Practice Questions

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

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. 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.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.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

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

Q75.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) 1500 (2) 750 (3) 720 (4) 1440 JEE Main 2018 (15 Apr Shift 1 Online) JEE Main Previous Year Paper

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.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.A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min for the angle of depression of the car to change from 30° to 45°, then the time taken (in min) by the car to reach the foot of the tower is (1) 9 + 2 (√3 −1) (2) 18(1 √3) + (3) 18(√3 −1) (4) 9(1 √3)

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

Q76.Consider the following two binary relations on the set A = {a, b, c} : R1 = {(c, a)(b, b), (a, c), (c, c), (b, c), (a, a)} and R2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c). Then (1) R2 is symmetric but it is not transitive (2) Both R1 and R2 are transitive (3) Both R1 and R2 are not symmetric (4) R1 is not symmetric but it is transitive is a scalar matrix and |3A| = 108 . Then A2 equals

Q76. PQR is a triangular park with PQ = PR = 200 m. A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively, 45°, 30° and 30°, then the height of the tower (in m ) is: JEE Main 2018 (08 Apr) JEE Main Previous Year Paper (1) 50√2 (2) 100 (3) 50 (4) 100√3

Q76.Let N denote the set of all natural numbers. Define two binary relations on N as R1 = {(x, y) ∈N × N : 2x + y = 10} and R2 = {(x, y) ∈N × N : x + 2y = 10}. Then (1) both R1 and R2 are transitive relations (2) range of R2 is {1, 2, 3, 4} (3) range of R1 is {2, 4, 8} (4) both R1 and R2 are symmetric relations Q77. ⎡ 1 0 0⎤ Let A = 1 1 0 and B = A20 . Then the sum of the elements of the first column of B is ⎣ 1 1 1⎦ (1) 210 (2) 211 (3) 251 (4) 231 JEE Main 2018 (16 Apr Online) JEE Main Previous Year Paper

Q76.Consider the following two binary relations on the set A = {a, b, c} : R1 = {(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)} and R2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}, then : (1) R2 is symmetric but it is not transitive (2) both R1 and R2 are not symmetric (3) both R1 and R2 are transitive (4) R1 is not symmetric but it is transitive

Q76.Suppose A is any 3 × 3 non-singular matrix and (A −3I)(A −5I) = O, where I = I3 and O = O3 . If αA+ βA−1 = 4I , then α + β is equal to (1) 8 (2) 12 (3) 13 (4) 7

Q77.Let A be a matrix such that A . [10 23 ] (1) [40 −3236 ] (2) [−324 360 ] (3) [−3236 04] (4) [360 −324 ]

Q77.Let the orthocentre and centroid of a triangle be A(−3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is: (1) 3√5 (2) √10 2 (3) 2√10 (4) 3√52

Q77.If the system of linear equations x + ay + z = 3 x + 2y + 2z = 6 x + 5y + 3z = b has no solution, then (1) a = 1, b ≠9 (2) a ≠−1, b = 9 (3) a = −1, b = 9 (4) a = −1, b ≠9

Q77.Let A be a matrix such that A ⋅[10 23 ] is a scalar matrix and |3A| = 108 . Then, A2 equals : (1) [−324 360 ] (2) [360 −324 ] (3) [−3236 04 ] (4) [40 −3236 ] JEE Main 2018 (15 Apr) JEE Main Previous Year Paper