Practice Questions

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},

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

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

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.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

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.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

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

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.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

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

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

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

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

Q73.Let a and b respectively be the semi-transverse and semi-conjugate axes of a standard hyperbola whose eccentricity satisfies the equation 9e2 −18e + 5 = 0 . If S(5, 0) is a focus and 5x = 9 is the corresponding directrix of this hyperbola, then a2 −b2 is equal to (1) −7 (2) −5 (3) 5 (4) 7 t2 f(x)−x2f(t)

Q73. (n+1) (n+2)….3n n1 is equal to lim n2n ) n→∞( (1) 9 (2) 3 log 3 −2 e2 (3) 18 (4) 27 e4 e2 1 2x

Q73.A hyperbola whose transverse axis is along the major axis of the conic x2 3 + 4 = 4 and has vertices at the foci of the conic. If the eccentricity of the hyperbola is 3 , then which of the following points does not lie on 2 the hyperbola ? (1) (√5, 2√2) (2) (0, 2) (3) (5, 2√3) (4) (√10, 2√3) is

Q74. lim 2x tan(1−cosx−x2x)2tan 2x x→0 (1) 2 (2) −12 (3) −2 (4) 12

Q74.Let P = lim (1 + tan2 √x ) , then log P is equal to x→0+ (1) 1 (2) 1 2 4 (3) 2 (4) 1

Q74.If f(x) is a differentiable function in the interval (0, ∞) such that f(1) = 1 and lim t−x = 1,for each t→x x > 0, then f( 23 ) is equal to JEE Main 2016 (09 Apr Online) JEE Main Previous Year Paper (1) 23 (2) 13 18 6 (3) 25 (4) 31 9 18 a − 4 ) 2x = e3 , then a is equal to x x2

Q75.The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times", is (1) if the area of a square increases four times, then (2) if the area of a square increases four times, then its side is not doubled. its side is doubled. (3) if the area of a square does not increase four (4) if the side of a square is not doubled, then its area times, then its side is not doubled. does not increase four times.

Q75.The Boolean Expression (p∧∼q) ∨q ∨(∼p ∧q) is equivalent to (1) p ∨q (2) p ∨∼q (3) ∼p ∧q (4) p ∧q