Practice Questions

Q90.If the distance of the point (1, −2, 3) from the plane x + 2y −3z + 10 = 0 measured parallel to the line, x−1 , then the value of |m| is equal to _______. 3 = 2−ym = z+31 is √72 JEE Main 2021 (16 Mar Shift 2) JEE Main Previous Year Paper

Q90.Let λ be an integer. If the shortest distance between the lines x −λ = 2y −1 = −2z and x = y + 2λ = z −λ is √7 , then the value of |λ| is _______. 2√2 JEE Main 2021 (24 Feb Shift 2) JEE Main Previous Year Paper

Q90.A fair coin is tossed n− times such that the probability of getting at least one head is at least 0. 9. Then the minimum value of n is _______. JEE Main 2021 (25 Jul Shift 2) JEE Main Previous Year Paper

Q90.If the shortest distance between the lines r1 = αˆi + 2ˆj + 2ˆk + λ(ˆi −2ˆj 2ˆk), → μ ∈R is 9, then α is equal to_____. r2 = −4ˆi −ˆk + μ(3ˆi −2ˆj −2ˆk), JEE Main 2021 (20 Jul Shift 1) JEE Main Previous Year Paper

Q90.Let →𝑝= 2 ^i + 3 ^j + ^k and →𝑞= ^i + 2 ^j + ^k be two vectors. If a vector →𝑟= 𝛼 ^i + 𝛽 ^j + 𝛾 ^k is perpendicular to each of the vectors ( →𝑝+ →𝑞) and ( →𝑝- →𝑞), and | →𝑟| = √3, then |𝛼| + | 𝛽| + | 𝛾| is equal to JEE Main 2021 (25 Jul Shift 1) JEE Main Previous Year Paper

Q90.Let →a = ˆi + 5ˆj + αˆk, b = ˆi + 3ˆj + βˆk and →c= −ˆi + 2ˆj −3ˆk be three vectors such that, b ×→c = 5√3 and →a → 2 is ________. is perpendicular to b. Then the greatest amongst the values of →a JEE Main 2021 (27 Aug Shift 1) JEE Main Previous Year Paper

Q90.Let P be a plane containing the line x−1 3 = 4 = z+52 and parallel to the line x−34 = y−2−3 = z+57 . If the point (1, −1, α) lies on the plane P , then the value of |5α| is equal to ___ . JEE Main 2021 (18 Mar Shift 2) JEE Main Previous Year Paper

Q90.A line l passing through origin is perpendicular to the lines l1 :→r= (3 + t)ˆi + (−1 + 2t)ˆj + (4 + 2t)ˆk l2 :→r= (3 + 2s)ˆi + (3 + 2s)ˆj + (2 + s)ˆk If the co-ordinates of the point in the first octant on l2 at a distance of √17 from the point of intersection of l and l1 are (a, b, c), then 18(a + b + c) is equal to ___ . JEE Main 2021 (25 Feb Shift 2) JEE Main Previous Year Paper

Q90.Let a plane P pass through the point (3, 7, −7) and contain the line, x−2−3 = y−32 = z+21 . If distance of the plane P from the origin is d, then d2 is equal to JEE Main 2021 (27 Jul Shift 1) JEE Main Previous Year Paper

Q90.Let Q be the foot of the perpendicular from the point P(7, −2, 13) on the plane containing the lines y−1 x+1 6 = 7 = z−38 and x−13 = y−25 = z−37 Then (PQ)2, is equal to ______. JEE Main 2021 (26 Aug Shift 2) JEE Main Previous Year Paper

Q90.The equation of the planes parallel to the plane x −2y + 2z −3 = 0 which are at unit distance from the point (1, 2, 3) is ax + by + cz + d = 0. If (b −d) = K(c −a), then the positive value of K is JEE Main 2021 (18 Mar Shift 1) JEE Main Previous Year Paper

Q90.The probability distribution of random variable X is given by: X 1 2 3 4 5 P(X) K 2K 2K 3K K Let p = P(1 < X < 4 ∣X < 3). If 5p = λK , then λ is equal to JEE Main 2021 (27 Aug Shift 2) JEE Main Previous Year Paper

Q90.For p > 0, a vector →v2 = 2ˆi + (p + 1)ˆj is obtained by rotating the vector →v1 = √3pˆi + ˆj by an angle θ about (α√3−2) origin in counter clockwise direction. If tan θ = , then the value of α is equal to (4√3+3) JEE Main 2021 (20 Jul Shift 2) JEE Main Previous Year Paper

Q90.Let 𝑋 be a random variable with distribution. 𝑥 -2 -1 3 4 6 1 1 1 𝑃( 𝑋= 𝑥) 𝑎 𝑏 5 3 5 If the mean of 𝑋 is 2 . 3 and variance of 𝑋 is 𝜎2, then 100𝜎2 is equal to : JEE Main 2021 (01 Sep Shift 2) JEE Main Previous Year Paper

Q90.Let (λ, 2, 1) be a point on the plane which passes through the point (4, −2, 2). If the plane is perpendicular to the line joining the points (−2, −21, 29) and (−1, −16, 23), then ( 11λ ) 2 −4λ11 −4 is equal to ________. JEE Main 2021 (26 Feb Shift 1) JEE Main Previous Year Paper

Q90.Let P be an arbitrary point having sum of the squares of the distance from the planes x + y + z = 0, lx −nz = 0 and x −2y + z = 0 equal to 9 units. If the locus of the point P is x2 + y2 + z2 = 9, then the value of l −n is equal to JEE Main 2021 (17 Mar Shift 2) JEE Main Previous Year Paper

Q90.Let 𝐵𝑖𝑖= 1, 2, 3 be three independent events in a sample space. The probability that only 𝐵1 occur is 𝛼, only 𝐵2 occurs is 𝛽 and only 𝐵3 occurs is 𝛾. Let 𝑝 be the probability that none of the events 𝐵𝑖 occurs and these 4 probabilities satisfy the equations 𝛼- 2𝛽𝑝= 𝛼𝛽 and 𝛽- 3𝛾𝑝= 2𝛽𝛾 (All the probabilities are assumed to lie in 𝑃𝐵1 the interval 0, 1 Then is equal to______. 𝑃𝐵3 JEE Main 2021 (24 Feb Shift 1) JEE Main Previous Year Paper

Q90.The distance of the point P(3, 4, 4) from the point of intersection of the line joining the points Q(3, −4, −5) and R(2, −3, 1) and the plane 2x + y + z = 7, is equal to _____. JEE Main 2021 (27 Jul Shift 2) JEE Main Previous Year Paper

Q90.Let the line L be the projection of the line x−1 2 = y−31 = z−42 in the plane x −2y −z = 3. If d is the distance of the point (0, 0, 6) from L, then d2 is equal to JEE Main 2021 (26 Aug Shift 1) JEE Main Previous Year Paper

Q1. For the four sets of three measured physical quantities as given below. Which of the following options is correct? (i) A1 = 24.36, B1 = 0.0724, C1 = 256.2 (ii) A2 = 24.44, B2 = 16.082, C2 = 240.2 (iii) A3 = 25.2, B3 = 19.2812, C3 = 236.183 (iv) A4 = 25, B4 = 236.191, C4 = 19.5 (1) A4 + B4 + C4 < A1 + B1 + C1 < A3 + B3 + C3 < A2 + B2 + C2 (2) A1 + B1 + C1 = A2 + B2 + C2 = A3 + B3 + C3 = A4 + B4 + C4 (3) A1 + B1 + C1 < A2 + B2 + C2 = A3 + B3 + C3 < A4 + B4 + C4 (4) A1 + B1 + C1 < A3 + B3 + C3 < A2 + B2 + C2 < A4 + B4 + C4

Q1. Given, B is magnetic field induction, and μ0 is the magnetic permeability of vacuum. The dimension of B2 is: 2μ0 (1) MLT−2 (2) ML2T−1 (3) ML2T−2 (4) ML−1T−2

Q1. where c is speed of light, G univasal gravitational constant and h is the A quantity f is given by f = √hc5G Planck’s constant. Dimension of f is that of: (1) area (2) energy (3) momentum (4) volume →

Q1. A simple pendulum is being used to determine the value of gravitational acceleration g at a certain place. The length of the pendulum is 25.0 cm and a stopwatch with 1 s resolution measures the time taken for 40 oscillations to be 50 s. The accuracy in g is: (1) 5.40% (2) 3.40% (3) 4.40% (4) 2.40%

Q1. A 60HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to : (1 HP = 746 W, g = 10 m s−2) (1) 1.7 m s−1 (2) 1.9 m s−1 (3) 1.5 m s−1 (4) 2.0 m s−1

Q1. The dimension of stopping potential V0 in photoelectric effect in units of Planck’s constant ‘ h ’, speed of light ‘ c ’ and Gravitational constant ‘ G ’ and ampere A is: (1) h 31 G 32 c 31 A−1 (2) h0c5G−1A−1 (3) h−23 c−13 G 34 A−1 (4) h2G 23 c 31 A−1