Practice Questions

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

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

Q79.For 𝑥∈𝑅- 0, 1, let 𝑓1𝑥= 𝑥, 𝑓2𝑥= 1 - 𝑥 and 𝑓3𝑥= 1 - 𝑥 be three given functions. If a function, 𝐽𝑥 satisfies 𝑓2𝑜𝐽𝑜𝑓1𝑥= 𝑓3𝑥 then 𝐽𝑥 is equal to: (1) 𝑓3𝑥 (2) 1 𝑥𝑓3𝑥 (3) 𝑓1𝑥 (4) 𝑓2𝑥

Q84.The value of 𝜋cos𝑥3𝑑𝑥 is ∫0 2 (1) (2) 0 3 (3) 4 (4) -4 3 3

Q87.Let α = (λ −2) →a+ b and β = (4λ −2) →a+ 3 b, be two given vectors where vectors →a and b are non-collinear. → → The value of λ for which vectors α and β are collinear, is: (1) −4 (2) −3 (3) 4 (4) 3

Q87.Let →a = 2ˆi + λ1ˆj + 3ˆk, b = 4ˆi + (3 −λ2)ˆj + 6ˆk and →c= 3ˆi + 6ˆj + (λ3 −1)ˆk be three vectors such that → b = 2→a and →a is perpendicular to →c. Then a possible value of (λ1, λ2, λ3) is (1) (−12 , 4, 0) (2) (1, 5, 1) (3) ( 12 , 4, −2) (4) (1, 3, 1)

Q87.If a unit vector →a makes angles θ ∈(0, π) with ˆk, then a value of θ is: 3 with ˆi, π4 with ˆj and (1) 5π (2) 5π 6 12 (3) π (4) 2π 4 3

Q89.In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is : (1) 1 (2) 5 6 6 (3) 1 (4) 2 3 3

Q90.Four persons can hit a target correctly with probabilities 1 2 , 13 , 14 and 18 respectively. If all hit at the target independently, then the probability that the target would be hit, is (1) 25 (2) 7 192 32 (3) 1 (4) 25 192 32 JEE Main 2019 (09 Apr Shift 1) JEE Main Previous Year Paper

Q90.Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is: (1) 8 (2) 6 (3) 5 (4) 7 JEE Main 2019 (10 Apr Shift 2) JEE Main Previous Year Paper

Q90.Let 𝐴 and 𝐵 be two non-null events such that 𝐴⊂𝐵. Then, which of the following statements is always correct? (1) 𝑃𝐴| 𝐵≥𝑃( 𝐴) (2) 𝑃𝐴| 𝐵= 𝑃𝐵- 𝑃𝐴 (3) 𝑃𝐴| 𝐵≤ 𝑃( 𝐴) (4) 𝑃𝐴| 𝐵= 1 JEE Main 2019 (08 Apr Shift 1) JEE Main Previous Year Paper

Q1. The relative error in the determination of the surface area of a sphere is α. The relative error in the determination of its volume is (1) 3 α (2) 2 α 2 3 (3) α (4) 5 α 2

Q1. The relative error in the determination of the surface area of a sphere is α. Then the relative error in the determination of its volume is (1) 2 α (2) 2 α 3 3 (3) 3 α (4) α 2

Q1. The density of a material, in the shape of a cube, is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are 1. 5% and 1%, respectively, the maximum error in determining the density is: (1) 6 % (2) 2.5 % (3) 3.5 % (4) 4.5 %

Q2. The percentage errors in quantities P , Q , R and S are 0. 5%, 1%, 3% and 1. 5% respectively in the P 3Q2 measurement of a physical quantity A= . The maximum percentage error in the value of A will be: √RS (1) 6.5 % (2) 7.5 % (3) 6.0 % (4) 8.5 %

Q3. An automobile, traveling at 40 km h−1 , can be stopped at a distance of 40 m by applying brakes. If the same automobile is traveling at 80 km h−1 , the minimum stopping distance in metres is (Assume no skidding): (1) 150 m (2) 100 m (3) 75 m (4) 160 m

Q10.One mole of an ideal monatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, 27oC . The magnitude of work done on the gas will be: (1) 300R (2) 300R ln 2 (3) 300 ln 6 (4) 300R ln 7

Q13.The end correction of a resonance column is 1 cm . If the shortest length resonating with the tuning fork is 10 cm, the next resonating length should be (1) 32 cm (2) 40 cm (3) 28 cm (4) 36 cm JEE Main 2018 (16 Apr Online) JEE Main Previous Year Paper

Q15.The equivalent capacitance between A and B in the circuit given below is: (1) 4.9μF (2) 3.6μF (3) 5.4μF (4) 2.4μF

Q15.The equivalent capacitance between A and B in the circuit is given below. (1) 3. 6 μF (2) 2. 4 μF (3) 4. 9 μF (4) 5. 4 μF

Q17.A heating element has a resistance of 100 Ω at room temperature. When it is connected to a supply of 220 V, a steady current of 2 A passes in it and temperature is 500 oC more than the room temperature. The temperature coefficient of resistance of the heating element is (1) 5 × 10−4 oC−1 (2) 2 × 10−4 oC−1 (3) 1 × 10−4 oC−1 (4) 0.5 × 10−4 oC−1

Q18.A galvanometer with its coil resistance 25 Ω requires a current of 1 mA for its full deflection. In order to construct an ammeter to read up to a current of 2 A the approximate value of the shunt resistance should be: (1) 1.25 × 10−2 Ω (2) 2.5 × 10−3 Ω (3) 2.5 × 10−2 Ω (4) 1.25 × 10−3 Ω