Practice Questions

Q74.The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then the absolute value of the difference of the other two observations, is : (1) 3 (2) 5 (3) 7 (4) 1

Q74.A student scores the following marks in five tests: 45,54,41,57,43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is: 10 100 (1) (2) 3 3 (3) 10 (4) 100 √3 √3

Q74. lim cot3x−tanxπ is x→π4 cos(x+ 4 ) (1) 4√2 (2) 8√2 (3) 4 (4) 8

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

Q75.The number of values of θ ∈(0, π) for which the system of linear equations x + 3y + 7z = 0 −x + 4y + 7z = 0 (sin 3θ)x + (cos 2θ)y + 2z = 0 has a non-trivial solution, is: (1) Two (2) Three (3) Four (4) One

Q75.If 𝐴 is a symmetric matrix and 𝐵 is skew- symmetric matrix such that 𝐴+ 𝐵= 2 3 , then 𝐴𝐵 is equal to: 5 -1 (1) -4 2 (2) 4 -2 1 4 1 -4 (3) 4 -2 (4) -4 -2 -1 -4 -1 4

Q75.The logical statement [~(~p ∨q) ∨(p ∧r)] ∧(~q ∧r) is equivalent to (1) (~p ∧~q) ∧r (2) (p ∧r) ∧~q (3) (p ∧~q) ∨r (4) ~p ∨r

Q75. ABC is a triangular park with AB = AC = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at, A and B are cot−1(3√2) and cosec−1(2√2) respectively, then the height of the tower (in metres) is (1) 100 (2) 20 3√3 (3) 25 (4) 10√5

Q75.If q is false and p ∧q ↔r is true, then which one of the following statements is a tautology? (1) (p ∨r) →(p ∧r) (2) (p ∧r) →(p ∨r) (3) p ∧r (4) p ∨r

Q75.Two vertical poles of height, 20 𝑚 and 80 𝑚 stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, from this horizontal plane is: (1) 16 (2) 12 (3) 18 (4) 15

Q75.If both the mean and the standard deviation of 50 observations 𝑥1, 𝑥2, … , 𝑥50 are equal to 16, then the mean of 𝑥1 - 42, 𝑥2 - 42, … , 𝑥50 - 42 is (1) 525 (2) 480 (3) 400 (4) 380

Q75.The mean and the median of the following ten numbers in increasing order 10, 22, 26, 29, 34, x, 42, 67, 70, y are 42 and 35 respectively, then xy is equal to: (1) 9 (2) 7 4 3 (3) 7 (4) 8 2 3

Q75.The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is (1) 10 : 3 (2) 4 : 9 (3) 6 : 7 (4) 5 : 8

Q75. y + 1 α β Let α and β be the roots of the equation x2 + x + 1 = 0. Then for y ≠0 in R, α y + β 1 is equal β 1 y + α to (1) y3 (2) y(y2–1) (3) y3–1 (4) y(y2–3)

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

Q75.If the angle of elevation of a cloud from a point P which is 25m above a lake be 30o and the angle of depression of reflection of the could in the lake from P be 60o , then the height of the cloud (in meters) from JEE Main 2019 (12 Jan Shift 2) JEE Main Previous Year Paper the surface of the lake is : (1) 50 (2) 60 (3) 45 (4) 42 and B = {x ∈Z : −3 < 2x −1 < 9},

Q75.Let A and B be two invertible matrices of order 3 × 3. If det (ABAT) (BA−1 BT) is equal to (1) 1 (2) 1 4 (3) 1 (4) 16 16

Q75.Let 𝐴= cos𝛼-sin𝛼 𝑎∈𝑅 such that 𝐴32 = 0 -1 . Then, a value of 𝛼 is: sin𝛼 cos𝛼, 1 0 (1) 0 (2) 𝜋 (3) 𝜋 (4) 𝜋 16 64 32 JEE Main 2019 (08 Apr Shift 1) JEE Main Previous Year Paper

Q76.If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is : (1) 30 (2) 51 (3) 50 (4) 31 Q77. ⎡ 1 0 0⎤ 5 q21+q31 Let P = 3 1 0 and Q = [qij] be two 3 × 3 matrices such that Q −P = I3 . Then q32 is equal to : ⎣ 9 3 1⎦ (1) 10 (2) 9 (3) 15 (4) 135

Q76.A data consists of n observations: x1, x2, … , xn. If ∑ni=1 (xi + 1)2 = 9n and ∑ni=1 (xi −1)2 = 5n, then the standard deviation of this data is JEE Main 2019 (09 Jan Shift 2) JEE Main Previous Year Paper (1) 5 (2) √7 (3) √5 (4) 2

Q76.Two poles standing on a horizontal ground are of heights 5 m and 10 m respectively. The line joining their tops makes an angle of 15° with the ground. Then the distance (in m) between the poles, is + (1) 10(√3 −1) (2) 52 (2 √3) + + (3) 5(2 √3) (4) 5(√3 1) Q77. ⎛ 0 2y 1 ⎞ The total number of matrices A = 2x y −1 , (x, y ∈R, x ≠y) for which ATA = 3I3 is: ⎝ 2x −y 1 ⎠ (1) 6 (2) 3 (3) 4 (4) 2

Q76.The greatest value of 𝑐∈𝑅 for which the system of linear equations 𝑥- 𝑐𝑦- 𝑐𝑧= 0, 𝑐𝑥- 𝑦+ 𝑐𝑧= 0, 𝑐𝑥+ 𝑐𝑦- 𝑧= 0 has a non-trivial solution, is (1) -1 (2) 2 (3) 1 (4) 0 2

Q76.The value of sin-1⁡12 - sin-1⁡3 is equal to: 13 5 33 𝜋 9 (1) 𝜋- cos-1⁡ (2) - cos-1⁡ 65 2 65 𝜋 56 (3) 𝜋- sin-163 (4) - sin-1⁡ 65 2 65

Q76.If the system of linear equations x + y + z = 5 , x + 2y + 2z = 6 , x + 3y + λz = µ, (λ, µ ∈R) , has infinitely many solutions, then the value of λ + µ is: (1) 7 (2) 10 (3) 12 (4) 9

Q76.If 𝐴= cos𝜃-sin𝜃 , then the matrix 𝐴-50 when 𝜃= 𝜋 is equal to: sin𝜃 cos𝜃 12, (1) √3 1 (2) 1 √3 2 2 2 2 -1 √3 -√3 1 2 2 2 2 (3) √3 -1 (4) 1 -√3 2 2 2 2 1 √3 √3 1 2 2 2 2