Practice Questions

Q5. A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle θ with the horizontal. The weight experienced by the person is : (1) W cos θ (2) W2 (3) W (4) W sin θ

Q6. A spherical ball of radius 1 × 10−4 m and density 105 kg/m3 falls freely under gravity through a distance h before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of h is approximately: (The coefficient of viscosity of water is 9.8 × 10−6 N s/m2 ) (1) 2296 m (2) 2518 m (3) 2249 m (4) 2396 m

Q7. A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is : (1) GmMπ2 (2) GMmπ L2 2 L2 (3) 0 (4) 2GmMπ L2

Q7. Two planets A and B having masses m1 and m2 move around the sun in circular orbits of r1 and r2 radii respectively. If angular momentum of A is L and that of B is 3 L, the ratio of time period ( TBTA ) is: (1) r2 32 (2) 1 m2 3 27 ( m1 ) ( r1 ) (3) m1 3 (4) r1 3 27( m2 ) ( r2 )

Q10.The specific heat at constant pressure of a real gas obeying PV 2 = RT equation is: (1) R 3 + CV (2) CV + R (3) CV + 2VR (4) R

Q14.The following figure represents two biconvex lenses L1 and L2 having focal length 10 cm and 15 cm respectively. The distance between L1&L2 is : (1) 10 cm (2) 35 cm (3) 25 cm (4) 15 cm

Q15.In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division = 49MSD; 20 divisions on main scale in each cm For mark on paper JEE Main 2024 (06 Apr Shift 2) JEE Main Previous Year Paper MSR = 8.45 cm, VC = 26 For mark on paper seen through slab MSR = 7.12 cm, V C = 41 For powder particle on the top surface of the glass slab MSR = 4.05 cm, VC = 1 (MSR = Main Scale Reading, VC = Vernier Coincidence) Refractive index of the glass slab is : (1) 1.52 (2) 1.35 (3) 1.42 (4) 1.24

Q15.A transformer has an efficiency of 80% and works at 10 V and 4 kW . If the secondary voltage is 240 V, then the current in the secondary coil is: (1) 1 . 59 A (2) 13 . 33 A (3) 1 . 33 A (4) 15 . 1 A

Q15.Two conducting circular loops A and B are placed in the same plane with their centers coinciding as shown in figure. The mutual inductance between them is : (1) μ0πb2 (2) μo ⋅b2a 2π 2a (3) μ0 2π ⋅a2b (4) μ0πa22b

Q18.In a nuclear fission reaction of an isotope of mass 𝑀, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect 𝛥𝑀 will be : JEE Main 2024 (30 Jan Shift 2) JEE Main Previous Year Paper (1) 2𝑐𝛥𝑀 (2) 𝛥𝑀𝑐2 √ 𝑀 3 (3) 2𝛥𝑀 (4) 3𝛥𝑀 𝑐√ 𝑀 𝑐√ 𝑀

Q18.The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is 25% of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be: (1) 1 (2) 1 1 8 (3) 8 (4) 1 1 4

Q18.The energy released in the fusion of 2 kg of hydrogen deep in the sun is EH and the energy released in the fission of 2 kg of 235U is EU . The ratio EHEU is approximately: (Consider the fusion reaction as 4 ∣H + 2e−→42He + 2v + 6γ + 26.7MeV, energy released in the fission reaction of 235U is 200MeV per fission nucleus and NA = 6.023 × 1023) JEE Main 2024 (09 Apr Shift 2) JEE Main Previous Year Paper (1) 7.62 (2) 25.6 (3) 15.04 (4) 9.13

Q20.In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its 4th division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is 0.04 mm then how many main scale divisions are there in 1 cm ? (1) 10 (2) 5 (3) 20 (4) 40

Q34. List - I List - II A. Melting Point [K] I. T1 > In > Ga > A1 > B Match List I with List II B. Ionic Radius [M+3/pm] II. B > T1 > A1 ≈Ga > In Choose the C. ΔiH1 [ kJ mol−1] III. T1 > In > A1 > Ga > B D. Atomic Radius [pm] IV. B > A1 > T1 > In > Ga correct answer from the options given below: (1) A-II, B-III, C-IV, D-I (2) A-IV, B-I, C-II, D-III (3) A-I, B-II, C-III, D-IV (4) A-III, B-IV, C-I, D-II

Q37. For the given compounds, the correct order of increasing pKa value : Choose the correct answer from the options given below : (1) (B) < (D) < (C) < (A) < (E) (2) (D) < (E) < (C) < (B) < (A) (3) (E) < (D) < ( C ) < ( B ) < ( A ) (4) (E) < (D) < (B) < (A) < (C) JEE Main 2024 (09 Apr Shift 1) JEE Main Previous Year Paper

Q47.Identify the major products A and B respectively in the following set of reactions. (1) (2) (3) (4)

Q49.Which one of the following reactions is NOT possible? (1) (2) (3) (4)

Q61.Let 𝑆 be the set of positive integral values of 𝑎 for which 𝑎𝑥2 + 2𝑎+ 1𝑥+ 9𝑎+ 4 < 0, ∀𝑥∈ℝ. Then, the number 𝑥2 - 8𝑥+ 32 of elements in 𝑆 is: (1) 1 (2) 0 (3) ∞ (4) 3

Q61.Let S1 = {z ∈C : |z| ≤5}, S2 = {z ( z+1−√3i1−√3i ) ≥0} area of the region S1 ∩S2 ∩S3 is : (1) 125π (2) 125π 12 4 (3) 125π (4) 125π 24 6 Q62.60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the 50th word is : (1) JBBOH (2) OBBJH (3) OBBHJ (4) HBBJO

Q62.Let 𝑎 and 𝑏 be two distinct positive real numbers. Let 11th term of a GP, whose first term is 𝑎 and third term is 𝑏, is equal to 𝑝th term of another GP, whose first term is 𝑎 and fifth term is 𝑏. Then 𝑝 is equal to (1) 20 (2) 25 (3) 21 (4) 24

Q62.In an A.P., the sixth term a6 = 2. If the a1a4a5 is the greatest, then the common difference of the A.P., is equal to (1) 3 (2) 8 2 5 (3) 2 (4) 5 3 8

Q62.Let 𝑆= 𝑧∈𝐶: 𝑧−1 = 1 and √2 −1𝑧+ ¯𝑧- 𝑖𝑧- ¯𝑧= 2√2. Let 𝑧1, 𝑧2 ∈𝑆 be such that 𝑧1 = max𝑧∈𝑠𝑧 and 2 𝑧2 = min𝑧∈𝑠𝑧. Then √2𝑧1 −𝑧2 equals: (1) 1 (2) 4 (3) 3 (4) 2

Q62.For 0 < 𝑐< 𝑏< 𝑎, let ( 𝑎+ 𝑏– 2𝑐) 𝑥2 + ( 𝑏+ 𝑐– 2𝑎) 𝑥+ ( 𝑐+ 𝑎– 2𝑏) = 0 and 𝛼≠1 be one of its root. Then, among the two statements (I) If 𝛼∈-1, 0, then 𝑏 cannot be the geometric mean of 𝑎 and 𝑐. (II) If 𝛼∈0, 1, then 𝑏 may be the geometric mean of 𝑎 and 𝑐. (1) Both (I) and (II) are true (2) Neither (I) nor (II) is true (3) Only (II) is true (4) Only (I) is true 1 2 3

Q62.Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to (1) 18 (2) 16 (3) 12 (4) 15

Q63.The coefficient of x70 in x2(1 + x)98 + x3(1 + x)97 + x4(1 + x)96 + … + x54(1 + x)46 is 99Cp −46Cq . Then a possible value of p + q is : (1) 55 (2) 83 (3) 61 (4) 68