Practice Questions

Q30.A nucleus has mass number 𝐴1 and volume 𝑉1. Another nucleus has mass number 𝐴2 and volume 𝑉2. If 𝑉2 relation between mass number is 𝐴2 = 4𝐴1, then = _______. 𝑉1

Q30.In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at 10.2 V. The wavelength of light emitted by hydrogen atom when excited to the first excitation level is _________ nm . (Given hc = 1245eVnm, e = 1.6 × 10−19C ).

Q30.Hydrogen atom is bombarded with electrons accelerated through a potential different of V , which causes excitation of hydrogen atoms. If the experiment is being formed at T = 0 K. The minimum potential difference needed to observe any Balmer series lines in the emission spectra will be α V , where α = 10 _________.(Write the value to the nearest integer)

Q30.An electron of hydrogen atom on an excited state is having energy En = −0. 85 eV. The maximum number of allowed transitions to lower energy level is _______.

Q30.A star has 100% helium composition. It starts to convert three 4He into one 12C via triple alpha process as 4He + 4He + 4He →12C + Q. The mass of the star is 2.0 × 1032 kg and it generates energy at the rate of 5.808 × 1030 W. The rate of converting these 4He to 12C is n × 1042 s−1 , where n is _________ [ Take, mass of 4He = 4.0026u, mass of 12C = 12u ]

Q30.If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be 7𝑅, where 𝛼= ______.

Q30.The mass defect in a particular reaction is 0 . 4 g. The amount of energy liberated is 𝑛× 107 kW h, where 𝑛= _____. (speed of light = 3 × 108 m s-1)

Q30.Radius of a certain orbit of hydrogen atom is 8.48Ã … . If energy of electron in this orbit is E/x. then x = _____ (Given a0 = 0.529Ã … , E = energy of electron in ground state).

Q30.In a nuclear fission process, a high mass nuclide (A ≈236) with binding energy 7. 6 MeV /Nucleon dissociated into two middle mass nuclides (A ≈118), having binding energy of 8. 6 MeV /Nucleon. The energy released in the process would be _______ MeV .

Q30.A particular hydrogen - like ion emits the radiation of frequency 3 × 1015 Hz when it makes transition from 𝑥 𝑛= 2 to 𝑛= 1 . The frequency of radiation emitted in transition from 𝑛=3 to 𝑛= 1 is × 1015 Hz, when 9 𝑥= _____.

Q30.The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is 915Ã … . The longest wavelength of spectral lines in the Balmer series will be _____ Ã … .

Q30.Monochromatic light of wavelength 500 nm is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index = 1.5 ), the central maximum is shifted to a position previously occupied by the 4th bright fringe. The thickness of the glass-plate is ______ μm .

Q30.A hydrogen atom changes its state from n = 3 to n = 2. Due to recoil, the percentage change in the wave length of emitted light is approximately 1 × 10−n . The value of n is_____. [Given Rhc = 13.6eV, hc = 1242eVnm, h = 6.6 × 10−34 J s mass of the hydrogenatom = 1.6 × 10−27 kg ] JEE Main 2024 (04 Apr Shift 1) JEE Main Previous Year Paper

Q1. If P = 3ˆi + √3ˆj + 2ˆk and Q = 4ˆi + √3ˆj + 2. 5ˆk then, the unit vector in the direction of P × Q is x is x 1 (√3ˆi +ˆj −2√3ˆk). The value of

Q1. In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5. 25 mm and apparent thickness of the glass slab at 5. 00 mm . Travelling microscope has 20 divisions in one cm on main scale and 50 divisions on Vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is x × 10−3 , where x is ______ 10

Q2. For a train engine moving with speed of 20 ms–1 , the driver must apply brakes at a distance of 500 m before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed √x ms−1 . The value of x is ______. (Assuming same retardation is produced by brakes)

Q2. A tennis ball is dropped on to the floor from a height of 9. 8 m. It rebounds to a height 5. 0 m. Ball comes in contact with the floor for 0. 2 s . The average acceleration during contact is ______ m s−2 . [Given g = 10 m s−2 ]

Q3. As per given figure, a weightless pulley 𝑃 is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if 𝑔= 10 m s-2) (1) 4√3 + 1 N (2) 4√3 + 1 N (3) 4√3 - 1 N (4) 4√3 - 1 N

Q4. A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is 2 ) s . The value of t is ______. moving with an initial speed of 54 km h−1 is t(1–e– π

Q4. A stone tied to 180 cm long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is 1936 x m s−2 . The value of x ______. [Take π = 227 ]

Q4. Two bodies are projected from ground with same speeds 40 m s−1 at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of 60° , with horizontal then sum of the maximum heights, attained by the two projectiles, is _____ m. (Given g = 10 m s−2 )

Q4. A block is fastened to a horizontal spring. The block is pulled to a distance x = 10 cm from its equilibrium position (at x = 0 ) on a frictionless surface from rest. The energy of the block at x = 5 cm is 0. 25 J . The spring constant of the spring is ______ N m−1 .

Q5. A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2 . The ratio of their 1 nuclear sizes will be ( x3 ) 3 . The value of ‘ x’ is:

Q5. To maintain a speed of 80 km h−1 by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be _____ kJ. [The coefficient of friction between tyre of bus and road is 0. 04 ]

Q5. An object of mass m initially at rest on a smooth horizontal plane starts moving under the action of force F = 2 N . In the process of its linear motion, the angle θ (as shown in figure) between the direction of force and horizontal varies as θ = kx , where k is a constant and x is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be E = nk sin θ . The value of n is ______.