Practice Questions

Q55.The coefficient of x7 in the expression (1 + x)10 + x(1 + x)9 + x2(1 + x)8+. . . . +x10 , is (1) 210 (2) 330 (3) 120 (4) 420

Q55.If {p} denotes the fractional part of the number p, then { 32008 } (1) 5 (2) 7 8 8 (3) 3 (4) 1 8 8 is incident at an angle 30° on the line x = 1 at the point A . The

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

Q55.If the sum of the first 20 terms of the series log(71/2) x + log(71/3) x + log(71/4) x + … is 460 , then x is equal to: (1) 72 (2) 71/2 (3) e2 (4) 746/21

Q55.The locus of a point which divides the line segment joining the point (0, −1) and a point on the parabola x2 = 4y internally in the ratio 1 : 2 is: (1) 9x2 −12y = 8 (2) 9x2 −3y = 2 (3) x2 −3y = 2 (4) 4x2 −3y = 2

Q55.If a ΔABC has vertices A(–1, 7), B(–7, 1) and C(5, –5), then its orthocentre has coordinates: (1) (– 3, 3) (2) (3, −3) (3) (−35 , 53 ) (4) ( 53 , −35 )

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 x = ∑∞n=0 (−1)ntan2θ and y = ∑∞n=0 cos2nθ, for 0 < θ < π4 , then: (1) x(1 + y) = 1 (2) y(1 −x) = 1 (3) y(1 + x) = 1 (4) x(1 −y) = 1 x when π

Q55.Let α > 0, β > 0 be such that α3 + β2 = 4 . If the maximum value of the term independent of x in the 1 10 10k, then k is equal to binomial expansion of (αx 9 + βx−16 ) is (1) 336 (2) 352 (3) 84 (4) 176

Q55.Let S be the sum of the first 9 term of the series : {x + ka} + {x2 + (k + 2)a} + {x3 + (k + 4)a} + {x4 + (k + 6)a} + … where a ≠0 and x ≠ 1 . If x10−x+45a(x−1) S = x−1 , then k is equal to (1) −5 (2) 1 (3) −3 (4) 3

Q55.If the number of integral terms in the expansion of (3 ) (1) 264 (2) 128 (3) 256 (4) 248

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.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.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.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.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

Q56.The centre of the circle passing through the point (0, 1) and touching the parabola y = x2 at the point (2, 4) is : JEE Main 2020 (06 Sep Shift 2) JEE Main Previous Year Paper (1) ( −5310 , 165 ) (2) ( 65 , 5310 ) (3) ( 103 , 165 ) (4) ( −165 , 5310 )

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.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.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 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.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.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