Practice Questions

Q21.An inductor of inductance L = 400mH and resistors of resistances R1 = 2Ω and R2 = 2Ω are connected to a battery of emf 12 V as shown in the figure. The internal resistance of the battery is negligible. The switch S is closed at t = 0. The potential drop across L as a function of time is (1) 6e−5tV (2) 12t e−3tV (3) 6 (1 −e−t/0.2)V (4) 12e−5tV JEE Main 2009 JEE Main Previous Year Paper

Q23.A transparent solid cylindrical rod has a refractive index of 2 . It is surrounded by air. A light ray is incident √3 at the mid point of one end of the rod as shown in the figure. The incident angle θ for which the light ray grazes along the wall of the rod is (1) sin−1 ( 21 ) (2) sin−1 ( √32 ) (3) sin−1 ( √32 ) (4) sin−1 ( √31 )

Q24.A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of the unknown light. From this data, the wavelength of the unknown light is (1) 393.4 nm (2) 885.0 nm (3) 442.5 nm (4) 776.8 nm

Q25.The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68eV. The work function of the metal is (hc = 1240eVnm) (1) 3.09eV (2) 1.41eV (3) 151eV (4) 1.68eV

Q26.The transition from the state n = 4 to n = 3 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from (1) 2 →1 (2) 3 →2 (3) 4 →2 (4) 5 →4

Q28.A p-n junction (D) shown in the figure can act as a rectifier. An alternating current source (V ) is connected in the circuit. (1) (2) (3) (4)

Q29.The logic circuit shown below has the input waveforms 'A' and 'B' as shown. Pick out the correct output waveform. (1) (2) (3) (4)

Q30.In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a- degree (= 0.5∘), then the least count of the instrument is (1) one minute (2) half minute (3) one degree (4) half degree

Q1. The dimension of magnetic field in M, L, T and C (Coulomb) is given as (1) MLT−1C−1 (2) MT2C−2 (3) MT−1C−1 (4) MT−2C−1

Q3. An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range (1) 200 J −500 J (2) 2 × 105 J −3 × 105 J (3) 20, 000 J −50, 000 J (4) 2, 000 J −5, 000 J

Q5. A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms−1 . The magnitude of its momentum is recorded as (1) 17.6 kg ms−1 (2) 17.565 kg ms−1 (3) 17.56 kg ms−1 (4) 17.57 kg ms−1

Q6. A block of mass 0.50 kg is moving with a speed of 2.00 m/s on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is (1) 0.16 J (2) 1.00 J (3) 0.67 J (4) 0.34 J

Q7. Consider a uniform square plate of side ' a ' and mass ' m '. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is (1) 5 ma2 (2) 1 ma2 6 12 (3) 7 ma2 (4) 2 ma2 12 3

Q8. A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11kms−1 , the escape velocity from the surface of the planet would be (1) 1.1kms−1 (2) 11kms−1 (3) 110kms−1 (4) 0.11kms−1

Q10.A spherical solid ball of volume V is made of a material of density ρ1 . It is falling through a liquid of density ρ2 (ρ2 < ρ1). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., Fviscous = −kv2(k > 0). The terminal speed of the ball is (1) (2) Vgρ1 k √Vg(ρ1−ρ2)k (3) gρ1 (4) Vg(ρ1−ρ2) k √V k

Q11.A jar filled with two non mixing liquids 1 and 2 having densities ρ1 and ρ2 respectively. A solid ball, made of a material of density ρ3 , is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which JEE Main 2008 JEE Main Previous Year Paper of the following is true for ρ1, ρ2 and ρ3 ? (1) ρ3 < ρ1 < ρ2 (2) ρ1 < ρ3 < ρ2 (3) ρ1 < ρ2 < ρ3 (4) ρ1 < ρ3 < ρ2

Q12.A capillary tube (A) is dropped in water. Another identical tube (B) is dipped in a soap water solution. Which of the following shows the relative nature of the liquid columns in the two tubes? (1) (2) (3) (4)

Q13.An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V1 and contains ideal gas at pressure P1 and temperature T1 . The other chamber has volume V2 and contains ideal gas at pressure P2 and temperature T2 . If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be (1) T1T2(P1V1+P2V2) (2) P1V1T1+P2V2T2 P1V1T2+P2V2T1 P1V1+P2V2 (3) P1V1T2+P2V2T1 (4) T1T2(P1V1+P2V2) P1V1+P2V2 P1V1T1+P2V2T2

Q14.While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be xcm for the second resonance. Then JEE Main 2008 JEE Main Previous Year Paper (1) 18 > x (2) x > 54 (3) 54 > x > 36 (4) 36 > x > 18

Q15.The speed of sound in oxygen (O2) at a certain temperature is 460 ms−1 . The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal) (1) 460 ms−1 (2) 500 ms−1 (3) 650 ms−1 (4) None of these

Q16.A wave travelling along the x-axis is described by the equation y(x, t) = 0.005 cos(αx −βt). If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then α and β in appropriate units are (1) α = 25.00π, β = π (2) α = 0.08π , 2.0π (3) α = 0.04π , β = 1.0π (4) α = 12.50π, β = 2.0π

Q18.A parallel plate capacitor with air between the plates has a capacitance of 9pF. The separation between its plates is ' d '. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant k1 = 3 and thickness d3 while the other one has dielectric constant k2 = 6 and thickness 23d . Capacitance of the capacitor is now (1) 1.8pF (2) 45pF (3) 40.5pF (4) 20.25pF

Q20.Paragraph: Consider a block of conducting material of resistivity ' ρ ' shown in the figure. Current 'l' enters at 'A' and leaves from ' D '. We apply superposition principle to find voltage ' ΔV ' developed between ' B ' and ' C '. The calculation is done in the following steps: (i) Take current 'l' entering from 'A' and assume it to spread over a hemispherical surface in the block. (ii) Calculate field E(r) at distance ' r ' from A by using Ohm's law E = ρj, where j is the current per unit area at ' r '. (iii) From the ' r ' dependence of E(r), obtain the potential V (r) at r. (iv) Repeat (i), (ii) and (iii) for current 'l' leaving ' D ' and superpose results for ' A ' and ' D '. Question: For current entering at A , the electric field at a distance ' r ' from A is (1) ρl (2) ρl 8πr2 r2 (3) ρl (4) ρl 2πr2 4πr2

Q21.A 5 V battery with internal resistance 2Ω and a 2 V battery with internal resistance 1Ω are connected to a 10Ω resistor as shown in the figure. The current in the 10Ω resistor is JEE Main 2008 JEE Main Previous Year Paper (1) 0.27AP2 to P1 (2) 0.03AP1 to P2 (3) 0.03AP2 to P1 (4) 0.27 APP1 to P2

Q23.A horizontal overhead power line is at a height of 4 m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is (μ0 = 4π × 10−7 T m A−1) (1) 2.5 × 10−7 T southward (2) 5 × 10−6 T northward (3) 5 × 10−6 T southward (4) 2.5 × 10−7 northward