Practice Questions

Q16.The de Broglie wavelength of a proton and α -particle are equal. The ratio of their velocities is (1) 4 : 1 (2) 4 : 3 (3) 1 : 4 (4) 4 : 2

Q16.The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100 V . What should nearly be the ratio of their wavelengths ? ( mp = 1. 00727 u, me = 0. 00055 u) (1) 1860 : 1 (2) (1860)2 : 1 (3) 41. 4 : 1 (4) 43 : 1

Q16.A 100Ω resistance, a 0. 1μF capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is 60 Hz. (1) 0. 70H (2) 70. 3 mH (3) 7. 03 × 10−5H (4) 70. 3 H

Q16.Given below are two statements : one is labeled as Assertion A and the other is labeled as Reason R. Assertion A : For a simple microscope, the angular size of the object equals the angular size of the image. Reason R: Magnification is achieved as the small object can be kept much closer to the eye than 25 cm and hence it subtends a large angle. In the light of the above statements, choose the most appropriate answer from the options given below: (1) A is false but R is true (2) Both A and R are true but R is NOT the correct explanation of A (3) A is true but R is false (4) Both A and R are true and R is the correct explanation of A →

Q16.A plane electromagnetic wave of frequency 500 MHz is traveling in a vacuum along the y−direction. At a → particular point in space and time, B = 8. 0 × 10−8ˆz T. The value of the electric field at this point is:(speed of light = 3 × 108 ms−1 ) ˆx, ˆy,ˆz are unit vectors along x, y and z direction. (1) −24ˆx V m−1 (2) 2. 6ˆx V m−1 (3) 24ˆx V m−1 (4) −2. 6ˆx V m−1 JEE Main 2021 (16 Mar Shift 1) JEE Main Previous Year Paper

Q17.In a Young's double slit experiment, the width of the one of the slit is three times the other slit. The amplitude of the light coming from a slit is proportional to the slit-width. Find the ratio of the maximum to the minimum intensity in the interference pattern. JEE Main 2021 (24 Feb Shift 1) JEE Main Previous Year Paper (1) 1: 4 (2) 2: 1 (3) 3: 1 (4) 4: 1

Q17.The de-Broglie wavelength of a particle having kinetic energy E is λ. How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to 75% of the initial value? (1) E (2) 7E 9 (3) 16E (4) E 9 9

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.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.If an electron is moving in the nth orbit of the hydrogen atom, then its velocity (vn) for the nth orbit is given as: (1) vn ∝n (2) vn ∝1n (3) vn ∝n2 (4) vn ∝ n21

Q17.There are two infinitely long straight current-carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductors is 1: 1. The magnetic field at point 𝑃 is_________ . (1) 𝜇0I + 𝑦2 - (𝑥+ 𝑦) (2) 𝜇0I𝑥𝑦 √𝑥2 + 𝑦2 - (𝑥+ 𝑦) 4πxy√𝑥2 4π (3) 𝜇0I + 𝑦2 + (𝑥+ 𝑦) (4) 𝜇0I𝑥𝑦 √𝑥2 + 𝑦2 + (𝑥+ 𝑦) 4πxy√𝑥2 4π

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 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.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.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.The radiation corresponding to 3 →2 transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of 5 × 10−4 T. Assume that the radius of the largest circular path followed by these electrons is 7 mm, the work function of the metal is: (Mass of electron = 9. 1 × 10−31 kg) (1) 1. 36 eV (2) 1. 88 eV (3) 0. 16 eV (4) 0. 82 eV

Q17.The light waves from two coherent sources have same intensity I1 = I2 = I0. In interference pattern the intensity of light at minima is zero. What will be the intensity of light at maxima? (1) I0 (2) 2I0 (3) 4I0 (4) 5I0

Q17.For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric (Ue) and magnetic (Um) fields is : (1) Ue = Um (2) Ue > Um (3) Ue < Um (4) Ue ≠Um

Q17.The incident ray, reflected ray and the outward drawn normal are denoted by the unitvectors →a, band →c respectively. Then choose the correct relation for these vectors. → → (1) (2) b =→a+ 2→c b = 2→a+→c → → (3) (4) b =→a−→c b =→a−2(→a⋅→c)→c

Q17.A particle is travelling 4 times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is 2 : 1, the mass of the particle is :- (1) 1 times the mass of e− (2) 8 times the mass of e− 16 (3) 16 times the mass of e− (4) 18 times the mass of e−

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.An electron of mass me and a proton of mass mP are accelerated through the same potential difference. The ratio of the de-Broglie wavelength associated with the electron to that with the proton is (1) mP (2) 1 me mp (3) √mpme (4) me

Q17.Find the distance of the image from object O, formed by the combination of lenses in the figure: JEE Main 2021 (27 Aug Shift 1) JEE Main Previous Year Paper (1) 75 cm (2) 10 cm (3) infinity (4) 20 cm

Q17.The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n = 2 to n = 1 state is: (1) 121. 8 nm (2) 194. 8 nm (3) 490. 7 nm (4) 913. 3 nm JEE Main 2021 (25 Feb Shift 2) JEE Main Previous Year Paper

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