Practice Questions

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

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

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

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 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. 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. 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. 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. 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

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. 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. 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 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

Q2. The SI unit of a physical quantity is Pascal ‐ sec. The dimensional formula of this quantity will be (1) ML2T −1 (2) M −1L3T 0 (3) ML−1T −1 (4) ML−1T −2

Q2. Motion of a particle in x −y plane is described by a set of following equations x = 4 sin( π2 −ωt) m and y = 4 sin(ωt) m. The path of the particle will be (1) circular (2) helical (3) parabolic (4) eliptical

Q2. At time t = 0 a particle starts travelling from a height 7ˆz cm in a plane keeping z coordinate constant. At any instant of time, it's position along the x and y directions are defined as 3t and 5t3 respectively. At t = 1 s acceleration of the particle will be (1) −30y (2) 30y (3) 3x + 15y (4) 3x + 15y + 7ˆz

Q2. A ball is projected from the ground with a speed 15 m s−1 at an angle θ with horizontal so that its range and maximum height are equal, then tan θ will be equal to (1) 1 (2) 1 4 2 (3) 2 (4) 4

Q2. A person can throw a ball upto a maximum range of 100 m . How high above the ground he can throw the same ball? (1) 25 m (2) 50 m (3) 100 m (4) 200 m

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

Q3. If t = √x + 4, then ( dxdt )t=4 is: (1) 4 (2) Zero (3) 8 (4) 16

Q3. A disc with a flat small bottom beaker placed on it at a distance 𝑅 from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity 𝜔. The coefficient of static friction between the bottom of the beaker and the surface of the disc is 𝜇. The beaker will revolve with the disc if : (1) 𝑅≤𝜇𝑔 (2) 𝑅≤𝜇𝑔 2𝜔2 𝜔2 𝜇𝑔 𝜇𝑔 (3) 𝑅≥ (4) 𝑅≥ 2𝜔2 𝜔2

Q3. A monkey of mass 50 kg climbs on a rope which can withstand the tension (T) of 350 N . If monkey initially climbs down with an acceleration of 4 m s−2 and then climbs up with an acceleration of 5 m s−2 . Choose the correct option (g = 10 m s−2) (1) T = 700 N while climbing upward (2) T = 350 N while going downward (3) Rope will break while climbing upward (4) Rope will break while going downward

Q4. In two different experiments, an object of mass 5 kg moving with a speed of 25 ms-1 hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out of the following : (1) Impulse and average force acting on the object (2) Impulse will be same for both the cases but the will be same for both the cases. average force will be different. (3) Average force will be same for both the cases but (4) Average force and impulse will be different for the impulse will be different. both the cases.