Practice Questions

Q68.A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q . If O is the origin and the rectangle OPRQ is completed, then the locus of R is: (1) 3x + 2y = 6xy (2) 3x + 2y = 6 (3) 2x + 3y = xy (4) 3x + 2y = xy

Q68.The locus of the point of intersection of the lines √2x −y + 4√2k = 0 and √2kx + ky −4√2 = 0 ( k is any non-zero real parameter) is (1) an ellipse whose eccentricity is 1 √3 (2) a hyperbola whose eccentricity is √3 (3) a hyperbola with length of its transverse axis 8√2 (4) an ellipse with length of its major axis 8√2 JEE Main 2018 (16 Apr Online) JEE Main Previous Year Paper

Q68.The foot of the perpendicular drawn from the origin, on the line, 3x + y = λ(λ ≠0) is P . If the line meets x- axis at A and y-axis at B, then the ratio BP : PA is (1) 9 : 1 (2) 1 : 3 (3) 1 : 9 (4) 3 : 1

Q68.In a triangle ABC , coordianates of A are (1, 2) and the equations of the medians through B and C are x + y = 5 and x = 4 respectively. Then area of △ABC (in sq. units) is (1) 5 (2) 9 (3) 12 (4) 4

Q69.A circle passes through the points (2, 3) and (4 , 5). If its centre lies on the line, y −4x + 3 = 0, then its radius is equal to (1) √5 (2) 1 (3) √2 (4) 2

Q69.If the tangent at (1, 7) to the curve x2 = y −6 touch the circle x2 + y2 + 16x + 12y + c = 0 then the value of c is: (1) 95 (2) 195 (3) 185 (4) 85

Q69.If a circle C , whose radius is 3, touches externally the circle x2 + y2 + 2x −4y −4 = 0 at the point (2, 2), then the length of the intercept cut by this circle C on the x-axis is equal to (1) 2√3 (2) √5 (3) 3√2 (4) 2√5

Q70.The tangent to the circle C1 : x2 + y2 −2x −1 = 0 at the point (2, 1) cuts off a chord of length 4 from a circle C2 whose centre is (3, −2). The radius of C2 is (1) √6 (2) 2 (3) √2 (4) 3

Q71.Two sets A and B are as under: A = {(a, b) ∈R × R : |a −5| < 1 and |b −5| < 1}; Then : B = {(a, b) ∈R × R : 4(a −6)2 + 9(b −5)2 ≤36}. (1) neither A ⊂B nor B ⊂A (2) B ⊂A (3) A ⊂B (4) A ∩B = ϕ (an empty set)

Q71.Tangents drawn from the point (−8, 0) to the parabola y2 = 8x touch the parabola at P and Q. If F is the focus of the parabola, then the area of the triangle PFQ (in sq. units) is equal to (1) 48 (2) 32 (3) 24 (4) 64 JEE Main 2018 (15 Apr Shift 2 Online) JEE Main Previous Year Paper

Q71.If the tangent drawn to the hyperbola 4y2 = x2 + 1 intersect the co-ordinates axes at the distinct points A and B, then the locus of the midpoint of AB is : (1) x2 −4y2 + 16x2y2 = 0 (2) 4x2 −y2 + 16x2y2 = 0 (3) x2 −4y2 −16x2y2 = 0 (4) 4x2 −y2 −16x2y2 = 0

Q71.If the length of the latus rectum of an ellipse is 4 units and the distance between a focus and its nearest vertex on the major axis is 3 units, then its eccentricity is 2 (1) 2 (2) 1 3 2 (3) 1 (4) 1 9 3

Q72. (27+x) 31 −3 lim 2 equals x→0 9−(27+x) 3 (1) −16 (2) 61 (3) 3 1 (4) −13

Q72.If (p ∧~q) ∧(p ∧r) →~p ∨q is false, then the truth values of p, q and r are respectively (1) T, T, T (2) F, T, F (3) T, F, T (4) F, F, F

Q72.Tangents are drawn to the hyperbola 4x2 −y2 = 36 at the points P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of ΔPTQ is: (1) 36√5 (2) 45√5 (3) 54√3 (4) 60√3

Q73.For each t ∈R, let [t] be the greatest integer less than or equal to t. Then lim x([ x1 ] + [ x2 ] + … + [ 15x ]) x→0+ (1) does not exist (in R) (2) is equal to 0 (3) is equal to 15 (4) is equal to 120

Q73.If (p∧∼q) ∧(p ∧r) →∼p ∨q is false, then the truth values of p, q and r are respectively (1) F, T, F (2) T, F, T (3) F, F, F (4) T, T, T

Q73. limx→0 x tan(1−cos2x−2x2x)2tan x equals. (1) 1 (2) −12 (3) 1 (4) 1 4 2

Q74.If the mean of the data: 7, 8, 9, 7, 8, 7, λ, 8 is 8 , then the variance of this data is (1) 9 (2) 2 8 (3) 7 (4) 1 8

Q74.An aeroplane flying at a constant speed, parallel to the horizontal ground, √3 km above it is observed at an elevation of 60° from a point on the ground. If after five seconds, its elevation from the same point is 30° , then the speed (in km / hr) of the aeroplane is (1) 720 (2) 1500 (3) 750 (4) 1440

Q74.The mean and the standard deviation (S. D. ) of five observations are 9 and 0, respectively. If one of the observation is increased such that the mean of the new set of five observations becomes 10, then their S. D. is (1) 0 (2) 2 (3) 4 (4) 1

Q75.A tower T1 of height 60 m is located exactly opposite to a tower T2 of height 80 m on a straight road. From the top of T1 , if the angle of depression of the foot of T2 is twice the angle of elevation of the top of T2 , then the width (in m ) of the road between the feet of the towers T1 and T2 is (1) 20√2 (2) 10√2 (3) 10√3 (4) 20√3

Q75.An aeroplane flying at a constant speed, parallel to the horizontal ground, √3 km above it, is observed at an elevation of 60∘ from a point on the ground. If, after five seconds, its elevation from the same point, is 30∘ , then the speed (in km/hr ) of the aeroplane is (1) 1500 (2) 750 (3) 720 (4) 1440 JEE Main 2018 (15 Apr Shift 1 Online) JEE Main Previous Year Paper

Q75.A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min for the angle of depression of the car to change from 30° to 45°, then the time taken (in min) by the car to reach the foot of the tower is (1) 9 + 2 (√3 −1) (2) 18(1 √3) + (3) 18(√3 −1) (4) 9(1 √3)

Q76.Consider the following two binary relations on the set A = {a, b, c} : R1 = {(c, a)(b, b), (a, c), (c, c), (b, c), (a, a)} and R2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c). Then (1) R2 is symmetric but it is not transitive (2) Both R1 and R2 are transitive (3) Both R1 and R2 are not symmetric (4) R1 is not symmetric but it is transitive is a scalar matrix and |3A| = 108 . Then A2 equals