Practice Questions

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)

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.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) √2 (3) 2 (4) 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

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

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

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

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

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

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.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.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

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

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

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.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

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

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

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

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