Practice Questions

Q49.Three conductors of same length having thermal conductivity k1, k2 and k3 are connected as shown in figure. Area of cross sections of 1st and 2nd conductor are same and for 3rd conductor it is double of the 1st conductor. The temperatures are given in the figure. In steady state condition, the value of θ is _______ ∘C. (Given : k1 = 60Js−1 m−1 K−1, k2 = 120Js−1 m−1 K−1, k3 = 135Js−1 m−1 K−1 ) ∣ ∣∣ 2025 (22 Jan Shift 1) JEE Main Previous Year Paper

Q49.The least count of a screw guage is 0.01 mm . If the pitch is increased by 75% and number of divisions on the circular scale is reduced by 50% , the new least count will be _____ ×10−3 mm

Q49.Two iron solid discs of negligible thickness have radii R1 and R2 and moment of intertia I1 and I2 , respectively. For R2 = 2R1 , the ratio of I1 and I2 would be 1/x, where x = ________ -

Q49.An ideal gas initially at 0∘C temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is 3/2, the change in temperature due to the thermodynamic process is _____ K.

Q50.The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in similar way, is n times higher than the moment of inertia of the given ring. Here, $\mathrm{n}=_________ Consider all the bodies have equal masses.

Q50.The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of 7 × 106 Pa, would be ____ mm3 . (Given bulk modulus of copper = 1.4 × 1011 N m−2 )

Q50.Two long parallel wires X and Y , separated by a distance of 6 cm , carry currents of 5A and 4A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance 2025 (22 Jan Shift 2) JEE Main Previous Year Paper of 4 cm from wire Y is x × 10−5 T. The value of x is__________ . Take permeability of free space as μ0 = 4π × 10−7SI units.

Q50.A wire of resistance 9Ω is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be _____ ohm.

Q50.The maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer at rest on the river bank, is _______ cm. (Take g = 10 m/s2 )

Q50.Acceleration due to gravity on the surface of earth is ' g '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is … … g.

Q50.At steady state the charge on the capacitor, as shown in the circuit below, is μC.

Q50.A physical quantity Q is related to four observables a, b, c, d as follows : Q = ab4cd where, a = (60 ± 3)Pa; b = (20 ± 0.1)m; c = (40 ± 0.2)Nsm−2 and d = (50 ± 0.1)m , then the percentage error in Q is x , where x = ________ . 1000

Q50.A particle is projected at an angle of 30∘ from horizontal at a speed of 60 m/s. The height traversed by the particle in the first second is h0 and height traversed in the last second, before it reaches the maximum height, is h1 . The ratio h0 : h1 is _________ [Take, g = 10 m/s2 ]

Q61.Given below are two statements about X-ray spectra of elements : Statement (I) : A plot of √v ( v = frequency of X -rays emitted) vs atomic mass is a straight line. Statement (II) : A plot of v(v = frequency of X -rays emitted) vs atomic number is a straight line. 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 false but Statement II is true (3) Both Statement I and Statement II are false (4) Statement I is true but Statement II is false

Q62.If a0 is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength (λ) of the electron present in the second orbit of hydrogen atom? [n : any integer] (1) 8πa0 (2) 2a0 n nπ (3) 4n (4) 4πa0 πa0 n

Q67. An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path A →B →C →D →A as shown in the three cases above. Choose the correct option regarding ΔU : (1) ΔU( Case-I ) = ΔU( Case-II ) = ΔU( Case-III (2) ΔU( Case-I ) > ΔU( Case-III ) > ΔU( Case-II ) ) (3) ΔU( Case-III ) > ΔU( Case-II ) > ΔU( Case-I (4) ΔU( Case-I ) > ΔU( Case-II ) > ΔU( Case-III ) )

Q68.Heat treatment of muscular pain involves radiation of wavelength of about 900 nm . Which spectral line of H atom is suitable for this? Given : Rydberg constant RH = 105 cm−1, h = 6.6 × 10−34 J s, c = 3 × 108 m/s ) (1) Balmer series, ∞→2 (2) Lyman series, ∞→1 (3) Paschen series, ∞→3 (4) Paschen series, 5 →3

Q68.Ice and water are placed in a closed container at a pressure of 1 atm and temperature 273.15 K . If pressure of the system is increased 2 times, keeping temperature constant, then identify correct observation from following (1) Volume of system increases . (2) The solid phase (ice) disappears completely. (3) Liquid phase disappears completely. (4) The amount of ice decreases.

Q1. If the percentage errors in measuring the length and the diameter of a wire are 0 . 1% each. The percentage error in measuring its resistance will be: (1) 0 . 2% (2) 0 . 3% (3) 0 . 1% (4) 0 . 144% Q2. 1 𝑏2 A force is represented by 𝐹= 𝑎𝑥2 + 𝑏𝑡 2, where 𝑥= distance and 𝑡= time. The dimensions of are : 𝑎 (1) [𝑀𝐿3 𝑇 – 3 ] (2) [𝑀𝐿𝑇– 2] (3) [𝑀𝐿– 1 𝑇– 1] (4) [𝑀𝐿2 𝑇– 3]

Q1. In an expression a × 10b ; (1) b is order of magnitude for a ≥5 (2) b is order of magnitude for a ≤5 (3) a is order of magnitude for b ≤5 (4) b is order of magnitude for 5 < a ≤10

Q1. A physical quantity Q is found to depend on quantities a, b, c by the relation Q = a4b3 . The percentage error in c2 a, b and c are 3%, 4% and 5% respectively. Then, the percentage error in Q is: (1) 66% (2) 43% (3) 34% (4) 14%

Q1. If mass is written as 𝑚= 𝑘𝑐𝑃𝐺-1 / 2 ℎ1 / 2, then the value of 𝑃 will be : (Constants have their usual meaning with 𝑘 a dimensionless constant) 1 1 (1) (2) 2 3 (3) 2 (4) -1 3

Q1. Match List-I with List-II. List-I List-II A. Coefficient of viscosity I. [ML2 T−2] B. Surface Tension II. [ML2 T−1] C. Angular momentum III. [ML−1 T−1] D. Rotational kinetic energy IV. [ML0 T−2] (1) A-II, B-I, C-IV, D-III (2) A-I, B-II, C-III, D-IV (3) A-III, B-IV, C-II, D-I (4) A-IV, B-III, C-II, D-I

Q1. If two vectors →𝐴 and →𝐵 having equal magnitude 𝑅 are inclined at an angle 𝜃, then 𝜃 2𝑅sin (1) →𝐴− →𝐵= √2𝑅sin 𝜃2 (2) →𝐴+ →𝐵= 2 → → 𝜃 → → 𝜃 (3) 𝐴+ 𝐵= 2𝑅cos (4) 𝐴− 𝐵= 2𝑅cos 2 2

Q1. The dimensional formula of latent heat is : (1) [ML2 T−2] (2) [M0 L2 T−2] (3) [MLT−2] (4) [M∘LT−2]