Practice Questions

Q81.Let S = {z ∈C : z2 + z = 0}. Then ∑z∈S(Re (z)+ Im (z)) is equal to _______.

Q82.A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168 , then b + 3g is equal to

Q90.The sum and product of the mean and variance of a binomial distribution are 82 . 5 and 1350 respectively. They the number of trials in the binomial distribution is JEE Main 2022 (29 Jul Shift 2) JEE Main Previous Year Paper

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. 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. 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

Q2. An object of mass 𝑚 is being moved with a constant velocity under the action of an applied force of 2 N along a frictionless surface with following surface profile. The correct applied force vs distance graph will be : (1) (2) (3) (4)

Q2. A mosquito is moving with a velocity →v= 0. 5t2ˆi + 3tˆj + 9ˆk m s−1 and accelerating in uniform conditions. What will be the direction of mosquitoes after 2 s ? y-axis (1) tan−1( 23 ) from x-axis (2) tan−1( √856 ) from (3) tan−1( 25 ) from y-axis (4) tan−1( 52 ) from x-axis

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, 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) h (Planck's constant) (i) [MLT−1] (b) E (kinetic energy) (ii) [ML2 T−1] (c) V (electric potential) (iii) [ML2 T−2] (d) P (linear momentum) (iv) [ML2 I−1 T−3] Choose the correct answer from the options given below: (1) (a) →(ii), (b) →(iii), (c) →(iv), (d) →(i) (2) (a) →(i), (b) →(ii), (c) →(iv), (d) →(iii) (3) (a) →(iii), (b) →(ii), (c) →(iv), (d) →(i) (4) (a) →(iii), (b) →(iv), (c) →(ii), (d) →(i)

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

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. The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by : (1) (2) (3) (4)

Q3. The ranges and heights for two projectiles projected with the same initial velocity at angles 42° and 48° with the horizontal are 𝑅1, 𝑅2 and 𝐻1, 𝐻2 respectively. Choose the correct option: (1) 𝑅1 = 𝑅2 and 𝐻1 = 𝐻2 (2) 𝑅1 = 𝑅2 and 𝐻1 < 𝐻2 (3) 𝑅1 > 𝑅2 and 𝐻1 = 𝐻2 (4) 𝑅1 < 𝑅2 and 𝐻1 < 𝐻2 JEE Main 2021 (01 Sep Shift 2) JEE Main Previous Year Paper

Q3. Which of the following is not a dimensionless quantity? (1) Power factor (2) Quality factor (3) Permeability of free space (μ0) (4) Relative magnetic permeability (μr)

Q3. If velocity 𝑉 time 𝑇 and force 𝐹 are chosen as the base quantities, the dimensions of the mass will be : (1) 𝐹𝑉𝑇-1 (2) 𝐹𝑇-1𝑉-1 (3) 𝐹𝑇2 𝑉 (4) 𝐹𝑇𝑉-1

Q3. A boy is rolling a 0. 5 kg ball on the frictionless floor with the speed of 20 m s−1. The ball gets deflected by an obstacle on the way. After deflection it moves with 5% of its initial kinetic energy. What is the speed of the ball now? (1) 19. 0 m s−1 (2) 4. 4 m s−1 (3) 14. 41 m s−1 (4) 1. 00 m s−1 →

Q4. A player kicks a football with an initial speed of 25 m s−1 at an angle of 45° from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion? (Take g = 10 m s−2 ) (1) hmax = 15. 625 m, T = 1. 77 s (2) hmax = 3. 54 m, T = 0. 125 s (3) hmax = 10 m, T = 2. 5 s (4) hmax = 15. 625 m, T = 3. 54 s

Q4. The maximum and minimum distances of a comet from the Sun are 1. 6 × 1012 m and 8. 0 × 1010 m respectively. If the speed of the comet at the nearest point is 6 × 104 m s−1 , the speed at the farthest point is (1) 1. 5 × 103 m s−1 (2) 6. 6 × 103 m s−1 (3) 3. 0 × 103 m s−1 (4) 4. 5 × 103 m s−1

Q4. A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time t1. If he remains stationary on a moving escalator then the escalator takes him up in time t2. The time taken by him to walk up on the moving escalator will be: (1) t1t2 (2) t1+t2 t2−t1 2 (3) t1t2 (4) t2 −t1 t2+t1

Q4. List- I List- II (a) MI of the rod (length L, Mass M, about an axis ⊥ to the rod passing (i) through the midpoint) 8ML2 3 (b) MI of the rod (length L, Mass 2M, about an axis ⊥ to the rod ML2 (ii) 3 passing through one of its end) (c) MI of the rod (length 2L, Mass M, about an axis ⊥ to the rod (iii) passing through its midpoint) ML2 12 (d) MI of the rod (Length 2L, Mass 2M, about an axis ⊥ to the rod (iv) passing through one of its end) 2ML2 3 Choose the correct answer from the options given below: JEE Main 2021 (27 Jul Shift 1) JEE Main Previous Year Paper (1) (a) −(ii), (b) −(iii), (c) −(i), (d) −(iv) (2) (a) −(ii), (b) −(i), (c) − (iii), (d) −(iv) (3) (a) −(iii), (b) −(iv), (c) − (ii), (d) −(i) (4) (a) − (iii), (b) −(iv), (c) −(i), (d) −(ii)

Q4. A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the work done by the porter in lowering the suitcase. (take g = 9. 8 ms−2 ) (1) −62720. 0 J (2) −627. 2 J (3) +627. 2 J (4) 784. 0 J

Q4. Consider two satellites 𝑆1 and 𝑆2 with periods of revolution 1hr and 8hr respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite 𝑆1 to the angular velocity of satellite 𝑆2 is: (1) 8: 1 (2) 2: 1 (3) 1: 4 (4) 1: 8