Practice Questions

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.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

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)

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. 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.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.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

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

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

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 ] (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

Q78. cos x x 1 f ′(x) If f(x) = 2 sin x x2 2x , then limx→0 x tan x x 1 (1) Exists and is equal to −2 (2) Does not exist (3) Exist and is equal to 0 (4) Exists and is equal to 2

Q78.The number of values of k for which the system of linear equations (k + 2)x + 10y = k & kx + (k + 3)y = k −1 has no solution is (1) 1 (2) 2 (3) 3 (4) 4

Q78. cos x x 1 f ′(x) If f(x) = 2 sin x x2 2x , then lim x x→0 tan x x 1 (1) does not exist (2) exists and is equal to −2 (3) exists and is equal to 0 (4) exists and is equal to 2

Q78.If the system of linear equations x + ky + 3z = 0 3x + ky −2z = 0 2x + 4y −3z = 0 has a non-zero solution (x, y, z), then xz is equal to: y2 (1) 30 (2) −10 (3) 10 (4) −30

Q78.Let f : A → B be a function defined as f(x) = x−1x−2 , where A = R −{2} and B = R −{1}. Then f is (1) invertible and f −1(y) = 2y+1y−1 (2) invertible and f −1(y) = 3y−1y−1 (3) no invertible (4) invertible and f −1(y) = 2y−1y−1 1 −1) 2−x , x > 1, x ≠2

Q79.Let f(x) = {(x k, x = 2 The value of k for which f is continuous at x = 2 is (1) e−2 (2) e (3) e−1 (4) 1

Q79.If the function f defined as f(x) = x1 − e2x−1k−1 , x ≠0 is continuous at x = 0, then ordered pair (k, f(0)) is equal to (1) (2, 1) (2) (3, 1) (3) (3, 2) (4) ( 13 , 2)

Q79. x −4 2x 2x If 2x x −4 2x = (A + Bx) (x −A)2, then the ordered pair (A, B) is equal to 2x 2x x −4 (1) (4, 5) (2) (−4, −5) (3) (−4, 3) (4) (−4, 5)

Q79.Let S be the set of all real values of k for which the system of linear equations x + y + z = 2 2x + y −z = 3 3x + 2y + kz = 4 has a unique solution. Then, S is : (1) equal to R –{0} (2) an empty set (3) equal to R (4) equal to {0}

Q79.Let S be the set of all real values of k for which the system of linear equations x + y + z = 2 2x + y −z = 3 3x + 2y + kz = 4 has a unique solution. Then S is (1) an empty set (2) equal to R −{0} (3) equal to {0} (4) equal to R

Q80.Let S = {t ∈R : f(x) = |x −π| ⋅(e|x| −1) sin|x| is not differentiable at t}. Then, the set S is equal to: (1) {0, π} (2) ϕ (an empty set) (3) {0} (4) {π}