Practice Questions

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

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.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

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 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

Q85.The remainder on dividing 599 by 11 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

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

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

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

Q1. The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1%, 2% and 3% respectively. The maximum percentage error in the detection of the dissipated heat will be: (1) 2 (2) 4 (3) 6 (4) 8

Q1. Identify the pair of physical quantities that have same dimensions: (1) Velocity gradient and decay constant (2) Angular frequency and angular momentum (3) Wave number and Avogadro number (4) Wein's constant and Stephan's constant

Q1. The dimension of mutual inductance is (1) ML2 T−2A−1 (2) ML2 T−2A−2 (3) ML2 T−3A−1 (4) ML2 T−3A−2

Q1. Two projectiles are thrown with same initial velocity making an angle of 45° and 30° with the horizontal respectively. The ratio of their respective ranges will be (1) 1: √2 (2) √2: 1 (3) 2: √3 (4) √3: 2

Q1. If 𝑍= 𝐴2𝐵3 , then the relative error in 𝑍 will be 𝐶4 2𝛥𝐴 3𝛥𝐵 4𝛥𝐶 𝛥𝐴 𝛥𝐵 𝛥𝐶 (1) 𝐴+ 𝐵+ 𝐶 (2) 𝐴+ 𝐵+ 𝐶 (3) 2𝛥𝐴 3𝛥𝐵 4𝛥𝐶 (4) 𝛥𝐴 𝛥𝐵 𝛥𝐶 𝐴+ 𝐵- 𝐶 𝐴+ 𝐵- 𝐶 Q2. →𝐴 is a vector quantity such that →𝐴= non-zero constant. Which of the following expression is true for →𝐴? (1) →𝐴· →𝐴= 0 (2) →𝐴× →𝐴< 0 (3) →𝐴× →𝐴= 0 (4) →𝐴× →𝐴> 0

Q1. Two buses 𝑃 and 𝑄 start from a point at the same time and move in a straight line and their positions are represented by 𝑥𝑃𝑡= 𝛼𝑡+ 𝛽𝑡2 and 𝑥𝑄𝑡= 𝑓𝑡- 𝑡2. At what time, both the buses have same velocity ? (1) 𝛼- 𝑓 (2) 𝛼+ 𝑓 1 + 𝛽 2𝛽- 1 (3) 𝛼+ 𝑓 (4) 𝑓- 𝛼 21 + 𝛽 21 + 𝛽

Q1. Match List I with List II. List I List II (A) Torque (I) Nms-1 (B) Stress (II) Jkg-1 (C) Latent Heat (III) Nm (D) Power (IV) Nm-2 Choose the correct answer from the options given below: (1) A - III, B - II, C - I, D - IV (2) A - III, B - IV, C - II, D - I (3) A - IV, B - I, C - III, D - II (4) A - II, B - III, C - I, D - IV

Q1. The distance of the Sun from earth is 1. 5 × 1011 m and its angular diameter is 2000′′ when observed from the earth. The diameter of the Sun will be (1) 2. 45 × 1010 m (2) 1. 45 × 1010 m (3) 1. 45 × 109 m (4) 0. 14 × 109 m

Q1. Two projectile thrown at 30° and 45° with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is (1) 1 : √2 (2) 2 : 1 (3) √2 : 1 (4) 1 : 2

Q2. A NCC parade is going at a uniform speed of 9 km h-1 under a mango tree on which a monkey is sitting at a height of 19 . 6 m. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is : (Given 𝑔= 9 . 8 m s-2) (1) 5 m (2) 10 m (3) 19 . 8 m (4) 24 . 5 m