Practice Questions

Q20.In a Vernier Caliper 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and 4th Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to 1 mm. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and 6th Vernier scale division exactly. coincides with the main scale reading. The diameter of the spherical body will be: (1) 3 . 02 cm (2) 3 . 06 cm (3) 3 . 10 cm (4) 3 . 20 cm

Q21.In an experiment of determine the Young's modulus of wire of a length exactly 1 m, the extension in the length of the wire is measured as 0. 4 mm with an uncertainty of ±0. 02 mm when a load of 1 kg is applied. The JEE Main 2022 (26 Jul Shift 1) JEE Main Previous Year Paper diameter of the wire is measured as 0. 4 mm with an uncertainty of ±0. 01 mm. The error in the measurement of Young's modulus (ΔY) is found to be x × 1010 N m−2 . The value of x is _____ .

Q25.A 220 V, 50 Hz AC source is connected to a 25 V, 5 W lamp and an additional resistance R in series (as shown in figure) to run the lamp at its peak brightness, then the value of R (in ohm) will be

Q1. If the length of the pendulum in pendulum clock increases by 0. 1% , then the error in time per day is: (1) 43. 2 s (2) 8. 64 s (3) 86. 4 s (4) 4. 32 s → → →

Q1. A wire of 1 Ω has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in resistance to the nearest integer is : (1) 12. 5% (2) 76% (3) 25% (4) 56%

Q1. A car accelerates from rest at a constant rate α for some time after which it decelerates at a constant rate β to come to rest. If the total time elapsed is t seconds, the total distance travelled is: (1) (α+β) 4αβ t2 (2) (α+β)2αβ t2 (3) 2(α+β) αβ t2 (4) 4(α+β)αβ t2

Q1. Two vectors P and Q have equal magnitudes. If the magnitude of P + Q is n times the magnitude of P − Q, → → then angle between P and Q is (1) sin−1( n−1n+1 ) (2) cos−1( n+1n−1 ) (3) sin−1( n2−1n2+1 ) (4) cos−1( n2+1n2−1 )

Q1. The velocity of a particle is v = (v0 + gt + Ft2) m s−1 . Its position is x = 0 at t = 0 ; then its displacement after time (t = 1 s) is : (1) v0 + g + F (2) v0 + 2g + F3 (3) v0 + 2g + F (4) v0 + 2g + 3F

Q1. Match List- (I) with List- (II). List- (I) List- (II) a RH (Rydberg constant) i kg m−1 s−1 b h (Planck's constant) ii kg m2 s−1 c μB (Magnetic field energy density) iii m−1 d η (coefficient of viscosity) iv kg m−1 s−2 Choose the most appropriate answer from the options given below: (1) (a) -( iv ), (b )-( ii ), (c )-( i ), (d )-( iii) (2) (a) −(ii), (b) −(iii), (c) −(iv), (d) −(i) (3) (a) −(iii), (b) −(ii), (c) −(iv), (d) −(i) (4) (a) −(iii), (b) −(ii), (c) −(i), (d) −(iv)

Q1. What will be the projection of vector A = ˆi +ˆj + ˆk on vector B = ˆi +ˆj ? + + (1) √2(ˆi +ˆj ˆk) (2) 2(ˆi +ˆj ˆk) (3) √2(ˆi +ˆj) (4) (ˆi +ˆj)

Q1. Match List I with List II. List I List II (a) →𝐶- →𝐴- →𝐵= 0 (i) → → → (b) 𝐴- 𝐶- 𝐵= 0 (ii) (c) →𝐵- →𝐴- →𝐶= 0 (iii) (d) →𝐴+ →𝐵= - →𝐶 (iv) Choose the correct answer from the options given below: (1) (a) → ( iv ) , (b) → ( i ) , (c) → ( iii ) , (d) → (ii) (2) (a) → (iv), (b) → (iii), (c) → (i), (d) → (ii) (3) (a) → (iii), (b) → (ii), (c) → (iv), (d) → (i) (4) (a) → (i), (b) → (iv), (c) → (ii), (d) → (iii)

Q1. The time period of a simple pendulum is given by T = 2π√lg pendulum is 10 cm known to a 1 mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1s resolution. The percentage accuracy in the determination of g using this pendulum is x. The value of x to the nearest integer is:- (1) 2% (2) 3% (3) 5% (4) 4%

Q1. If A and B are two vectors satisfying the relation A ⋅→B = A × B . Then the value of A −→B will be: (1) √A2 + B2 (2) √A2 + B2 + √2AB (3) √A2 + B2 + 2AB (4) √A2 + B2 −√2AB

Q1. Which of the following equations is dimensionally incorrect? Where t =time, h =height, s =surface tension, θ =angle, ρ =density , a, r =radius, g = the acceleration due to gravity, V =volume, p =pressure, W =work done, τ =torque, ϵ =permittivity, E =electric field, J =current density, L =length. (1) W = τθ (2) V = πpa48ηL (3) h = 2 scosρrg θ (4) J = ϵ ∂E∂t

Q1. The work done by a gas molecule in an isolated system is given by, 𝑊= 𝛼𝛽2𝑒- 𝛼𝑘 𝑇, where 𝑥 is the displacement, 𝑘 is the Boltzmann constant and 𝑇 is the temperature. 𝛼 and 𝛽 are constants. Then the dimensions of 𝛽 will be: (1) M2 L T2 (2) ML2 T-2 (3) MLT-2 (4) M0 L T0

Q1. If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity hc 4πε0 has dimensions of : (1) [MLT0] (2) [M0 L0 T0] (3) [MLT−1] (4) [LC−1]

Q1. In a typical combustion engine the workdone by a gas molecule is given by W = α2βe −βx2k T , where x is the displacement, k is the Boltzmann constant and T is the temperature. If α and β are constants, dimensions of α will be: (1) [MLT−2] (2) [M2 LT−2] (3) [MLT−1] (4) [M0 LT0]

Q1. A physical quantity y is represented by the formula y = m2r−4 gxl−32 If the percentage errors found in y, m, r, l and g are 18, 1, 0. 5, 4 and p respectively, then find the value of x and p. (1) 5 and ±2 (2) 4 and ±3 (3) 16 3 and ± 23 (4) 8 and ±2

Q2. The force is given in terms of time t and displacement x by the equation F = A cos Bx + C sin Dt The dimensional formula of AD is: B (1) [M0 L T−1] (2) [ML2 T−3] (3) [M1 L1 T−2] (4) [M2 L2 T−3]

Q2. A bullet of 4 g mass is fired from a gun of mass 4 kg. If the bullet moves with the muzzle speed of 50 ms1, the impulse imparted to the gun and velocity of recoil of gun are (1) 0. 4 kg m s−1, 0. 1 m s−1 (2) 0. 2 kg m s−1, 0. 05 m s−1 (3) 0. 2 kg m s−1, 0. 1 m s−1 (4) 0. 4 kg m s−1, 0. 05 m s−1

Q2. If two similar springs each of spring constant K1 are joined in series, the new spring constant and time period would be changed by a factor: (1) 12 , 2√2 (2) 41 , √2 (3) 14 , 2√2 (4) 21 , √2

Q2. If E and H represents the intensity of electric field and magnetizing field respectively, then the unit of HE will be: (1) joule (2) ohm (3) newton (4) mho

Q2. If E, L, M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula P = EL2M −5G−2 are: (1) [M1L1 T−2] (2) [M0 L1 T0] (3) [M−1L−1T2] (4) [M0 L0 T0]

Q2. Match List - I with List - II. List - I List - II a Torque i MLT−1 b Impulse ii MT−2 c Tension iii ML2 T−2 d Surface Tension iv MLT−2 Choose the most appropriate answer from the option given below : (1) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii) (2) (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii) (3) (a)-(i), (b)-(iii), (c)-(iv), (d)-(ii) (4) (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)

Q2. A ball is thrown up with a certain velocity so that it reaches a height h. Find the ratio of the two different times of the ball reaching h in both the directions. 3 (1) √2−1 (2) 1 √2+1 3 (3) √3−√2 (4) √3−1 √3+√2 √3+1