Practice Questions

Q88.The vertices B and C of a ΔABC lie on the line, x+2 3 = y−10 = 4z such that BC = 5 units. Then the area (in sq. units) of this triangle, given the point A(1, −1, 2), is (1) 6 (2) 2√34 (3) √34 (4) 5√17

Q88.The plane containing the line x−3 2 = y+2−1 = z−13 and also containing its projection on the plane 2x + 3y −z = 5 , contains which one of the following points? (1) (2,2,0) (2) (-2,2,2) (3) (0,-2,2) (4) (2,0,-2)

Q89.The equation of the line passing through -4, 3, 1, parallel to the plane 𝑥+ 2𝑦- 𝑧- 5 = 0 and intersecting the 𝑥 + 1 𝑦- 3 𝑧- 2 line = = is -3 2 -1 𝑥+ 4 𝑦- 3 𝑧- 1 𝑥+ 4 𝑦- 3 𝑧- 1 (1) = = (2) = = 3 -1 1 1 1 3 (3) 𝑥+ 4 = 𝑦- 3 = 𝑧- 1 (4) 𝑥- 4 = 𝑦+ 3 = 𝑧+ 1 -1 1 1 2 1 4

Q89.The equation of the plane containing the straight line x 2 = 3y = 4z and perpendicular to the plane containing the straight lines x 3 = 4y = 2z and x4 = 2y = 3z is: (1) 3x + 2y −3z = 0 (2) x + 2y −2z = 0 (3) x −2y + z = 0 (4) 5x + 2y −4z = 0

Q89.Let S = {1, 2, … . . , 20}. A subset B of S is said to be "nice", if the sum of the elements of B is 203 . Than the probability that a randomly chosen subset of S is "nice" is : JEE Main 2019 (11 Jan Shift 2) JEE Main Previous Year Paper (1) 7 (2) 5 220 220 (3) 4 (4) None of the above 220

Q90.Assume that each born child is equally likely to be a boy or girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is: (1) 1 (2) 1 12 10 (3) 1 (4) 1 11 17 JEE Main 2019 (10 Apr Shift 1) JEE Main Previous Year Paper

Q90.In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to : (1) 150 (2) 175 65 65 (3) 225 (4) 200 65 65 JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper

Q63.The set of all α ∈R, for which w = 1+(1−8α)z1−z is a purely imaginary number, for all and Re(z) ≠1 , is : (1) {0} (2) {0, 14 , −14 } (3) equal to R (4) an empty set

Q66.If n is the degree of the polynomial, 1 8 1 8 + [ √5x3 + 1 −√5x3 −1 ] [ √5x3 + 1 + √5x3 −1 ] and m is the coefficient of xn in it, then the ordered pair (n, m) is equal to (1) (12, (20)4) (2) (8, 5(10)4) (3) (24, (10)8) (4) (12, 8(10)4) JEE Main 2018 (15 Apr Shift 1 Online) JEE Main Previous Year Paper

Q67.If n is the degree of the polynomial, 8 8 m is the coefficient of xn + [ √5x3+1−√5x3−12 ] [ √5x3+1+√5x3−12 ] and in it, then the ordered pair (n, m) is equal to (1) (8, 5(10)4) (2) (12, 8(10)4) (3) (12, (20)4) (4) (24, (10)8)

Q69.Two parabolas with a common vertex and with axes along the x-axis and y-axis respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3 , then the equation of the common tangent to the two parabolas is : (1) 3(x + y) + 4 = 0 (2) 8(2x + y) + 3 = 0 (3) x + 2y + 3 = 0 (4) 4(x + y) + 3 = 0 JEE Main 2018 (15 Apr) JEE Main Previous Year Paper cos θ, √3 sin

Q69.The sides of a rhombus ABCD are parallel to the lines, x −y + 2 = 0 and 7x −y + 3 = 0. If the diagonals of the rhombus intersect at P(1, 2) and the vertex A (different from the origin) is on the y axis, then the ordinate of A is (1) 2 (2) 7 4 (3) 7 (4) 5 2 2

Q70.If β is one of the angles between the normals to the ellipse x2 + 3y2 = 9 at the points (3 θ) and θ ∈(0, π2 ); then 2sincot2θβ is equal to : (−3 sin θ, √3 cos θ); (1) 1 (2) √3 √3 4 (3) 2 (4) √2 √3

Q70.Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the parabola at A & B, respectively. If C is the center of the circle through the points P, A & B and ∠CPB = θ, then a value of tan θ is: (1) 4 (2) 1 3 2 (3) 2 (4) 3

Q70.Let P be a point on the parabola x2 = 4y. If the distance of P from the center of the circle x2 + y2 + 6x + 8 = 0 is minimum, then the equation of the tangent to the parabola at P is (1) x + y + 1 = 0 (2) x + 4y −2 = 0 (3) x + 2y = 0 (4) x −y + 3 = 0

Q70.Two parabolas with a common vertex and with axes along x-axis and y-axis, respectively, intersect each other in the first quadrant. if the length of the latus rectum of each parabola is 3 , then the equation of the common tangent to the two parabolas is? (1) 3(x + y) + 4 = 0 (2) 8(2x + y) + 3 = 0 (3) 4(x + y) + 3 = 0 (4) x + 2y + 3 = 0

Q71.If β is one of the angles between the normals to the ellipse, x2 + 3y2 = 9 at the points (3 cos θ, √3 sin θ) and (−3 sin θ, √3 cos θ); ∈(0, π2 ); then 2sincot2θβ is equal to (1) √2 (2) 2 √3 (3) 1 (4) √3 √3 4

Q72.A normal to the hyperbola, 4x2 −9y2 = 36 meets the co-ordinate axes x and y at A and B, respectively. If the parallelogram OABP(O being the origin) is formed, then the locus of P is (1) 4x2 −9y2 = 121 (2) 4x2 + 9y2 = 121 (3) 9x2 −4y2 = 169 (4) 9x2 + 4y2 = 169

Q72.If the tangents drawn to the hyperbola 4y2 = x2+ 1 intersect the co-ordinate axes at the distinct points A and B, then the locus of the mid point of AB is (1) x2 −4y2 + 16x2y2 = 0 (2) 4x2 −y2 + 16x2y2 = 0 (3) 4x2 −y2 −16x2y2 = 0 (4) x2 −4y2 −16x2y2 = 0

Q75.In a triangle ABC , coordinates of A are (1, 2) and the equations of the medians through B and C are respectively, x + y = 5 and x = 4 . Then area of ΔABC (in sq. units) is : (1) 12 (2) 4 (3) 9 (4) 5

Q77.Let A be a matrix such that A . [10 23 ] (1) [40 −3236 ] (2) [−324 360 ] (3) [−3236 04] (4) [360 −324 ]

Q80.Let S = {(λ, μ) ∈R × R : f(t) = (|λ |e|t| −μ) sin(2|t|), t ∈R is a differential function}. Then, S is a subset of : (1) (−∞, 0) × R (2) R × [0 , ∞) (3) [0 , ∞) × R (4) R × (−∞, 0)

Q82.Let f(x) be a polynomial of degree 4 having extreme values at x = 1 and x = 2. If limx→0 f(x)x2 + = 3 ( 1) then f(−1) is equal to (1) 1 (2) 3 2 2 (3) 5 (4) 9 2 2

Q82.If a right circularcone having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2 ) of this cone is (1) 8√3π (2) 6√2π (3) 6√3π (4) 8√2π

Q82.If ∫ 1+tantanx+tan2x x dx = x − √AK tan−1( K tan√Ax+1 ) (K, A) is equal to (1) (2, 1) (2) (2, 3) (3) (−2, 1) (4) (−2, 3) x −sin t)dt, then