Practice Questions

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.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.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.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. 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

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

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.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

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

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

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.If x→∞(1lim + (1) 2 (2) 32 (3) 1 (4) 2 2 3

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

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.

Q76.Consider the following two statements: P : If 7 is an odd number, then 7 is divisible by 2 . Q : If 7 is a prime number, then 7 is an odd number. If V1 is the truth value of the contrapositive of P and V2 is the truth value of contrapositive of Q, then the ordered pair (V1, V2) equals (1) (F, T) (2) (F, F) (3) (T, F) (4) (T, T)

Q76.If the standard deviation of the numbers 2, 3, a and 11 is 3. 5, then which of the following is true ? (1) 3a2 −34a + 91 = 0. (2) 3a2 −23a + 44 = 0. (3) 3a2 −26a + 55 = 0. (4) 3a2 −32a + 84 = 0.

Q76.The mean of 5 observations is 5 and their variance is 12. 4. If three of the observations are 1, 2 & 6; then the value of the remaining two is : (1) 1, 11 (2) 5, 5 (3) 5, 11 (4) None of these

Q77.A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30° . After walking for 10 minutes from JEE Main 2016 (03 Apr) JEE Main Previous Year Paper A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60° . Then the time taken (in minutes) by him, from B to reach the pillar, is (1) 20 (2) 5 (3) 6 (4) 10

Q77.The angle of elevation of the top of a vertical tower from a point A, due east of it is 45o . The angle of elevation of the top of the same tower from a point B, due south of A is 30o . If the distance between A and B is 54√2m , then the height of the tower (in meters), is: (1) 108 (2) 36√3 (3) 54√3 (4) 54

Q77.If the mean deviation of the numbers 1, 1 + d, … , 1 + 100d from their mean is 255 , then a value of d is : (1) 10. 1 (2) 5. 05 (3) 20. 2 (4) 10 Q78. ⎡ √32 21 ⎤ 1 1 T If P = , A = and Q = PAP T, then P Q2015 P is : √3 [0 1 ] ⎣−12 2 ⎦ (1) [00 20150 ] (2) [20151 20150 ] (3) [10 20151 ] (4) [20150 20151 ]