Practice Questions

Q89.The area of the region S = {(x, y) : 3x2 ≤4y ≤6x + 24} is______.

Q89.Let P be a plane passing through the points (1, 0, 1), (1, −2, 1) and (0, 1, −2). Let a vector →a = αˆi + βˆj + γˆk = 2 , then be such that →a is parallel to the plane P , perpendicular to (ˆi + 2ˆj + 3ˆk) and →a⋅(ˆi + ˆj + 2ˆk) (α −β + γ)2 equals______. → + λ ∈R, α > 0 and

Q89.If the lines x−k k is _______. 1 = 2 = z−33 and x+13 = y+22 = z+31 are co-planar, then the value of

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.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 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.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.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

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.Let there be three independent events E1, E2 and E3. The probability that only E1 occurs is α only E2 occurs is β and only E3 occurs is γ. Let ′p′ denote the probability of none of events occurs that satisfies the equations (α −2β)p = αβ and (β −3γ)p = 2βγ. All the given probabilities are assumed to lie in the interval (0, 1). Then, Probability of occurrence of E1 is equal to ________. Probability of occurrence of E3 JEE Main 2021 (17 Mar Shift 1) JEE Main Previous Year Paper

Q90.Suppose the line 𝑥- 2 = 𝑦- 2 = 𝑧+ 2 lies on the plane 𝑥+ 3𝑦- 2𝑧+ 𝛽= 0 . Then ( 𝛼+ 𝛽) is equal to 𝛼 -5 2 . JEE Main 2021 (31 Aug Shift 2) 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.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.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.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.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.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 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 →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.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 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.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 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 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.If Im,n = ∫10 xm−1(1 −x)n−1dx, for m, n ⩾1, and ∫10 xm−1+xn−1(1+x)m+n ________. JEE Main 2021 (26 Feb Shift 2) JEE Main Previous Year Paper