Practice Questions

Q64.If the 2nd, 5th and 9th terms of a non-constant arithmetic progression are in geometric progression, then the common ratio of this geometric progression is (1) 1 (2) 74 (3) 8 (4) 4 5 3 is 16 m , then m

Q65.The value of ∑15r=1 r2( 15Cr−115Cr ) (1) 1240 (2) 560 (3) 1085 (4) 680 JEE Main 2016 (09 Apr Online) JEE Main Previous Year Paper

Q65.If the sum of the first ten terms of the series (1 35 ) 2 + (2 25 ) 2 + (3 15 ) 2 + 42 + (4 45 ) 2 + … . , 5 is equal to (1) 100 (2) 99 (3) 102 (4) 101 n , x, y ≠0, is 28, then the sum of the coefficients

Q65.The sum ∑10r=1(r2 + 1) × (r!), is equal to: (1) 11 × (11!) (2) 10 × (11! ) (3) (11)! (4) 101 × (10!) 1

Q66.If the number of terms in the expansion of (1 −2x + y24 ) of all the terms in this expansion is (1) 243 (2) 729 (3) 64 (4) 2187

Q66.If the coefficients of x−2 and x−4 , in the expansion of 3 18 + 1 1 , (x > 0) , are m and n respectively, then (x 2x 3 ) m is equal to n (1) 27 (2) 182 (3) 54 (4) 54

Q66.For x ∈R, x ≠−1, if (1 + x)2016 + x(1 + x)2015 + x2(1 + x)2014 + … + x2016 = 2016 aixi , then a17 is ∑ i=0 equal to (1) 2017! (2) 2016! 17!2000! 17!1999! (3) 2016! (4) 2017! 16! 2000!

Q67.If 0 ≤x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x + cos 3x + cos 4x = 0, is (1) 7 (2) 9 (3) 3 (4) 5 JEE Main 2016 (03 Apr) JEE Main Previous Year Paper

Q67.If m and M are the minimum and the maximum values of 4 + 12 sin22x −2cos4x, x ∈R, then M −m is equal to: (1) 15 (2) 9 4 4 (3) 7 (4) 1 4 4

Q67.If A > 0, B > 0 and A + B = π6 , then the minimum positive value of (tan A + tan B) is : (1) √3 −√2 (2) 4 −2√3 (3) 2 (4) 2 −√3 √3 be two sets. Then and Q = : sin θ −cos θ = √2 cos θ} {θ : sin θ + cos θ = √2 sin θ},

Q68.The number of x ∈[0, 2π] for which √2 sin4 x + 18 cos2 x − √2 cos4 x + 18 sin2 x = 1 is: (1) 2 (2) 6 (3) 4 (4) 8

Q68.Two sides of a rhombus are along the lines, x −y + 1 = 0 and 7x −y −5 = 0 . If its diagonals intersect at (−1, −2) , then which one of the following is a vertex of this rhombus ? (1) ( 31 , −83 ) (2) (−103 , −73 ) (3) (−3, −9) (4) (−3, −8)

Q68.Let P = {θ (1) P ⊂Q and Q −P ≠ ϕ (2) Q ⊄ P (3) P = Q (4) P ⊄ Q

Q69.If a variable line drawn through the intersection of the lines x 3 + 4y = 1 and x4 + 3y = 1 , meets the coordinate axes at A and B, (A ≠B),then the locus of the midpoint of AB is: (1) 7xy = 6(x + y) (2) 4(x + y)2 −28(x + y) + 49 = 0 (3) 6xy = 7(x + y) (4) 14(x + y)2 −97(x + y) + 168 = 0

Q69.The centres of those circles which touch the circle, x2 + y2 −8x −8y −4 = 0, externally and also touch the x - axis, lie on (1) A hyperbola (2) A parabola (3) A circle (4) An ellipse which is not a circle

Q69.A straight line through origin O meets the lines 3y = 10 −4x and 8x + 6y + 5 = 0 at points A and B respectively. Then, O divides the segment AB in the ratio (1) 2 : 3 (2) 1 : 2 (3) 4 : 1 (4) 3 : 4

Q70.The point (2, 1) is translated parallel to the line L : x −y = 4 by 2√3 units. If the new point Q lies in the third quadrant, then the equation of the line passing through Q and perpendicular to L is (1) x + y = 2 −√6 (2) 2x + 2y = 1 −√6 (3) x + y = 3 −3√6 (4) x + y = 3 −2√6

Q70.If one of the diameters of the circle, given by the equation, x2 + y2 −4x + 6y −12 = 0, is a chord of a circle S , whose centre is at (−3, 2), then the radius of S is (1) 5 (2) 10 (3) 5√2 (4) 5√3

Q70.A ray of light is incident along a line which meets another line 7x −y + 1 = 0 at the point (0, 1). The ray is then reflected from this point along the line y + 2x = 1 . Then the equation of the line of incidence of the ray of light is : (1) 41x −25y + 25 = 0 (2) 41x + 25y −25 = 0 (3) 41x −38y + 38 = 0 (4) 41x + 38y −38 = 0

Q71.Let P be the point on the parabola, y2 = 8x which is at a minimum distance from the center C of the circle x2 + (y + 6)2 = 1. Then the equation of the circle, passing through C and having its center at P is (1) x2 + y2 −x4 + 2y −24 = 0 (2) x2 + y2 −4x + 9y + 18 = 0 (3) x2 + y2 −4x + 8y + 12 = 0 (4) x2 + y2 −x + 4y −12 = 0

Q71.A circle passes through (−2, 4) and touches the y−axis at (0, 2). Which one of the following equations can represent a diameter of this circle ? (1) 2x −3y + 10 = 0 (2) 3x + 4y −3 = 0 (3) 4x + 5y −6 = 0 (4) 5x + 2y + 4 = 0 y2

Q71.Equation of the tangent to the circle, at the point (1, −1), whose center, is the point of intersection of the straight lines x −y = 1 and 2x + y = 3 is: JEE Main 2016 (10 Apr Online) JEE Main Previous Year Paper (1) x + 4y + 3 = 0 (2) 3x −y −4 = 0 (3) x −3y −4 = 0 (4) 4x + y −3 = 0

Q72.If the tangent at a point on the ellipse x2 27 + 3 = 1 meets the coordinate axes at A and B, and O is the origin, then the minimum area (in sq. units) of the triangle OAB is (1) 3√3 (2) 92 (3) 9 (4) 9√3

Q72.The eccentricity of the hyperbola whose length of its conjugate axis is equal to half of the distance between its foci, is (1) 2 (2) √3 √3 (3) 4 (4) 4 3 √3

Q72. P and Q are two distinct points on the parabola, y2 = 4x, with parameters t and t1 , respectively. If the normal at P passes through Q, then the minimum value of t21 , is (1) 8 (2) 4 (3) 6 (4) 2 y2