Practice Questions

Q68.If cosec θ = p−qp+q (p ≠q, p ≠0), then cot( π4 + 2θ ) is equals to: (1) pq (2) √pq (3) √qp (4) √pq

Q68.Let PS be the median of the triangle with vertices P(2, 2), Q(6, −1) and R(7, 3). The equation of the line passing through (1, −1) and parallel to PS is (1) 4x + 7y + 3 = 0 (2) 2x −9y −11 = 0 (3) 4x −7y −11 = 0 (4) 2x + 9y + 7 = 0

Q68.If a line intercepted between the coordinate axes is trisected at a point A(4, 3), which is nearer to x-axis, then its equation is: (1) 4x −3y = 7 (2) 3x + 2y = 18 (3) 3x + 8y = 36 (4) x + 3y = 13

Q68.The circumcentre of a triangle lies at the origin and its centroid is the midpoint of the line segment joining the points (a2 + 1, a2 + 1) and (2a , - 2 a), a≠0. Then for any a, the orthocentre of this triangle lies on the line (1) y −(a2 + 1)x = 0 (2) y −2ax = 0 (3) y + x = 0 (4) (a −1)2x −(a + 1)2y = 0

Q68.The base of an equilateral triangle is along the line given by 3x + 4y = 9. If a vertex of the triangle is (1, 2), then the length of a side of the triangle is: (1) 2√3 (2) 4√3 15 15 (3) 4√3 (4) 2√3 5 5

Q69.Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax + 2ay + c = 0 & 5bx + 2by + d = 0 lies in the fourth quadrant and is equidistant from the two axes then (1) 3bc −2ad = 0 (2) 3bc + 2ad = 0 (3) 2bc −3ad = 0 (4) 2bc + 3ad = 0

Q69.If the three distinct lines x + 2ay + a = 0, x + 3by +b = 0 and x + 4ay + a = 0 are concurrent, then the point (a, b) lies on a : (1) circle (2) hyperbola (3) straight line (4) parabola

Q69.The equation of the circle described on the chord 3x + y + 5 = 0 of the circle x2 + y2 = 16 as the diameter is (1) x2 + y2 + 3x + y + 1 = 0 (2) x2 + y2 + 3x + y −22 = 0 (3) x2 + y2 + 3x + y −11 = 0 (4) x2 + y2 + 3x + y −2 = 0

Q69.The set of all real values of λ for which exactly two common tangents can be drawn to the circles x2 + y2 −4x −4y + 6 = 0 and x2 + y2 −10x −10y + λ = 0 is the interval: (1) (12, 32) (2) (18, 42) (3) (12, 24) (4) (18, 48)

Q69.The number of values of α in [0, 2π] for which 2 sin3 α −7 sin2 α + 7sinα = 2, is : (1) 3 (2) 1 (3) 6 (4) 4 JEE Main 2014 (09 Apr Online) JEE Main Previous Year Paper

Q70.Let C be the circle with center at (1, 1) and radius = 1. If T is the circle centered at (0, y), passing through the origin and touching the circle C externally, then the radius of T is equal to (1) 1 (2) 1 2 4 (3) √3 (4) √3 √2 2

Q70.Given three points P, Q, R with P(5, 3) and R lies on the x−axis. If the equation of RQ is x −2y = 2 and PQ is parallel to the x−axis, then the centroid of ΔPQR lies on the line (1) x −2y + 1 = 0 (2) 2x + y −9 = 0 (3) 2x −5y = 0 (4) 5x −2y = 0

Q70.Let L1 be the length of the common chord of the curves x2 + y2 = 9 and y2 = 8x, and L2 be the length of the latus rectum of y2 = 8x, then: (1) L1 > L2 (2) L1 = L2 (3) L1 < L2 (4) L1L2 = √2

Q70.For the two circles x2 + y2 = 16 and x2 + y2 −2y = 0, there is/are (1) one pair of common tangents (2) two pair of common tangents (3) three pair of common tangents (4) no common tangent

Q70.A chord is drawn through the focus of the parabola y2 = 6x such that its distance from the vertex of this parabola is √5 , then its slope can be 2 (1) √5 (2) 2 2 √3 (3) √3 (4) 2 2 √5 JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper

Q71.Let a and b be any two numbers satisfying 1 + 1 = 14 . Then, the foot of perpendicular from the origin on a2 b2 the variable line x a + yb = 1 lies on : (1) A circle of radius = 2 (2) A hyperbola with each semi-axis = √2 . (3) A hyperbola with each semi-axis = 2 (4) A circle of radius = √2

Q71.A stair-case of length l rests against a vertical wall and a floor of a room. Let P be a point on the stair-case, nearer to its end on the wall, that divides its length in the ratio 1 : 2. If the staircase begins to slide on the floor, then the locus of P is: (1) an ellipse of eccentricity 1 (2) an ellipse of eccentricity √3 2 2 (3) a circle of radius 2 1 (4) a circle of radius √32 l

Q71.The tangent at an extremity (in the first quadrant) of the latus rectum of the hyperbola x24 −y25 = 1 , meets the x-axis and y-axis at A and B, respectively. Then OA2 −OB2 , where O is the origin, equals (1) −209 (2) 169 (3) 4 (4) −43

Q71.Two tangents are drawn from a point (−2, −1) to the curve, y2 = 4x. If α is the angle between them, then |tan α| is equal to: (1) 1 (2) 1 3 √3 (3) √3 (4) 3 y2

Q71.The locus of the foot of perpendicular drawn from the centre of the ellipse x2 + 3y2 = 6 on any tangent to it is (1) (x2 + y2) 2 = 6x2 + 2y2 (2) (x2 + y2) 2 = 6x2 −2y2 (3) (x2 −y2) 2 = 6x2 + 2y2 (4) (x2 −y2) 2 = 6x2 −2y2

Q72.Let P(3 sec θ, 2 tan θ) and Q(3 sec ϕ, 2 tan ϕ) where θ + ϕ = π2 , be two distinct points on the hyperbola x2 . Then the ordinate of the point of intersection of the normals at P and Q is: 9 −y24 = 1 (1) 11 3 (2) −113 (3) 13 2 (4) −132 = 5, then k is equal to:

Q72.The minimum area of a triangle formed by any tangent to the ellipse x2 = 1 and the co-ordinate axes is: 16 + 81 (1) 12 (2) 18 (3) 26 (4) 36

Q72.If the point (1, 4) lies inside the circle x2 + y2 −6x + 10y + p = 0 and the circle does not touch or intersect the coordinate axes, then the set of all possible values of p is the interval (1) (25, 39) (2) (25, 29) (3) (0, 25) (4) (9, 25)

Q72. sin(πcos2x) lim is equal to x→0 x2 (1) −π (2) π (3) π (4) 1 2

Q72.The contrapositive of the statement ''if I am not feeling well, then I will go to the doctor" is (1) if I will go to the doctor, then I am not feeling (2) if I am feeling well, then I will not go to the well. doctor. (3) if I will not go to the doctor, then I am feeling (4) if I will go to the doctor, then I am feeling well. well. ¯