Practice Questions

Q17.A short straight object of height 100 cm lies before the central axis of a spherical mirror whose focal length has absolute value |f| = 40 cm . The image of object produced by the mirror is of height 25 cm and has the same orientation of the object. One may conclude from the information: (1) Image is real, same side of convex mirror. (2) Image is virtual, opposite side of concave mirror. (3) Image is real, same side of concave mirror. (4) Image is virtual, opposite side of convex mirror.

Q17.A 0. 07 H inductor and a 12 Ω resistor are connected in series to a 220 V, 50 Hz AC source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take π as 22 7 ] (1) 8. 8 A and tan−1( 116 ) (2) 88 A and tan−1( 116 ) (3) 0. 88 A and tan−1( 116 ) (4) 8. 8 A and tan−1( 116 ) JEE Main 2021 (27 Jul Shift 1) JEE Main Previous Year Paper

Q17.Two radioactive substances X and Y originally have N1 and N2 nuclei respectively. Half life of X is half of the half life of Y . After three half lives of Y , number of nuclei of both are equal. The ratio N1 will be equal to N2 : (1) 1 (2) 8 3 1 (3) 3 (4) 1 1 8

Q17.A moving proton and electron have the same de-Broglie wavelength. If K and P denote the K. E. and momentum respectively. Then choose the correct option : (1) Kp > Ke and Pp = Pe (2) Kp < Ke and Pp = Pe (3) Kp < Ke and Pp < Pe (4) Kp = Ke and Pp = Pe

Q17.A particular hydrogen like ion emits radiation of frequency 2. 92 × 1015 Hz when it makes transition from n = 3 to n = 1. The frequency in Hz of radiation emitted in transition from n = 2 to n = 1 will be: (1) 6. 57 × 1015 (2) 2. 46 × 1015 (3) 0. 44 × 1015 (4) 4. 38 × 1015

Q17.Two identical photocathodes receive the light of frequencies f1 and f2 respectively. If the velocities of the photo-electrons coming out are v1 and v2 respectively, then (1) v21 −v22 = 2mh [f1 −f2] (2) v21 + v22 = 2hm [f1 + f2] (3) 2 h 21 (4) 2 h 21 v1 + v2 = [ m (f1 + f2)] v1 −v2 = [ m (f1 −f2)]

Q17.A prism of refractive index μ and angle of prism A is placed in the position of minimum angle of deviation. If minimum angle of deviation is also A , then in terms of refractive, (1) 2 cos−1( μ2 ) (2) sin−1( μ2 ) (3) (4) cos−1( μ2 ) 2 sin−1(√μ−1 )

Q17.Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to: 𝑚𝑝 𝑚𝑝 (1) (2) √ 𝑚𝑒 𝑚𝑒 (3) 𝑚𝑝 32 (4) 𝑚𝑒 √ 𝑚𝑝 𝑚𝑒 JEE Main 2021 (31 Aug Shift 2) JEE Main Previous Year Paper

Q17.Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as: (where 𝜆 is the decay constant) JEE Main 2021 (25 Jul Shift 1) JEE Main Previous Year Paper (1) 1 𝑙n2 (2) 𝑙𝑛2 2 𝜆 𝜆 (3) 2𝑙n2 (4) 𝑙n32 𝜆 𝜆

Q17.Three rays of light, namely red (R), green (G) and blue (B) are incident on the face PQ of a right angled prism PQR as shown in figure. The refractive indices of the material of the prism for red, green and blue wavelength are 1. 27, 1. 42 and 1. 49 respectively. The colour of the ray(s) emerging out of the face PR is : (1) green (2) red (3) blue and green (4) blue

Q17.For a series LCR circuit with R = 100 Ω, L = 0. 5 mH and C = 0. 1 pF connected across 220 V −50 Hz AC supply, the phase angle between current and supplied voltage and the nature of the circuit is: (1) 0°, resistive circuit (2) ≈90°, predominantly inductive circuit (3) 0°, resonance circuit (4) ≈90°, predominantly capacitive circuit →

Q17.The half-life of Au198 is 2. 7 days. The activity of 1. 50 mg of Au198 , if its atomic weight is 198 g mol−1 is, (NA = 6 × 1023 mol−1) (1) 240 Ci (2) 357 Ci (3) 535 Ci (4) 252 Ci JEE Main 2021 (16 Mar Shift 2) JEE Main Previous Year Paper

Q18.A ray of light entering from air into a denser medium of refractive index 4 , as shown in figure. 3 The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle θ should be equal to: JEE Main 2021 (25 Jul Shift 2) JEE Main Previous Year Paper (1) sin−1 √73 (2) sin−1 √54 (3) sin−1 √74 (4) sin−1 √53

Q18. The logic circuit shown above is equivalent to : JEE Main 2021 (24 Feb Shift 2) JEE Main Previous Year Paper (1) (2) (3) (4)

Q18.A nucleus with mass number 184 initially at rest emits an α− particle. If the Q value of the reaction is 5. 5 MeV, calculate the kinetic energy of the α− particle. (1) 5. 0 MeV (2) 5. 5 MeV (3) 0. 12 MeV (4) 5. 38 MeV

Q18.Identify the logic operation carried out by the given circuit: (1) OR (2) AND (3) NAND (4) NOR

Q18.The truth table for the following logic circuit is : (1) (2) (3) (4)

Q18.A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years, respectively. What will be the time after the which one third of the material remains ? (Take ln 3 = 1. 1 ) (1) 1110 years (2) 700 years (3) 340 years (4) 740 years

Q18.A free electron of 2 . 6 eV energy collides with a H+ ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. ℎ= 6 . 6 × 10-34 J s (1) 9 . 0 × 1027 MHz (2) 1 . 45 × 109 MHz (3) 0 . 19 × 1015 MHz (4) 1 . 45 × 1016 MHz

Q18.The half-life of 198Au is 3 days. If atomic weight of 198Au is 198 g mol-1, then the activity of 2 mg of 198Au is [in disintegration second-1]: (1) 2 . 67 × 1012 (2) 6 . 06 × 1018 (3) 32 . 36 × 1012 (4) 16 . 18 × 1012

Q18.Given below are two statements: Statement I: Two photons having equal linear momenta have equal wavelengths. Statement II: If the wavelength of the photon is decreased, then the momentum and energy of a photon will also decrease. In the light of the above statements, choose the correct answer from the options given below. (1) Both Statement I and Statement II are false (2) Both Statement I and Statement II are true (3) Statement I is true but Statement II is false (4) Statement I is false but Statement II is true

Q18.The speed of electrons in a scanning electron microscope is 1 × 107 ms−1 . If the protons having the same speed are used instead of electrons, then the resolving power of scanning proton microscope will be changed by a factor of: (1) 1837 (2) 18371 (3) √1837 (4) 1 √1837

Q18.A 5 V battery is connected across the points X and Y . Assume D1 and D2 to be normal silicon diodes. Find the current supplied by the battery if the +ve terminal of the battery is connected to point X . (1) ~0. 86 A (2) ~0. 5 A (3) ~1. 5 A (4) ~0. 43 A

Q18.A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turn disintegrates to some other stable nucleus C. Plot of a graph showing the variation of number of atoms of nucleus B vesus time is : (Assume that at t = 0, there are no B atoms in the sample) (1) (2) (3) (4)

Q18.Imagine that the electron in a hydrogen atom is replaced by a muon (μ). The mass of muon particle is 207 times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be:- (1) 13. 6 eV (2) 2815. 2 eV (3) 331. 2 eV (4) 27. 2 eV JEE Main 2021 (18 Mar Shift 1) JEE Main Previous Year Paper