-region to p-region because: (1) electrons travel across the junction due to (2) only electrons move from n to p region and not potential difference the vice - versa (3) electron concentration in n - region is more as (4) holes in p - region attract them compared to that in p - region

Q30.The value of the resistor, RS , needed in the DC voltage regulator circuit shown here, equals: (1) (Vi+VL) (2) (Vi−VL) (n+1)IL n IL (3) (Vi+VL) (4) (Vi−VL) n IL (n+1)IL JEE Main 2015 (11 Apr Online) JEE Main Previous Year Paper

Q30.A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant signal is/are: JEE Main 2015 (04 Apr) JEE Main Previous Year Paper (1) 2000 kHz and 1995 kHz (2) 2 MHz only (3) 2005 kHz and 1995 kHz (4) 2005 kHz, 2000 kHz and 1995 kHz

Q30.Diameter of a steel ball is measured using a Vernier calipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its Vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as: S.No. MS (cm) VS divisions 1. 0.5 8 2. 0.5 4 3. 0.5 6 If the zero error is - 0.03 cm, then mean corrected diameter is: (1) 0. 53 cm (2) 0. 56 cm (3) 0. 59 cm (4) 0. 52 cm

Q1. An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be : (1) 4.4% (2) 2.27% (3) 1.7% (4) 2.7%

Q1. The current voltage relation of diode is given by I = (e1000 V/T - 1) mA, where the applied voltage V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring ±0.01 V while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA ? (1) 0.2 mA (2) 0.02 mA (3) 0.5 mA (4) 0.05 mA