Practice Questions

Q29.Two radioactive substances A and B have decay constants 5λ and λ respectively. At t = 0, a sample has the 1 2 same number of the two nuclei. The time taken for the ratio of the number of nuclei to become will be e 1 1 (1) (2) λ 2λ 2 1 (3) (4) λ 4λ

Q29.The surface of certain metal is first illuminated with light of wavelength 𝜆1 = 350 nm and then, by a light of wavelength 𝜆2 = 540 nm . It is found that the maximum speed of the photoelectrons in the two cases differ by a factor of 2. The work function of the metal (in eV) is close to 1240 (Energy of photon = eV ) 𝜆in nm (1) 2.5 (2) 1.8 (3) 5.6 (4) 1.4

Q29.An amplitude modulated signal is given by V(t) = 10[1 + 0.3 cos (2.2 × 104t)] sin (5.5 × 105t). Here t is in seconds. The sideband frequencies (in kHz ) are, [Given π = 22/7 ] (1) 1785 and 1715 (2) 178.5 and 171.5 (3) 89.25 and 85.75 (4) 892.5 and 857.5

Q29.The truth table for the circuit given in the figure is: (1) A B Y (2) A B Y 0 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 (3) A B Y (4) A B Y 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 1 0

Q29.To double the covering range of a TV transmitting tower, its height should be multiplied by: (1) 1 (2) 4 √2 (3) 2 (4) √2

Q29.A common emitter amplifier circuit, built using an NPN transistor, is shown in the figure. Its dc current gain is 250, 𝑅𝐶= 1 kΩ and 𝑉𝐶𝐶= 10 V . The minimum base current for VCE to reach saturation is (1) 10 μA (2) 40 μA (3) 7 μA (4) 100 μA

Q29.The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 μm diameter of a wire is: (1) 50 (2) 100 (3) 500 (4) 200

Q30.The physical sizes of the transmitter and receiver antenna in a communication system are: (1) proportional to carrier frequency (2) independent of both carrier and modulation frequency (3) inversely proportional to modulation frequency (4) inversely proportional to carrier frequency

Q30.A signal Acosωt is transmitted using ν0sinω0t as carrier wave. The correct amplitude modulated (AM) signal is: JEE Main 2019 (09 Apr Shift 1) JEE Main Previous Year Paper (1) ν0sin[ω0(1 + 0.01Asinωt)t] (2) (ν0 + A)cosωt sinω0t (3) ν0 sinω0t + Acosωt (4) ν0sinω0t + A2 sin(ω0 −ω)t + A2 sin(ω0 + ω)t

Q30.A potentiometer wire AB having length L and resistance 12r is joined to a cell D of emf ε and internal resistance r. A cell C having EMF ε/2 and internal resistance 3r is connected. The length AJ, at which the galvanometer, as shown in the figure, shows no deflection is (1) 5 L (2) 11 L 12 24 (3) 11 L (4) 13 L 12 24

Q30.In a meter bridge experiment, the circuit diagram and the corresponding observation table are shown in figure. JEE Main 2019 (10 Apr Shift 1) JEE Main Previous Year Paper S. No. R(Ω) l(cm) 1. 1000 60 2. 100 13 3. 10 1.5 1 1.0 4. Which of the reading is inconsistent? (1) 1 (2) 3 (3) 2 (4) 4

Q30.The wavelength of the carrier waves in a modern optical fiber communication network is close to: (1) 2400 nm (2) 900 nm (3) 600 nm (4) 1500 nm

Q30.In the experimental set up of metre bridge shown in the figure, the null point is obtaine data distance of 40 cm from A. If a 10Ω resistor is connected in series with R1, the null point shifts by 10 cm. The resistance that should be connected in parallel with (R1 + 10)Ω such that the null point shifts back to its initial position is (1) 20Ω (2) 40Ω (3) 60Ω (4) 30Ω Q31. 25 mL of the given HCl solution requires 30 mL of 0.1M sodium carbonate solution. What is the volume of this HCl solution required to titrate 30 mL of 0.2M aqueous NaOH solution? (1) 25 mL (2) 75 mL (3) 50 mL (4) 12.5 mL JEE Main 2019 (11 Jan Shift 2) JEE Main Previous Year Paper

Q30.In a line of sight radio communication, a distance of about 50 km is kept between the transmitting and receiving antennas. If the height of the receiving antenna is 70 m, then the minimum height of the transmitting antenna should be: (Radius of the Earth = 6 . 4 × 106 m) (1) 20 m (2) 51 m (3) 40 m (4) 32 m

Q30.A tunning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, l1 = 30 cm and l2 = 70 cm. Then, ν is equal to: (1) 384 m s−1 (2) 332 m s−1 (3) 338 m s−1 (4) 379 m s−1 Q31. 25 g of an unknown hydrocarbon upon burnig produces 88 g of CO2 and 9g of H2O. This unknown hydrocarbon contains: (1) 24 g of carbon and 1 g of hydrogen (2) 18 g of carbon annd 7 g of hydrogen (3) 22 g of carbon and 3 g of hydrogen (4) 20 g carbon and 5 g of hydrogen

Q30.The transfer characteristic curve of a transistor, having input and output resistance 100 Ω and 100 kΩ respectively, is shown in the figure. The voltage and power gain, are respectively: JEE Main 2019 (12 Apr Shift 1) JEE Main Previous Year Paper (1) 5 × 104, 2.5 × 106 (2) 2.5 × 104, 2.5 × 106 (3) 5 × 104, 5 × 106 (4) 5 × 104, 5 × 105 Q31.5 moles of AB2 weigh 125 × 10-3 kg and 10 moles of A2B2 weigh 300 × 10-3 kg . The molar mass of A ( MA ) in kg mol-1 are: (1) MA = 5 × 10-3 and MB = 10 × 10-3 (2) MA = 25 × 10-3 and MB = 50 × 10-3 (3) MA = 50 × 10-3 and MB = 25 × 10-3 (4) MA = 10 × 10-3 and MB = 5 × 10-3

Q30.A Sample of radioactive material 𝐴, that has an activity of 10 𝑚 Ci 1 𝐶𝑖= 3.7 × 1010 decays s-1, has twice the number of nuclei as another sample of a different radioactive material 𝐵 which has an activity of 20 𝑚 Ci. The correct choices for half-lives of 𝐴 and 𝐵 would then be, respectively: (1) 5 days and 10 days (2) 10 days and 40 days (3) 20 days and 10 days (4) 20 days and 5 days JEE Main 2019 (09 Jan Shift 1) JEE Main Previous Year Paper 1

Q30.The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is 6 V and the load resistance is, RL = 4 kΩ . The series resistance of the circuit is Ri = 1 kΩ . If the battery voltage VB varies from 8 V to 16 V , what are the minimum and maximum values of the current through Zener diode? (1) 0.5 mA; 6 mA (2) 1 mA; 8.5 mA (3) 0.5 mA; 8.5 mA (4) 1.5 mA; 8.5 mA

Q30.The resistance of the meter bridge AB in given figure is 4Ω. With a cell of emf ε = 0.5 V and rheostat resistance Rh = 2Ω the null point is obtained at some point J. When the cell is replaced by another one of emf ε = ε2 the same null point J is found for Rh = 6Ω. The emf ε2 is: (1) 0.4 V (2) 0.3 V (3) 0.6 V (4) 0.5 V

Q30.The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0. 5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are 5 .5 mm and 48 respectively, the thickness of this sheet is: (1) 5.755 mm (2) 5.740 mm (3) 5.725 mm (4) 5.950 mm

Q30.In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the variation dRdl of its resistance R with length l is dRdl ∝ √l1 . Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP? JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper (1) 0.2 m (2) 0.35 m (3) 0.3 m (4) 0.25 m o

Q30.A load of mass M kg is suspended from a steel wire of length 2m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is: (1) 4.0 mm (2) Zero (3) 5.0mm (4) 3.0mm Q31. 8 g of NaOH is dissolved in 18g of H2O. Mole fraction of NaOH in solution and molality (in mol kg−1 ) of the solution respectively are: (1) 0.167, 11.11 (2) 0.167, 22.20 (3) 0.2, 11.11 (4) 0.2, 22.20 JEE Main 2019 (12 Jan Shift 2) JEE Main Previous Year Paper

Q30.The modulation frequency of an AM radio station is 250kHz, which is 10% of the carrier wave. If another AM station approaches you for license what broadcast frequency will you allot? (1) 2750 kHz (2) 2000 kHz (3) 2250 kHz (4) 2900kHz

Q31.What would be the molality of 20% (mass/mass) aqueous solution of KI ? (molar mass of KI = 166 g mol−1 ) (1) 1.35 (2) 1.51 (3) 1.08 (4) 1.48

Q31.Which of the graphs shown below does not represent the relationship between incident light and the electron ejected from metal surface? JEE Main 2019 (10 Jan Shift 1) JEE Main Previous Year Paper (1) (2) (3) (4)