Practice Questions

Q73.For each t ∈R, let [t] be the greatest integer less than or equal to t. Then, lim x→1+ |1−x|[1−x] (1) equals 0 (2) equals −1 (3) does not exist (4) equal 1

Q74. a −b −c 2a 2a If 2b b −c −a 2b = (a + b + c)(x + a + b + c)2, x ≠0 and a + b + c ≠0, then x is 2c 2c c −a −b equal to (1) abc (2) −(a + b + c) (3) 2(a + b + c) (4) −2(a + b + c) = 8 and det (AB−1) = 8, then det

Q74.If the Boolean expression 𝑝⊕𝑞∧~𝑝⊙𝑞 is equivalent to 𝑝∧𝑞, where ⊕, ⊙∈∧, ∨, then the ordered pair ⊕, ⊙ is (1) ∨, ∧ (2) ∧, ∧ (3) ∨, ∨ (4) ∧, ∨ Q75.5 students of a class have an average height 150 𝑐𝑚 and variance 18 𝑐𝑚2 . A new student, whose height is 156 𝑐𝑚, joined them. The variance in 𝑐𝑚2 of the height of these six students is: (1) 22 (2) 16 (3) 18 (4) 20

Q74.Consider the statement: " P(n) : n2 −n + 41 is prime". Then which one of the following is true? (1) P(3) is false but P(5) is true (2) Both P(3) and P(5) are false (3) Both P(3) and P(5) are true (4) P(5) is false but P(3) is true

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

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. lim x+2sinx is x→0 √x2+2 sin x+1 − √sin2x−x+1 (1) 3 (2) 1 (3) 2 (4) 6

Q74.If p ⇒(q ∨r) is False , then the truth values of p, q, r are respectively, (where T is True and F is False ) (1) T, F, F (2) F, T, T (3) F, F, F (4) T, T, F

Q74.The mean and variance for seven observations are 8 and 16 respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the product of the remaining two observations is (1) 48 (2) 45 (3) 49 (4) 40

Q74.If for some x ∈R, the frequency distribution of the marks obtained by 20 students in a test is: Marks 2 3 5 7 Frequency distribution (x + 1)2 (2x −5) x2 −3x x JEE Main 2019 (10 Apr Shift 1) JEE Main Previous Year Paper Then the mean of the marks is : (1) 3.0 (2) 2.5 (3) 3.2 (4) 2.8

Q74.The negation of the Boolean expression ~𝑠∨~𝑟∧𝑠 is equivalent to (1) 𝑟 (2) 𝑠∧𝑟 (3) 𝑠∨𝑟 (4) ~𝑠∧~𝑟

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.For each x ∈R, let [x] be the greatest integer less than or equal to x . Then lim x([x]+|x|) sin[x] is equal to x→0− |x| (1) 1 (2) 0 (3) −sin 1 (4) sin 1

Q74.If [10 11 ][10 21 ][10 31 ] [10 n −11 ] [10 781 ], [10 n1 ] (1) [10 –121 ] (2) [121 10 ] (3) [131 10 ] (4) [10 –131 ]

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

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

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 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