Practice Questions

Q90.Let a line passing through the point ( - 1, 2, 3 ) intersect the lines 𝐿1: 𝑥- 1 = 𝑦- 2 = 𝑧+ 1 at 𝑀( 𝛼, 𝛽, 𝛾) and 3 2 -2 𝑥+ 2 𝑦- 2 𝑧- 1 ( 𝛼+ 𝛽+ 𝛾) 2 equals ________________. = = at 𝑁( 𝑎, 𝑏, 𝑐) . Then the value of 𝐿2: -3 -2 4 ( 𝑎+ 𝑏+ 𝑐) 2 JEE Main 2024 (30 Jan Shift 2) JEE Main Previous Year Paper

Q90.If the shortest distance between the lines x+2 2 = y+33 = z−54 and x−31 = y−2−3 = z+42 is 3√538 k , and α −√α, where [x] denotes the greatest integer function, then 6α3 is equal to________ ∫k0 [x2]dx = JEE Main 2024 (04 Apr Shift 1) JEE Main Previous Year Paper

Q90.Let O be the origin, and M and N be the points on the lines x−5 4 = y−41 = z−53 and x+812 = y+25 = z+119 −−→ → respectively such that MN is the shortest distance between the given lines. Then OM ⋅ON is equal to _________. JEE Main 2024 (29 Jan Shift 2) JEE Main Previous Year Paper

Q90.Let the line of the shortest distance between the lines 𝐿1: →𝑟= ^𝑖+ 2 ^𝑗+ 3 ^𝑘+ 𝜆 ^𝑖− ^𝑗+ ^𝑘 and 𝐿2: →𝑟= 4 ^𝑖+ 5 ^𝑗+ 6 ^𝑘+ 𝜇 ^𝑖+ ^𝑗− ^𝑘 intersect 𝐿1 and 𝐿2 at 𝑃 and 𝑄 respectively. If 𝛼, 𝛽, 𝛾 is the midpoint of the line segment 𝑃𝑄, then 2𝛼+ 𝛽+ 𝛾 is equal to___________ JEE Main 2024 (01 Feb Shift 1) JEE Main Previous Year Paper

Q90.In a tournament, a team plays 10 matches with probabilities of winning and losing each match as 1 and 2 3 3 respectively. Let x be the number of matches that the team wins, and y be the number of matches that team loses. If the probability P(|x −y| ≤ 2) is p , then 39p equals ______ JEE Main 2024 (04 Apr Shift 2) JEE Main Previous Year Paper

Q90.A line with direction ratio 2, 1, 2 meets the lines x = y + 2 = z and x + 2 = 2y = 2z respectively at the point P and Q. if the length of the perpendicular from the point (1, 2, 12) to the line PQ is l, then l2 is JEE Main 2024 (29 Jan Shift 1) JEE Main Previous Year Paper

Q90.Let a, b and c denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked 1, 2, 3, 4. If the probability that ax2 + bx + c = 0 has all real roots is mn , gcd(m, n) = 1, then m + n is equal to ________ JEE Main 2024 (09 Apr Shift 1) JEE Main Previous Year Paper

Q90.Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables X and Y respectively denote the number of blue and yellow balls. If ¯X and ¯Y are the means of X and Y respectively, then 7¯X + 4¯Y is equal to________ JEE Main 2024 (08 Apr Shift 1) JEE Main Previous Year Paper

Q90.Let →a = ^i −3^j + 7^k, b = 2^i −^j + ^k and→cbe a vector such that (→a+ 2b) ×→c= 3(→c×→a) . If →a ⋅→c = 130 , then →b ⋅→c is equal to _______ JEE Main 2024 (05 Apr Shift 1) JEE Main Previous Year Paper

Q90.A line passes through 𝐴4, −6, −2 and 𝐵16, −2, 4. The point 𝑃𝑎, 𝑏, 𝑐 where 𝑎, 𝑏, 𝑐 are non-negative integers, on the line 𝐴𝐵 lies at a distance of 21 units, from the point 𝐴. The distance between the points 𝑃𝑎, 𝑏, 𝑐 and 𝑄4, −12, 3 is equal to ______. JEE Main 2024 (31 Jan Shift 2) JEE Main Previous Year Paper

Q1. Match List I with List II List List II A Young's Modulus (Y ) I [ML–1 T –1] B Co-efficient of Viscosity (η) II [ML2 T –1] C Planck's Constant (h) III [ML–1 T –2] D Work Function (ϕ) IV [ML2 T–2] Choose the correct answer from the options given below: (1) A-II, B-III, C-IV, D-I (2) A-III, B-I, C-II, D-IV (3) A-I, B-III, C-IV, D-II (4) A-I, B-II, C-III, D-IV

Q1. Given below are two statements : Statement I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances. Statement II : Au < Parsec (Pc) < ly In the light of the above statements, choose the most appropriate answer from the options given below: (1) Both Statements I and Statements II are incorrect (2) Statements I is correct but Statements II is incorrect (3) Both Statements I and Statements II are correct (4) Statements I is incorrect but Statements II is correct

Q1. If 𝑅, 𝑋𝐿 and 𝑋𝐶 represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless: 𝑅 (1) 𝑅 𝑋𝐿 𝑋𝐶 (2) √𝑋𝐿𝑋𝑐 𝑅 𝑋𝐿 (3) (4) 𝑅 𝑋𝐿𝑋𝑐 𝑋𝑐

Q1. If P = 3ˆi + √3ˆj + 2ˆk and Q = 4ˆi + √3ˆj + 2. 5ˆk then, the unit vector in the direction of P × Q is x is x 1 (√3ˆi +ˆj −2√3ˆk). The value of

Q1. Two trains A and B of length l and 4l are travelling into a tunnel of length L in parallel tracks from opposite directions with velocities 108 km h−1 and 72 km h−1, respectively. If train A take 35 s less time than train B to cross the tunnel then, length L of tunnel is: (Given L = 60 l) (1) 1200 m (2) 900 m (3) 1800 m (4) 2700 m

Q1. In the equation 𝑋+ 𝑎 𝑏] = 𝑅𝑇, 𝑋 is pressure, 𝑌 is volume, 𝑅 is universal gas constant and 𝑇 is 𝑌2[𝑌- temperature. The physical quantity equivalent to the ratio 𝑎 is: 𝑏 (1) Pressure gradient (2) Energy (3) Impulse (4) Coefficient of viscosity

Q1. A body is moving with constant speed, in a circle of radius 10 m. The body completes one revolution in 4 s. At the end of 3rd second, the displacement of body (in m) from its starting point is: (1) 30 (2) 15 π (3) 5 π (4) 10√2

Q1. Match List I with List II List I List II A Torque I kg m–1 s–2 B Energy density II kg m s–1 C Pressure gradient III kg m–2 s–2 D Impulse IV kg m2 s–2 Choose the correct answer from the options given below : (1) A-IV, B-III, C-I, D-II (2) A-I, B-IV, C-III, D-II (3) A-IV, B-I, C-II, D-III (4) A-IV, B-I, C-III, D-II

Q1. In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5. 25 mm and apparent thickness of the glass slab at 5. 00 mm . Travelling microscope has 20 divisions in one cm on main scale and 50 divisions on Vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is x × 10−3 , where x is ______ 10

Q1. If two vectors P = ˆi + 2mˆj + mˆk and Q = 4ˆi −2ˆj + mˆk are perpendicular to each other. Then, the value of m will be (1) −1 (2) 2 (3) 3 (4) 1

Q1. A vector in x −y plane makes an angle of 30o with y -axis. The magnitude of y -component of vector is 2√3. The magnitude of x-component of the vector will be : (1) 1 (2) 6 √3 (3) 2 (4) √3

Q1. hello dummy text (1) A - III, B - I, C - II, D - IV (2) A - III, B - IV, C - I, D - II (3) A - II, B - IV, C - III, D - I (4) A - I, B - III, C - IV, D - II

Q1. Match List I with List II : List-I (Physical Quantity) List-II (Dimensional Formula) A Pressure gradient I [M0L2T−2] B Energy density II [M1L−1T−2] C Electric Field III [M1L−2T−2] D Latent heat IV [M1L1T−3A−1] Choose the correct answer from the options given below: (1) A-III, B-II, C-I, D-IV (2) A-II, B-III, C-IV, D-I (3) A-III, B-II, C-IV, D-I (4) A-II, B-III, C-I, D-IV

Q1. Electric field in a certain region is given by →𝐸= 𝐴 ^i + 𝐵 ^j. The SI unit of 𝐴 and 𝐵 are : 𝑥2 𝑦3 (1) N m3 C-1; N m2 C-1 (2) N m2 C-1; N m3 C-1 (3) N m3 C; N m2 C (4) N m2 C; N m3 C

Q1. When vector A = 2ˆi + 3ˆj + 2ˆk is subtracted from vector B, it gives a vector equal to 2ˆj. Then the magnitude of → vector B will be: (1) √5 (2) 3 (3) √6 (4) √33