Practice Questions

Q70.If β is one of the angles between the normals to the ellipse x2 + 3y2 = 9 at the points (3 θ) and θ ∈(0, π2 ); then 2sincot2θβ is equal to : (−3 sin θ, √3 cos θ); (1) 1 (2) √3 √3 4 (3) 2 (4) √2 √3

Q70.The tangent to the circle C1 : x2 + y2 −2x −1 = 0 at the point (2, 1) cuts off a chord of length 4 from a circle C2 whose centre is (3, −2). The radius of C2 is (1) √6 (2) 2 (3) √2 (4) 3

Q70.Let P be a point on the parabola x2 = 4y. If the distance of P from the center of the circle x2 + y2 + 6x + 8 = 0 is minimum, then the equation of the tangent to the parabola at P is (1) x + y + 1 = 0 (2) x + 4y −2 = 0 (3) x + 2y = 0 (4) x −y + 3 = 0

Q71.Two sets A and B are as under: A = {(a, b) ∈R × R : |a −5| < 1 and |b −5| < 1}; Then : B = {(a, b) ∈R × R : 4(a −6)2 + 9(b −5)2 ≤36}. (1) neither A ⊂B nor B ⊂A (2) B ⊂A (3) A ⊂B (4) A ∩B = ϕ (an empty set)

Q71.If the tangent drawn to the hyperbola 4y2 = x2 + 1 intersect the co-ordinates axes at the distinct points A and B, then the locus of the midpoint of AB is : (1) x2 −4y2 + 16x2y2 = 0 (2) 4x2 −y2 + 16x2y2 = 0 (3) x2 −4y2 −16x2y2 = 0 (4) 4x2 −y2 −16x2y2 = 0

Q71.Tangents drawn from the point (−8, 0) to the parabola y2 = 8x touch the parabola at P and Q. If F is the focus of the parabola, then the area of the triangle PFQ (in sq. units) is equal to (1) 48 (2) 32 (3) 24 (4) 64 JEE Main 2018 (15 Apr Shift 2 Online) JEE Main Previous Year Paper

Q71.If the length of the latus rectum of an ellipse is 4 units and the distance between a focus and its nearest vertex on the major axis is 3 units, then its eccentricity is 2 (1) 2 (2) 1 3 2 (3) 1 (4) 1 9 3

Q72.Tangents are drawn to the hyperbola 4x2 −y2 = 36 at the points P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of ΔPTQ is: (1) 36√5 (2) 45√5 (3) 54√3 (4) 60√3

Q72.A normal to the hyperbola, 4x2 −9y2 = 36 meets the co-ordinate axes x and y at A and B, respectively. If the parallelogram OABP(O being the origin) is formed, then the locus of P is (1) 4x2 −9y2 = 121 (2) 4x2 + 9y2 = 121 (3) 9x2 −4y2 = 169 (4) 9x2 + 4y2 = 169

Q72.If (p ∧~q) ∧(p ∧r) →~p ∨q is false, then the truth values of p, q and r are respectively (1) T, T, T (2) F, T, F (3) T, F, T (4) F, F, F

Q72. (27+x) 31 −3 lim 2 equals x→0 9−(27+x) 3 (1) −16 (2) 61 (3) 3 1 (4) −13

Q72.If the tangents drawn to the hyperbola 4y2 = x2+ 1 intersect the co-ordinate axes at the distinct points A and B, then the locus of the mid point of AB is (1) x2 −4y2 + 16x2y2 = 0 (2) 4x2 −y2 + 16x2y2 = 0 (3) 4x2 −y2 −16x2y2 = 0 (4) x2 −4y2 −16x2y2 = 0

Q73. limx→0 x tan(1−cos2x−2x2x)2tan x equals. (1) 1 (2) −12 (3) 1 (4) 1 4 2

Q73.For each t ∈R, let [t] be the greatest integer less than or equal to t. Then lim x([ x1 ] + [ x2 ] + … + [ 15x ]) x→0+ (1) does not exist (in R) (2) is equal to 0 (3) is equal to 15 (4) is equal to 120

Q73.If p →(~p ∨~q) is false, then the truth values of p and q are, respectively (1) F, F (2) T, T (3) F, T (4) T, F

Q73.The mean of a set of 30 observation is 75 . If each observations is multiplied by non-zero number λ and then each of them is decreased by 25 , their mean remains the same. Then, λ is equal to : (1) 4 (2) 1 3 3 (3) 10 (4) 2 3 3

Q73.If (p∧∼q) ∧(p ∧r) →∼p ∨q is false, then the truth values of p, q and r are respectively (1) F, T, F (2) T, F, T (3) F, F, F (4) T, T, T

Q74.If the mean of the data: 7, 8, 9, 7, 8, 7, λ, 8 is 8 , then the variance of this data is (1) 9 (2) 2 8 (3) 7 (4) 1 8

Q74.The Boolean expression ~(p ∨q) ∨(~p ∧q) is equivalent to (1) ~q (2) ~p (3) p (4) q

Q74.An aeroplane flying at a constant speed, parallel to the horizontal ground, √3 km above it is observed at an elevation of 60° from a point on the ground. If after five seconds, its elevation from the same point is 30° , then the speed (in km / hr) of the aeroplane is (1) 720 (2) 1500 (3) 750 (4) 1440

Q74.The mean of a set of 30 observations is 75 . If each other observation is multiplied by a nonzero number λ and then each of them is decreased by 25 , their mean remains the same. The λ is equal to equal to {0} (1) 103 (2) 43 (3) 1 (4) 2 3 3

Q74.The mean and the standard deviation (S. D. ) of five observations are 9 and 0, respectively. If one of the observation is increased such that the mean of the new set of five observations becomes 10, then their S. D. is (1) 0 (2) 2 (3) 4 (4) 1

Q75.A tower T1 of height 60 m is located exactly opposite to a tower T2 of height 80 m on a straight road. From the top of T1 , if the angle of depression of the foot of T2 is twice the angle of elevation of the top of T2 , then the width (in m ) of the road between the feet of the towers T1 and T2 is (1) 20√2 (2) 10√2 (3) 10√3 (4) 20√3

Q75.If ∑9i=1(xi −5) = 9 and ∑9i=1 (xi −5)2 = 45, then the standard deviation of the 9 items x1, x2, … . , x9 is (1) 3 (2) 9 (3) 4 (4) 2

Q75.In a triangle ABC , coordinates of A are (1, 2) and the equations of the medians through B and C are respectively, x + y = 5 and x = 4 . Then area of ΔABC (in sq. units) is : (1) 12 (2) 4 (3) 9 (4) 5