Practice Questions

Q76.Let A = {0, 3, 4, 6, 7, 8, 9, 10} and R be the relation defined on A such that R{(x, y) ∈A × A : x −y is odd positive integer or x −y = 2}. The minimum number of elements that must be added to the relation R, so that it is a symmetric relation, is equal to _________ Q77. ⎡2 1 0 ⎤ Let 1 2 −1 . If |adj(adj(adj2A))| = (16)n , then n is equal to ⎣0 −1 2 ⎦ (1) 8 (2) 10 (3) 9 (4) 12 Q78. ⎡ √32 12 ⎤ 1 1 T a b Let P = , A = and Q = PAP . If P TQ2007 P = then 2a + b −3c −4d is equal √3 [0 1] [ c d ] ⎣−12 2 ⎦ to (1) 2004 (2) 2005 (3) 2007 (4) 2006

Q76.The domain of f(x) = e2 loge x−(2x+3) (1) R −{−1, 3} (2) (2, ∞) −{3} (3) (−1, ∞) −{3} (4) R −{3}

Q76.For x ∈R, two real valued functions f(x) and g(x) are such that, g(x) = √x + 1 and fog(x) = x + 3 −√x. Then f(0) is equal to (1) 1 (2) 5 (3) 0 (4) −3

Q80.Let 𝛺 be the sample space and 𝐴⊆𝛺 be an event. Given below are two statements: (S1): If 𝑃( 𝐴) = 0, then 𝐴= 𝜙 (S2): If 𝑃( 𝐴) = , then 𝐴= 𝛺 Then (1) only (S1) is true (2) only (S2) is true (3) both (S1) and (S2) are true (4) both (S1) and (S2) are false

Q81.The integral ∫(( x2 ) x + ( x2 ) x) log2 C (1) ( x2 ) x + ( x2 ) x + C (2) ( x2 ) x −( x2 ) x + C (3) ( x2 ) x log2( x2 ) + C (4) ( x2 ) x log2( x2 ) +

Q82.The coefficient of 𝑥18 in the expansion of 𝑥4 - is ____________ 𝑥3

Q85.Let the vectors →a, b, →crepresent three coterminous edges of a parallelopiped of volume V . Then the volume of → → the parallelopiped, whose coterminous edges are represented by →a, b +→cand →a+ 2 b + 3→cis equal to (1) 2V (2) 6V (3) V (4) 3V

Q85.The remainder on dividing 599 by 11 is _____ .

Q85.The number of elements in the set {n ∈N : 10 ≤n ≤100 and 3n −3 is a multiple of 7} is _______. JEE Main 2023 (15 Apr Shift 1) JEE Main Previous Year Paper

Q88.The value of 8 𝜋∫0 sin𝑥2023 + cos𝑥2023𝑑𝑥 is ______. 3

Q88.Let →𝑎 and →𝑏 be two vector such that →𝑎= √14, →𝑏= √6 and →𝑎× →𝑏= √48. Then →𝑎· →𝑏 is equal to _____ . 𝑥- 1 𝑦+ 1 𝑧- 3

Q88.The number of elements in the set 𝑛∈ℤ: 𝑛2 - 10𝑛+ 19 < 6 is _______ .

Q88.Let P be the plane, passing through the point (1, −1, −5) and perpendicular to the line joining the points (4, 1, −3) and (2, 4, 3). Then the distance of P from the point (3, −2, 2) is (1) 6 (2) 4 (3) 5 (4) 7

Q89.The value of 12 ∫0 𝑥2 - 3𝑥+ 2dx is ______ 𝑥- 2 𝑦+ 1 𝑧- 6 𝑥- 6 1 - 𝑦 𝑧+ 8

Q90.Three dice are rolled. If the probability of getting different numbers on the three dice is p q , where p and q are co-prime, then q −p is equal to (1) 2 (2) 1 (3) 3 (4) 4 JEE Main 2023 (06 Apr Shift 2) JEE Main Previous Year Paper

Q61.If z = 2 + 3i, then z5 + (z)5 is equal to: (1) 244 (2) 224 (3) 245 (4) 265

Q63.The number of solutions of cos𝑥= sin𝑥, such that -4𝜋≤𝑥≤4𝜋 is (1) 4 (2) 6 (3) 8 (4) 12

Q64.If a1, a2, a3 … and b1, b2, b3 … . are A.P. and a1 = 2, a10 = 3, a1b1 = 1 = a10b10 then a4b4 is equal to (1) 28 (2) 28 27 24 (3) 23 (4) 22 26 23 Q65. α = sin 36° is a root of which of the following equation (1) 16x4 −20x2 + 5 = 0 (2) 16x4 + 20x2 + 5 = 0 (3) 10x4 −10x2 −5 = 0 (4) 16x4 −10x2 + 5 = 0

Q64.The remainder when 32022 is divided by 5 is (1) 1 (2) 2 (3) 3 (4) 4

Q65.Let p : Ramesh listens to music. q : Ramesh is out of his village r : It is Sunday s : It is Saturday Then the statement "Ramesh listens to music only if he is in his village and it is Sunday or Saturday" can be expressed as (1) ((~q) ∧(r ∨s)) ⇒p (2) (q ∧(r ∨s)) ⇒p (3) p ⇒(q ∧(r ∨s)) (4) p ⇒((~q) ∧(r ∨s))

Q66.Let p, q, r be three logical statements. Consider the compound statements S1 : ((~p) ∨q) ∨((~p) ∨r) and S2 : p →(q ∨r) Then, which of the following is NOT true? (1) If S2 is True, then S1 is True (2) If S2 is False, then S1 is False (3) If S2 is False, then S1 is True (4) If S1 is False, then S2 is False

Q67.If vertex of parabola is (2, −1) and equation of its directrix is 4x −3y = 21, then the length of latus rectum is (1) 2 (2) 8 (3) 12 (4) 16

Q67.The boolean expression (~(p ∧q)) ∨q is equivalent to (1) q →(p ∧q) (2) p →q (3) p →(p →q) (4) p →(p ∨q)

Q67.Consider the following two propositions : 𝑃1: ~𝑝→~𝑞 𝑃2: 𝑝∧~𝑞∧~𝑝∨𝑞 If the proposition 𝑝→~𝑝∨𝑞 is evaluated as FALSE, then (1) 𝑃1 is TRUE and 𝑃2 is FALSE (2) 𝑃1 is FALSE and 𝑃2 is TRUE (3) Both 𝑃1 and 𝑃2 are FALSE (4) Both 𝑃1 and 𝑃2 are TRUE

Q67.The statement (p ∧q) ⇒(p ∧r) is equivalent to (1) q ⇒(p ∧r) (2) p ⇒(p ∧r) (3) (p ∧r) ⇒(p ∧q) (4) (p ∧q) ⇒r JEE Main 2022 (29 Jul Shift 1) JEE Main Previous Year Paper