Practice Questions

Q67.If 2 cos θ + sin θ = 1 (θ ≠π2 ), then 7 cos θ + 6 sin θ is equal to: (1) 1 (2) 2 2 (3) 11 (4) 46 2 5

Q67.Let fk(x) = k1 (sink x + cosk x) where x ∈R and k≥1. Then f4(x) −f6(x) equals (1) 1 (2) 1 4 12 (3) 1 (4) 1 6 3

Q67.If a line L is perpendicular to the line 5x −y = 1, and the area of the triangle formed by the line L and the coordinate axes is 5 sq units, then the distance of the line L from the line x + 5y = 0 is (1) 7 units (2) 7 units √13 √5 (3) 5 units (4) 5 units √13 √7

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.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.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 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.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.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.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.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

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.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.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

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.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

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

Q73.Let x , M and σ2 be respectively the mean, mode and variance of n observations x1, x2, . ..., xn and di = −xi −a, i = 1, 2, . ..., n, where a is any number. Statement I: Variance of d1, d2, . . . , dn is σ2 . ¯Statement II: Mean and mode of d1, d2, . . . . , dn are −x −a and −M −a, respectively. (1) Statement I and Statement II are both true (2) Statement I and Statement II are both false (3) Statement I is true and Statement II is false (4) Statement I is false and Statement II is true

Q73.If limx→2 tan(x−2{x2+k+2x−2k}x2−4x+4 JEE Main 2014 (11 Apr Online) JEE Main Previous Year Paper (1) 0 (2) 1 (3) 2 (4) 3

Q73.If OB is the semi-minor axis of an ellipse, F1 and F2 are its focii and the angle between F1B and F2B is a right angle, then the square of the eccentricity of the ellipse is (1) 1 (2) 1 4 √2 (3) 1 (4) 1 2 2√2