Practice Questions

Q68.The term independent of x in the binomial expansion of (1 −1x + 3x5) (2x2 −1x ) 8 (1) − 496 (2) −400 (3) 496 (4) 400

Q69.Locus of the image of the point (2, 3) in the line (2x −3y + 4) + k(x −2y + 3) = 0, k∈R , is a (1) Circle of radius √3 (2) Straight line parallel to x-axis. (3) Straight line parallel to y-axis. (4) Circle of radius √2

Q69.If cos α + cos β = 23 and sin α + sin β = 12 and θ is the arithmetic mean of α & β, then sin 2θ + cos 2θ is equal to: (1) 3 (2) 7 5 5 (3) 4 (4) 8 5 5

Q69.The points (0, 38 ), (1, 3) and (82, 30) (1) form an obtuse angled triangle (2) form an acute angled triangle (3) lie on a straight line (4) form a right angled triangle

Q70.If y + 3x = 0 is the equation of a chord of the circle x2 + y2 −30x = 0 , then the equation of the circle with this chord as diameter is : (1) x2 + y2 + 3x −9y = 0 (2) x2 + y2 −3x + 9y = 0 (3) x2 + y2 + 3x + 9y = 0 (4) x2 + y2 −3x −9y = 0 JEE Main 2015 (10 Apr Online) JEE Main Previous Year Paper

Q70.The number of common tangents to the circles x2 + y2 −4x −6y −12 = 0 and x2 + y2 + 6x + 18y + 26 = 0 , is (1) 4 (2) 1 (3) 2 (4) 3

Q70.A straight line L through the point (3, −2) is inclined at an angle of 60° to the line √3x + y = 1. If L also intersects the X -axis, then the equation of L is: (1) y + √3 x + 2 −3√3 = 0 (2) √3 y −x + 3 + 2√3 = 0 (3) √3 y + x −3 + 2√3 = 0 (4) y −√3x + 2 + 3√3 = 0

Q71.Let O be the vertex and Q be any point on the parabola, x2 = 8y. If the point P divides the line segment OQ internally in the ratio 1 : 3 , then the locus of P is (1) x2 = 2y (2) x2 = y (3) y2 = x (4) y2 = 2x

Q71.Let the tangents drawn to the circle, x2 + y2 = 16 from the point P(0, h) meet the x -axis at points A and B . If the area of ΔAPB is minimum, then positive value of h is: (1) 4√2 (2) 3√2 (3) 4√3 (4) 3√3

Q71.If a circle passing through the point (−1, 0) touches y-axis at (0, 2), then the x-intercept of the circle is (1) 5 (2) 5 2 (3) 3 (4) 3 2

Q72.If the tangent to the conic, y −6 = x2 at (2, 10) touches the circle, x2 + y2 + 8x −2y = k (for some fixed k ) at a point (α, β); then (α, β) is (1) (−717 , 176 ) (2) (−817 , 172 ) (3) (−617 , 1017 ) (4) (−417 , 171 )

Q72.If the incentre of an equilateral triangle is (1, 1) and the equation of its one side is 3x + 4y + 3 = 0 , then the equation of the circumcircle of this triangle is: (1) x2 + y2 −2x −2y −2 = 0 (2) x2 + y2 −2x −2y + 2 = 0 (3) x2 + y2 −2x −2y −7 = 0 (4) x2 + y2 −2x −2y −14 = 0

Q72.The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latus ractum to the x2 y2 ellipse 9 + 5 = 1, is (1) 27 (2) 274 (3) 18 (4) 272

Q73. lim (1−cos2x)(3+cosx)xtan4x = x→0 (1) 12 (2) 4 (3) 3 (4) 2

Q73.An ellipse passes through the foci of the hyperbola, 9x2 −4y2 = 36 and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is 1 , then which of the following points does not lie on the ellipse? 2 , (1) ( √392 √3) (2) ( √132 , √32 ) 2 , (3) (√13 (4) √6) (√13, 0) x is equal to

Q73.If PQ be a double ordinate of the parabola, y2 = −4x, where P lies in the second quadrant. If R divides PQ in the ratio 2 : 1, then the locus of R is: JEE Main 2015 (11 Apr Online) JEE Main Previous Year Paper (1) 3y2 = −2x (2) 9y2 = 4x (3) 9y2 = −4x (4) 3y2 = 2x

Q74. lim ex2−cos x→0 sin2 x (1) 2 (2) 32 (3) 5 (4) 3 4

Q74.If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is: (1) 1 (2) √2 −1 2 (3) √2−1 (4) 2√2−1 2 2

Q74.The negation of ∽s ∨(∽r ∧s) is equivalent to JEE Main 2015 (04 Apr) JEE Main Previous Year Paper (1) s ∧ r (2) s ∧~r (3) s ∧(r ∧~s) (4) s ∨(r ∨~s)

Q75.Consider the following statements: P: Suman is brilliant Q: Suman is rich R: Suman is honest The negation of the statement, "Suman is brilliant and dishonest if and only if Suman is rich" can be equivalently expressed as (1) ~Q ↔~P ∨R (2) ~Q ↔P ∨~R (3) ~Q ↔P ∧~R (4) ~Q ↔~P ∧R

Q75.The contrapositive of the statement "If it is raining, then I will not come", is (1) if I will come, then it is not raining. (2) if I will come, then it is raining. (3) if I will not come, then it is raining. (4) if I will not come, then it is not raining.

Q75.The mean of a data set comprising of 16 observations is 16 . If one of the observation value 16 is deleted and three new observations valued 3 , 4 and 5 are added to the data, then the mean of the resultant data is (1) 14 .0 (2) 16 .8 (3) 16 .0 (4) 15 .8

Q76.If the angles of elevation of the top of a tower from three collinear points A, B and C on a line leading to the foot of the tower are 30°, 45° and 60° respectively, then the ratio AB : BC , is (1) 2 : 3 (2) √3 : 1 (3) √3 : √2 (4) 1 : √3 Q77. ⎡ 1 2 2 ⎤ If A = 2 1 −2 is a matrix satisfying the equation AAT = 9I , where I is 3 × 3 identity matrix, then the ⎣ a 2 b ⎦ ordered pair (a, b) is equal to (1) (−2, −1) (2) (2, −1) (3) (−2, 1) (4) (2, 1)

Q76.A factory is operating in two shifts, day and night, with 70 and 30 workers, respectively.If per day mean wage of the day shift workers is, ₹ 54 and per day mean wage of all the workers is ₹ 60, then per day mean wage of the night shift workers (in ₹ ) is : (1) 75 (2) 74 (3) 69 (4) 66

Q76.Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation α at a point O on this line and all the poles are on the same side of O. If the height of the longest pole is h and the distance of the foot of the smallest pole from O is a; then the distance between two consecutive poles, is (1) h sin α+a cos α (2) h cos α−a sinα 9 cos α 9 sin α (3) h sin α+a cos α (4) h cos α−a sin α 9 sin α 9 cos α