Practice Questions

Q55.The value of ∑20r=0 50−rC6 is equal to: (1) 51C7 −30C7 (2) 50C7 −30C7 (3) 50C6 −30C6 (4) 51C7 + 30C7

Q55.If the perpendicular bisector of the line segment joining the points P(1, 4) and Q(k, 3) has y-intercept equal to −4, then a value of k is; (1) −2 (2) −4 (3) √14 (4) √15

Q55.If the common tangent to the parabolas, y2 = 4 x and x2 = 4 y also touches the circle, x2 + y2 = c2, then c is equal to : (1) 1 (2) 1 2√2 √2 (3) 41 (4) 12 P is any point on the

Q56.In the expansion of ( cosx θ + x sin1 θ )16, if l1 is the least value of the term independent of 8 ≤θ ≤π4 and l2 is the least value of the term independent of x when 16π ≤θ ≤π8 , then the ratio l2 : l1 is equal to: (1) 1 : 8 (2) 16 : 1 (3) 8 : 1 (4) 1 : 16

Q56.If the equation cos4 θ + sin4 θ + λ = 0 has real solutions for θ then λ lies in interval (1) (−54 , −1) (2) [−1, −12 ] (3) (−12 , −14 ] (4) [−32 , −54 ]

Q56.If L = sin2( 16π ) −sin2( π8 ) and M = cos2( 16π ) −sin2( π8 ) (1) L = − 2√2 1 + 21 cos π8 (2) L = 4√21 −14 cos π8 (3) M = 4√2 1 + 41 cos π8 (4) M = 2√21 + 21 cos π8

Q56.The circle passing through the intersection of the circles, x2 + y2 −6x = 0 and x2 + y2 −4y = 0 having its centre on the line, 2x −3y + 12 = 0, also passes through the point : (1) (–1, 3) (2) (–3, 6) (3) (–3, 1) (4) (1, –3)

Q56.If the co-ordinates of two points A and B are (√7, 0) and (−√7, 0) respectively and conic, 9x2 + 16y2 = 144, then PA + PB is equal to : (1) 16 (2) 8 (3) 6 (4) 9

Q56.A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0) . Which of the following lines is not a tangent to this circle? (1) 4x −3y + 17 = 0 (2) 3x −4y −24 = 0 (3) 3x + 4y −6 = 0 (4) 4x + 3y −8 = 0 and the hyperbola x2 respectively and

Q56.A triangle ABC lying in the first quadrant has two vertices as A(1, 2) and B(3, 1). If ∠BAC = 90o,and ar (Δ ABC) = 5√5 sq. units, then the abscissa of the vertex C is : JEE Main 2020 (04 Sep Shift 1) JEE Main Previous Year Paper (1) 1 + √5 (2) 1 + 2√5 (3) 2 + √5 (4) 2√5 −1 y2

Q56.For a > 0, let the curves C1 : y2 = ax and C2 : x2 = ay intersect at origin O and a point P. Let the line x = b(0 < b < a) intersect the chord OP and the x -axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, C1 and C2, and the area of ΔOQR = 21 , then ‘ a ’ satisfies the equation: (1) x6 −6x3 + 4 = 0 (2) x6 −12x3 + 4 = 0 (3) x6 + 6x3 −4 = 0 (4) x6 −12x3 −4 = 0

Q56.A ray of light coming from the point (2, 2√3) ray gets reflected on the line x = 1 and meets x -axis at the point B. Then, the line AB passes through the point (1) (3, −1√3 ) (2) (4, −√32 ) (3) (3, −√3) (4) (4, −√3)

Q56.A line parallel to the straight line 2x −y = 0 is tangent to the hyperbola x24 −y22 = 1 at the point (x1, y1). Then x21 + 5y21 is equal to (1) 6 (2) 8 (3) 10 (4) 5 JEE Main 2020 (02 Sep Shift 1) JEE Main Previous Year Paper

Q56.Let P be a point on the parabola, y2 = 12x and N be the foot of the perpendicular drawn from P , on the axis of the parabola. A line is now drawn through the mid-point M of PN , parallel to its axis which meets the parabola at Q . If the y−intercept of the line NQ is 43 , then : JEE Main 2020 (03 Sep Shift 1) JEE Main Previous Year Paper (1) PN = 4 (2) MQ = 13 (3) MQ = 14 (4) PN = 3

Q56.If y = mx + 4 is a tangent to both the parabolas, y2 = 4x and x2 = 2by, then b is equal to (1) −32 (2) −64 (3) −128 (4) 128

Q56.Let the latus rectum of the parabola y2 = 4x be the common chord to the circles C1 and C2 each of them having radius 2√5. Then, the distance between the centres of the circles C1 and C2 is : (1) 12 (2) 8 (3) 8√5 (4) 4√5 = 1

Q56.If a hyperbola passes through the point P(10, 16), and it has vertices at (±6, 0), then the equation of the normal to it at P , is. (1) 3x + 4y = 94 (2) 2x + 5y = 100 (3) x + 2y = 42 (4) x + 3y = 58

Q56.The number of ordered pairs (r, k) for which 6. 35Cr = (k2 −3). 36Cr+1, where k is an integer is JEE Main 2020 (07 Jan Shift 2) JEE Main Previous Year Paper (1) 3 (2) 2 (3) 6 (4) 4

Q57.Let x2 a2 + b2 = 1(a > b) be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function, ϕ(t) = 125 + t −t2 , then a2 + b2 is equal to : (1) 145 (2) 116 (3) 126 (4) 135

Q57.Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is 12 . If P(1, β), β > 0 is a point on this ellipse, then the equation of the normal to it at P is JEE Main 2020 (04 Sep Shift 2) JEE Main Previous Year Paper (1) 4x–3y = 2 (2) 8x–2y = 5 (3) 7x–4y = 1 (4) 4x–2y = 1

Q57.If one end of a focal chord AB of the parabola y2 = 8x is at A( 12 , −2), then the equation of the tangent to it at B is: (1) 2x + y −24 = 0 (2) x −2y + 8 = 0 (3) x + 2y + 8 = 0 (4) 2x −y −24 = 0

Q57.The locus of the mid-points of the perpendiculars drawn from points on the line x = 2y, to the line x = y, is. (1) 2x −3y = 0 (2) 5x −7y = 0 (3) 3x −2y = 0 (4) 7x −5y = 0

Q57.If the point P on the curve, 4x2 + 5y2 = 20 is farthest from the point Q(0, −4), then PQ2 is equal to (1) 36 (2) 48 (3) 21 (4) 29

Q57.If e1 and e2 are the eccentricities of the ellipse x218 + y24 = 1 9 −y24 = 1 (e1, e2) is a point on the ellipse 15x2 + 3y2 = k , then the value of k is equal to (1) 16 (2) 17 (3) 15 (4) 14

Q57.The set of all possible values of θ in the interval (0, π) for which the points (1, 2) and (sin θ, cos θ) lie on the same side of the line x + y = 1 is? (1) (0, π2 ) (2) ( π4 , 3π4 ) (3) (0, 3π4 ) (4) (0, π4 )