Practice Questions

Q68.If the truth value of the statement (P ∧(~R)) →((~R) ∧Q) is F , then the truth value of which of the following is F ? (1) P ∨Q →~R (2) R ∨Q →~P (3) ~(P ∨Q) →~R (4) ~(R ∨Q) →~P

Q69.The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y where x < y are 6 and 49 respectively. Then x4 + y2 is equal to (1) 320 (2) 420 (3) 162 (4) 674

Q69.Negation of the Boolean statement (p ∨q) ⇒((~r) ∨p) is equivalent to: (1) p ∧(~q) ∧r (2) (~p) ∧(~q) ∧r (3) (~p) ∧q ∧r (4) p ∧q ∧(~r)

Q69.Which of the following matrices can NOT be obtained from the matrix -1 2 by a single elementary row 1 -1 operation? (1) 0 1 (2) 1 -1 1 -1 -1 2 (3) -1 2 (4) -1 2 -2 7 -1 3

Q72.The value of tan-1cos15𝜋 is equal to sin𝜋 4 𝜋 𝜋 (1) - (2) - 4 8 (3) -5𝜋 (4) -4𝜋 12 9

Q74.The value of the integral ∫2−2 (ex|x|+1)x3+x (1) 5e2 (2) 3e−2 (3) 4 (4) 6 dy ax−by+a

Q75.The odd natural number a, such that the area of the region bounded by y = 1, y = 3, x = 0, x = ya is 3643 , equal to: (1) 3 (2) 5 (3) 7 (4) 9

Q80.A random variable X has the following probability distribution: X 0 1 2 3 4 P(X) k 2k 4k 6k 8k The value of P( 1<x<4x≤2 )is equal to (1) 4 (2) 2 7 3 (3) 3 (4) 4 7 5 ¯

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) →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

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)

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. 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. 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

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. 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. 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]

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. 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. 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 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. 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)