Practice Questions

Q64. n-digit numbers are formed using only three digits 2, 5 and 7 . The smallest value of n for which 900 such distinct numbers can be formed is : (1) 9 (2) 7 (3) 8 (4) 6

Q65.If x1, x2, … . , xn and h11 , h21 , … . . hn1 are two A.P's such that x3 = h2 = 8 and x8 = h7 = 20 , then x5. h10 equals. (1) 2560 (2) 2650 (3) 3200 (4) 1600

Q65.Let 1 , 1 , … , 1 ≠0 for i = 1, 2, … . , n) be in A.P. such that x1 = 4 and x21 = 20. If n is the least x1 x2 xn (xi is equal to positive integer for which xn > 50, then ∑ni=1( xi1 ) (1) 3 (2) 18 (3) 13 (4) 13 4 8

Q65.Let a1, a2, a3, … … , a49 be in A. P. such that Σ12 = 416 and a9 + a43 = 66. If k=0a4k+1 a21 + a22 + … + a217 = 140m, then m is equal to: (1) 33 (2) 66 (3) 68 (4) 34

Q65.If b is the first term of an infinite geometric progression whose sum is five, then b lies in the interval (1) [10, ∞) (2) (−∞, −10] (3) (−10, 0) (4) (0, 10)

Q65.The coefficient of x10 in the expansion of (1 + x)2 (1 + x2)3(1 + x3)4 is equal to (1) 52 (2) 44 (3) 50 (4) 56

Q66.The sum of the first 20 terms of the series 1 + 23 + 47 + 158 + 1631 + … is (1) 39 + 1 (2) 38 + 1 219 220 (3) 38 + 1 (4) 39 + 1 219 220 is

Q66.If n is the degree of the polynomial, 1 8 1 8 + [ √5x3 + 1 −√5x3 −1 ] [ √5x3 + 1 + √5x3 −1 ] and m is the coefficient of xn in it, then the ordered pair (n, m) is equal to (1) (12, (20)4) (2) (8, 5(10)4) (3) (24, (10)8) (4) (12, 8(10)4) JEE Main 2018 (15 Apr Shift 1 Online) JEE Main Previous Year Paper

Q66.The sum of the co-efficient of all odd degree terms in the expansion of 5 5 + , (x > 1) is (x + √x3 −1) (x −√x3 −1) (1) 2 (2) −1 (3) 0 (4) 1

Q66.The number of solutions of sin 3x = cos 2x, in the interval ( π2 , π) is (1) 3 (2) 4 (3) 2 (4) 1

Q66.If x1, x2, … . . , xn and h11 , h21 , … . . , hn1 are two A.P.s such that x3 = h2 = 8 & x8 = h7 = 20 , then x5 ⋅h10 is equal to (1) 3200 (2) 1600 (3) 2650 (4) 2560

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)

Q67.If sum of all the solutions of the equation 8 cos x ⋅(cos( π6 + x) ⋅cos( π6 −x) −12 ) = 1 in [0, π] is kπ, then k is equal to: JEE Main 2018 (08 Apr) JEE Main Previous Year Paper (1) 20 (2) 2 9 3 (3) 13 (4) 8 9 9

Q67.The coefficient of x2 in the expansion of the product (2 −x2){(1 + 2x + 3x2) 6 + (1 −4x2) 6} (1) 107 (2) 108 (3) 155 (4) 106

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.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 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.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.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.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

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