Practice Questions

Q49.A tube of length 1 m is filled completely with an ideal liquid of mass 2 M , and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is in SI unit. The value of α is __________. √FαM

Q4. A car of 800 kg is taking turn on a banked road of radius 300 m and angle of banking 30∘ . If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: = 10 m/s2, √3 = 1.73) (g (1) 264 m/s (2) 51.4 m/s (3) 70.4 m/s (4) 102.8 m/s

Q4. A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle ( θ ) of thread deflection in the extreme position will be : (1) tan-1 ( √2 ) (2) 2tan-112 (3) tan-11 (4) 2tan-1 1 2 √5

Q5. A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle θ with the horizontal. The weight experienced by the person is : (1) W cos θ (2) W2 (3) W (4) W sin θ

Q6. A spherical ball of radius 1 × 10−4 m and density 105 kg/m3 falls freely under gravity through a distance h before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of h is approximately: (The coefficient of viscosity of water is 9.8 × 10−6 N s/m2 ) (1) 2296 m (2) 2518 m (3) 2249 m (4) 2396 m

Q7. A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is : (1) GmMπ2 (2) GMmπ L2 2 L2 (3) 0 (4) 2GmMπ L2

Q7. Two planets A and B having masses m1 and m2 move around the sun in circular orbits of r1 and r2 radii respectively. If angular momentum of A is L and that of B is 3 L, the ratio of time period ( TBTA ) is: (1) r2 32 (2) 1 m2 3 27 ( m1 ) ( r1 ) (3) m1 3 (4) r1 3 27( m2 ) ( r2 )

Q10.The specific heat at constant pressure of a real gas obeying PV 2 = RT equation is: (1) R 3 + CV (2) CV + R (3) CV + 2VR (4) R

Q14.The following figure represents two biconvex lenses L1 and L2 having focal length 10 cm and 15 cm respectively. The distance between L1&L2 is : (1) 10 cm (2) 35 cm (3) 25 cm (4) 15 cm

Q14.Given below are two statements : Statement (I) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account. Statement (II) : Ampere's circuital law does not depend on Biot-Savart's law. In the light of the above statements, choose the correct answer from the options given below : (1) Both Statement I and Statement II are true (2) Statement I is true but Statement II is false (3) Both Statement I and Statement II are false (4) Statement I is false but Statement II is true

Q15.Two conducting circular loops A and B are placed in the same plane with their centers coinciding as shown in figure. The mutual inductance between them is : (1) μ0πb2 (2) μo ⋅b2a 2π 2a (3) μ0 2π ⋅a2b (4) μ0πa22b

Q15.A transformer has an efficiency of 80% and works at 10 V and 4 kW . If the secondary voltage is 240 V, then the current in the secondary coil is: (1) 1 . 59 A (2) 13 . 33 A (3) 1 . 33 A (4) 15 . 1 A

Q15.In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division = 49MSD; 20 divisions on main scale in each cm For mark on paper JEE Main 2024 (06 Apr Shift 2) JEE Main Previous Year Paper MSR = 8.45 cm, VC = 26 For mark on paper seen through slab MSR = 7.12 cm, V C = 41 For powder particle on the top surface of the glass slab MSR = 4.05 cm, VC = 1 (MSR = Main Scale Reading, VC = Vernier Coincidence) Refractive index of the glass slab is : (1) 1.52 (2) 1.35 (3) 1.42 (4) 1.24

Q15.The position of the image formed by the combination of lenses is : (1) 15 cm (right of second lens) (2) 30 cm (left of third lens) (3) 15 cm (left of second lens) (4) 30 cm (right of third lens)

Q18.The energy released in the fusion of 2 kg of hydrogen deep in the sun is EH and the energy released in the fission of 2 kg of 235U is EU . The ratio EHEU is approximately: (Consider the fusion reaction as 4 ∣H + 2e−→42He + 2v + 6γ + 26.7MeV, energy released in the fission reaction of 235U is 200MeV per fission nucleus and NA = 6.023 × 1023) JEE Main 2024 (09 Apr Shift 2) JEE Main Previous Year Paper (1) 7.62 (2) 25.6 (3) 15.04 (4) 9.13

Q18.In a nuclear fission reaction of an isotope of mass 𝑀, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect 𝛥𝑀 will be : JEE Main 2024 (30 Jan Shift 2) JEE Main Previous Year Paper (1) 2𝑐𝛥𝑀 (2) 𝛥𝑀𝑐2 √ 𝑀 3 (3) 2𝛥𝑀 (4) 3𝛥𝑀 𝑐√ 𝑀 𝑐√ 𝑀

Q18.The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is 25% of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be: (1) 1 (2) 1 1 8 (3) 8 (4) 1 1 4

Q20.In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its 4th division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is 0.04 mm then how many main scale divisions are there in 1 cm ? (1) 10 (2) 5 (3) 20 (4) 40

Q21.A particle is moving in a circle of radius 50 cm in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at t = 0 is 4 m s−1 , the time taken to complete the first revolution will be 1 [1 −e−2π] s, where α =______. α

Q21.A body starts falling freely from height 𝐻 hits an inclined plane in its path at height ℎ. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of 𝐻 for which ℎ the body will take the maximum time to reach the ground is _____.

Q22.A circular table is rotating with an angular velocity of ωrad/s about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of 1 m on the groove. All the surfaces are smooth. If the radius of the table is 3 m , the radial velocity of the ball w.r.t. the table at the time ball leaves the table is x√2ωm/s, where the value of x is _____.

Q23.A wire of cross sectional area A, modulus of elasticity 2 × 1011Nm−2 and length 2 m is stretched between two vertical rigid supports. When a mass of 2 kg is suspended at the middle it sags lower from its original position JEE Main 2024 (06 Apr Shift 2) JEE Main Previous Year Paper making angle θ = 1001 radian on the points of support. The value of A is _______ ×10−4 m2 (consider x << L ). (given : g = 10 m/s2 )

Q25.A thin metallic wire having cross sectional area of 10−4 m2 is used to make a ring of radius 30 cm. A positive charge of 2π C is uniformly distributed over the ring, while another positive charge of 30 pC is kept at the centre of the ring. The tension in the ring is _______ N; provided that the ring does not get deformed (neglect the influence of gravity). (Given, 1 = 9 × 109 SI units) 4πϵ0

Q25.A capacitor of 10μF capacitance whose plates are separated by 10 mm through air and each plate has area 4 cm2 is now filled equally with two dielectric media of K1 = 2, K2 = 3 respectively as shown in figure. If new force between the plates is 8 N . The supply voltage is _________ ×10−4 V . (we modified language of question to make it correct)

Q25.An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density +σ. The electron at t = 0 is at a distance of 1 m from S and has a speed of 1 m s−1 . The maximum value of σ, if the electron strikes S at t = 1 s is α[ mϵ0e ] m2C . The value of α is _____.