Practice Questions

Q54.Let an be the nth term of a G.P. of positive terms. If ∑100n=1 a2n+1 = 200 and ∑100n=1 a2n = 100, then ∑200n=1 an is equal to: (1) 300 (2) 225 (3) 175 (4) 150

Q54.If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of (1 + x)n+5 are in the ratio 5 : 10 : 14, then the largest coefficient in the expansion is : (1) 462 (2) 330 (3) 792 (4) 252

Q54.If 32 sin 2α−1, 14 and 34−2 sin 2α are the first three terms of an A.P. for some α , then the sixth term of this A.P. is (1) 66 (2) 81 (3) 65 (4) 78

Q54.If |x| < 1, |y| < 1 and x ≠1 , then the sum to infinity of the following series (x + y) + (x2 + xy + y2) + (x3 + x2y + xy2 + y3)+. . . . . is (1) x+y−xy (2) x+y+xy (1+x)(1+y) (1+x)(1+y) (3) x+y−xy (4) x+y+xy (1−x)(1−y) (1−x)(1−y)

Q54.If the constant term in the binomial expansion of (√x − x2k ) 10 (1) 9 (2) 1 (3) 3 (4) 2

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

Q55.Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the image of the point (−1, −4) in the line is : (1) ( 115 , 285 ) (2) ( 295 , 85 ) (3) ( 85 , 295 ) (4) ( 295 , 115 )

Q55.The greatest positive integer k, for which 49k + 1 is a factor of the sum 49125 + 49124 + … + 492 + 49 + 1, is (1) 32 (2) 63 (3) 60 (4) 35

Q55.If a line y = mx + c, is a tangent to the circle (x −3)2 + y2 = 1 , and it is perpendicular to a line L1, where , 1 ), then L1 is the tangent to the circle x2 + y2 = 1 , at the point ( √21 √2 (1) c2 −7c + 6 = 0 (2) c2 + 7c + 6 = 0 (3) c2 + 6c + 7 = 0 (4) c2 −6c + 7 = 0

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

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.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 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 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.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

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.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 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.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.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.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.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