Practice Questions

Q28.A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is 30 s. The effective half-life of the nucleus is calculated to be 11α s. The value of α is ______.

Q28.The energy released per fission of nucleus of 240X is 200 MeV . The energy released if all the atoms in 120 g of pure 240X undergo fission is _____ ×1025 MeV . (Given NA = 6 × 1023 )

Q28.A nucleus with mass number 242 and binding energy per nucleon as 7. 6 MeV breaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8. 1 MeV, the total gain in binding energy is _______ MeV.

Q28.If the binding energy of ground state electron in a hydrogen atom is 13. 6 eV , then, the energy required to remove the electron from the second excited state of Li 2+ will be: x × 10−1 eV . The value of x is _____.

Q28.An inductor of 0 . 5 mH, a capacitor of 20 μF and resistance of 20 Ω are connected in series with a 220 V ac source. If the current is in phase with the emf, the amplitude of current of the circuit is √𝑥 A. The value of 𝑥 is-

Q28.In the circuit shown in the figure, the ratio of the quality factor and the band width is _____ s.

Q28.A square loop of side 2 . 0 cm is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude 2 . 5 A and angular frequency 700 rad s-1. The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is 𝑥× 10-4 V. The value of 𝑥 is ___________ ( Take, 𝜋= 22 7

Q28.In Young’s double slit experiment, two slits 𝑆1 and 𝑆2 are 𝑑 distance apart and the separation from slits to screen is 𝐷 (as shown in figure). Now if two transparent slabs of equal thickness 0 . 1 mm but refractive index 1 . 51 and 1 . 55 are introduced in the path of beam λ = 4000 Å from 𝑆1 and 𝑆2 respectively. The central bright fringe spot will shift by ________ number of fringes.

Q28.The magnetic field B crossing normally a square metallic plate of area 4 m2 is changing with time as shown in figure. The magnitude of induced emf in the plate during 𝑡= 2 s to 𝑡= 4 s, is _____ 𝑚𝑉.

Q28.An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area 24 cm2. The two ends of the wire are connected to a resistor. The total resistance in the circuit is 12 Ω. If an externally applied uniform magnetic field in the core along its axis changes from 1 . 5 T in one direction to 1 . 5 T in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be _____ mC.

Q28.An ideal transformer with purely resistive load operates at 12 kV on the primary side. It supplies electrical energy to a number of nearby houses at 120 V . The average rate of energy consumption in the houses served by the transformer is 60 kW . The value of resistive load ( 𝑅𝑠) required in the secondary circuit will be _________mΩ .

Q28.A series LCR circuit is connected to an ac source of 220 V, 50 Hz. The circuit contain a resistance 𝑅= 100 Ω and an inductor of inductive reactance 𝑋𝐿= 79 . 6 Ω. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be ______ μF.

Q28.A 1 m long metal rod 𝑋𝑌 completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density 0 . 15 T. If the resistance of the circuit is 5 Ω, the force needed to move the rod in direction, as indicated, with a constant speed of 4 m s-1 will be _______10 – 3 N.

Q28.A common example of alpha decay is 23892U →23490 Th +2 He4 + Q Given: 23892U = 238. 05060 u 23490Th = 234. 04360 u 42He = 4. 00260 u and 1u = 931. 5 MeVc2 The energy released (Q) during the alpha decay of 23892U is _____ MeV.

Q28.Nucleus a having Z = 17 and equal number of protons and neutrons has 1. 2 MeV binding energy per nucleon. Another nucleus B of Z = 12 has total 26 nucleons and 1. 8 MeV binding energy per nucleons. The JEE Main 2023 (01 Feb Shift 2) JEE Main Previous Year Paper difference of binding energy of B and A will be ______ MeV.

Q29.A pole is vertically submerged in swimming pool, such that it gives a length of shadow 2 . 15 m within water when sunlight is incident at an angle of 30° with the surface of water. If swimming pool is filled to a height of ) ________ . 1 . 5 m, then the height of the pole above the water surface in centimeters is (𝑛𝑤= 43 ∘

Q29.A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of 24 W. The radius of curvature of hemisphere is 10 cm and the inner surface is completely reflecting. The force on the hemisphere due to the light falling on it is ______ × 10-8 N.

Q29.A bi convex lens of focal length 10 cm is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is _____ D.

Q29.A thin cylindrical rod of length 10 cm is placed horizontally on the principle axis of a concave mirror of focal length 20 cm. The rod is placed in a such a way that mid point of the rod is at 40 cm from the pole of mirror. The length of the image formed by the mirror will be 𝑥 cm. The value of 𝑥 is ______. 3

Q29.From the given transfer characteristic of a transistor in CE configuration, the value of power gain of this configuration is 10x , for RB = 10 kΩ, and RC = 1 kΩ. The value of x is _____. JEE Main 2023 (13 Apr Shift 1) JEE Main Previous Year Paper

Q29.In a medium the speed of light wave decreases to 0 . 2 times to its speed in free space. The ratio of relative permittivity to the refractive index of the medium is 𝑥: 1. The value of 𝑥 is ______. (Given speed of light in free space = 3 × 108 m s-1 and for the given medium 𝜇𝑟= 1)

Q29.The refractive index of a transparent liquid filled in an equilateral hollow prism is √2. The angle of minimum deviation for the liquid will be _______ °.

Q29.As shown in the figure, a combination of a thin plano-concave lens and a thin plano-convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm and refraction index of the material for both the lenses is 1 . 75. Both the lenses are placed at distance of 40 cm from each other. Due to the combination, the image of the object is formed at distance x = ______ cm, from concave lens.

Q29.Unpolarised light of intensity 32 W m−2 passes through the combination of three polaroids such that the pass axis of the last polaroids is perpendicular to that of the pass axis of first polaroids. If intensity of emerging light is 3 W m−2, then the angle between pass axis of first two polaroids is _________°.

Q29.A point object 𝑂 is placed in front of two thin symmetrical coaxial convex lenses 𝐿1 and 𝐿2 with focal length 24 cm and 9 cm respectively. The distance between two lenses is 10 cm and the object is placed 6 cm away from lens 𝐿1 as shown in the figure. The distance between the object and the image formed by the system of two lenses is _____________ cm