Practice Questions

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 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.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 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.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

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.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.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.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.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 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 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.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 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

Q1. The relative error in the determination of the surface area of a sphere is α. The relative error in the determination of its volume is (1) 3 α (2) 2 α 2 3 (3) α (4) 5 α 2

Q1. The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c. Which of the following correctly gives the Planck length? (1) G2hc (2) Gh 21 ( c3 ) (3) G 12 h2c (4) G (h2c3

Q1. The relative error in the determination of the surface area of a sphere is α. Then the relative error in the determination of its volume is (1) 2 α (2) 2 α 3 3 (3) 3 α (4) α 2

Q1. Let A = + and B = − . The magnitude of a coplanar vector C such that (ˆi ˆj) (2ˆi ˆj) → → → → → → A . C = B. C = A . B is given by: (1) √912 (2) √209 (3) √59 (4) √109

Q1. The density of a material, in the shape of a cube, is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are 1. 5% and 1%, respectively, the maximum error in determining the density is: (1) 6 % (2) 2.5 % (3) 3.5 % (4) 4.5 %

Q2. The velocity time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in 15 s and (ii) the time at which the car will catch up with the scooter are, respectively. (1) 112. 5 m and 22. 5 s (2) 337. 5 m and 25 s (3) 225. 5 m and 10 s (4) 112. 5 m and 15 s

Q2. A man in a car at location Q on a straight highway is moving with speed v . He decides to reach a point P in a field at a distance d from highway (point M ) as shown in the figure.Speed of the car in the field is half to that on the highway. What should be the distance RM, so that the time taken to reach P is minimum? (1) d (2) d √3 2 (3) d (4) d √2

Q2. An automobile, travelling at 40 km/h, can be stopped at a distance of 40 m by applying brakes. If the same automobile is travelling at 80 km/h, the minimum stopping distance, in metres, is (assume no skidding) (1) 75 m (2) 160 m (3) 100 m (4) 150 m

Q2. The percentage errors in quantities P , Q , R and S are 0. 5%, 1%, 3% and 1. 5% respectively in the P 3Q2 measurement of a physical quantity A= . The maximum percentage error in the value of A will be: √RS (1) 6.5 % (2) 7.5 % (3) 6.0 % (4) 8.5 %

Q3. An automobile, traveling at 40 km h−1 , can be stopped at a distance of 40 m by applying brakes. If the same automobile is traveling at 80 km h−1 , the minimum stopping distance in metres is (Assume no skidding): (1) 150 m (2) 100 m (3) 75 m (4) 160 m

Q3. Two masses m1 = 5 kg and m2 = 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0. 15. The minimum weight m that should be put on top of m2 to stop the motion is: (1) 10 .3 kg (2) 18 .3 kg (3) 27 .3 kg (4) 43 .3 kg