Practice Questions

Q89.Let →𝑎= 2 ^𝑖- ^𝑗+ 2 ^𝑘 and →𝑏= ^𝑖+ 2 ^𝑗- ^𝑘. Let a vector →𝑣 be in the plane containing →𝑎 and →𝑏. If →𝑣 is 2 is equal to _____. perpendicular to the vector 3 ^𝑖+ 2 ^𝑗- ^𝑘 and its projection on →𝑎 is 19 units, then |2→𝑣|

Q89.Let →cbe a vector perpendicular to the vectors →a = ˆi + ˆj −ˆk and b = ˆi + 2ˆj + ˆk. If →c⋅(ˆi + ˆj + 3ˆk) → is equal to × the value of →c⋅(→a b)

Q89.If the line 𝑦= 𝑚𝑥 bisects the area enclosed by the lines 𝑥= 0, 𝑦= 0, 𝑥= and the curve 2 𝑦= 1 + 4𝑥- 𝑥2, then 12𝑚 is equal to .

Q89.Let f : R →R be a continuous function such that f(x) + f(x + 1) = 2 for all x ∈R . If I1 = ∫80 f(x)dx and I2 = ∫3−1 f(x)dx , then the value of I1 + 2I2 is equal to ________.

Q89.Let →a = ˆi + αˆj + 3ˆk and →b = 3ˆi −αˆj + ˆk. If the area of the parallelogram whose adjacent sides are represented → → by the vectors →a and b is 8√3 square units, then →a⋅ b is equal to ___ .

Q89.If the equation of the plane passing through the line of intersection of the planes 2x −7y + 4z −3 = 0, 3x −5y + 4z + 11 = 0 and the point (−2, 1, 3) is ax + by + cz −7 = 0, then the value of 2a + b + c −7 is _________.

Q90.Let the curve y = y(x) be the solution of the differential equation, dxdy = 2(x + 1). If the numerical value of area bounded by the curve y = y(x) and x-axis is 4√83 , then the value of y(1) is equal to ________. JEE Main 2021 (16 Mar Shift 1) 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 →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.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 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.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.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 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.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 →a = ˆi + 2ˆj −ˆk, b = ˆi −ˆj and →c= ˆi −ˆj −ˆk be three given vectors. If →ris a vector such that →r×→a =→c×→a → and →r⋅ b = 0, then →r⋅→a is equal to JEE Main 2021 (25 Feb Shift 1) 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.An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0. 9 and that of the second unit is 0. 8. The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is p, then 98p is equal to JEE Main 2021 (31 Aug Shift 1) 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

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 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. 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. 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