Practice Questions

Q23.A wire of cross sectional area A, modulus of elasticity 2 × 1011Nm−2 and length 2 m is stretched between two vertical rigid supports. When a mass of 2 kg is suspended at the middle it sags lower from its original position JEE Main 2024 (06 Apr Shift 2) JEE Main Previous Year Paper making angle θ = 1001 radian on the points of support. The value of A is _______ ×10−4 m2 (consider x << L ). (given : g = 10 m/s2 )

Q25.A capacitor of 10μF capacitance whose plates are separated by 10 mm through air and each plate has area 4 cm2 is now filled equally with two dielectric media of K1 = 2, K2 = 3 respectively as shown in figure. If new force between the plates is 8 N . The supply voltage is _________ ×10−4 V . (we modified language of question to make it correct)

Q25.An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density +σ. The electron at t = 0 is at a distance of 1 m from S and has a speed of 1 m s−1 . The maximum value of σ, if the electron strikes S at t = 1 s is α[ mϵ0e ] m2C . The value of α is _____.

Q25.A thin metallic wire having cross sectional area of 10−4 m2 is used to make a ring of radius 30 cm. A positive charge of 2π C is uniformly distributed over the ring, while another positive charge of 30 pC is kept at the centre of the ring. The tension in the ring is _______ N; provided that the ring does not get deformed (neglect the influence of gravity). (Given, 1 = 9 × 109 SI units) 4πϵ0

Q26.Two identical charged spheres are suspended by strings of equal lengths. The string make an angle of 37° with each other. When suspended in a liquid of density 0 . 7 g cm-3, the angle remains same. If density of material 3 of the sphere is 1 . 4 g cm-3, the dielectric constant of the liquid is _____ tan37° = 4

Q26.Twelve wires each having resistance 2Ω are joined to form a cube. A battery of 6 V emf is joined across point a and c. The voltage difference between e and f is ______V.

Q26.A heater is designed to operate with a power of 1000 W in a 100 V line. It is connected in combination with a resistance of 10Ω and a resistance R, to a 100 V mains as shown in figure. For the heater to operate at 62.5 W, the value of R should be _____ Ω.

Q27.A square loop of edge length 2 m carrying current of 2 A is placed with its edges parallel to the x y axis. A magnetic field is passing through the x −y plane and expressed as →B = B0(1 + 4x)^k, where B0 = 5 T. The net magnetic force experienced by the loop is _______ N .

Q28.An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of 20μF is _____V.

Q28.A small square loop of wire of side 𝑙 is placed inside a large square loop of wire of side 𝐿𝐿= 𝑙2. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is √𝑥× 10-7 H, where 𝑥= ______.

Q28.A rectangular loop of sides 12 cm and 5 cm, with its sides parallel to the 𝑥-axis and 𝑦-axis respectively moves with a velocity of 5 cm s-1 in the positive 𝑥 axis direction, in a space containing a variable magnetic field in the positive 𝑧 direction. The field has a gradient of 10-3 T cm-1 along the negative 𝑥 direction and it is decreasing with time at the rate of 10-3 T s-1 . If the resistance of the loop is 6 m𝛺, the power dissipated by the loop as heat is ______ × 10-9 W .

Q28.A square loop PQRS having 10 turns, area 3.6 × 10−3 m2 and resistance 100Ω is slowly and uniformly being pulled out of a uniform magnetic field of magnitude B = 0.5 T as shown. Work done in pulling the loop out of JEE Main 2024 (08 Apr Shift 1) JEE Main Previous Year Paper the field in 1.0 s is ______ ×10−6 J.

Q29.Two slits are 1 mm apart and the screen is located 1 m away from the slits. A light of wavelength 500 nm is used. The width of each slit to obtain 10 maxima of the double slit pattern within the central maximum of the JEE Main 2024 (08 Apr Shift 2) JEE Main Previous Year Paper single slit pattern is _____ ×10−4 m

Q30.A star has 100% helium composition. It starts to convert three 4He into one 12C via triple alpha process as 4He + 4He + 4He →12C + Q. The mass of the star is 2.0 × 1032 kg and it generates energy at the rate of 5.808 × 1030 W. The rate of converting these 4He to 12C is n × 1042 s−1 , where n is _________ [ Take, mass of 4He = 4.0026u, mass of 12C = 12u ]

Q30.When a hydrogen atom going from n = 2 to n = 1 emits a photon, its recoil speed is x5 m s−1 . Where x = _______. (Use: mass of hydrogen atom = 1. 6 × 10−27 kg , charge of electron e = 1. 6 × 10−19 C)

Q30.A hydrogen atom changes its state from n = 3 to n = 2. Due to recoil, the percentage change in the wave length of emitted light is approximately 1 × 10−n . The value of n is_____. [Given Rhc = 13.6eV, hc = 1242eVnm, h = 6.6 × 10−34 J s mass of the hydrogenatom = 1.6 × 10−27 kg ] JEE Main 2024 (04 Apr Shift 1) JEE Main Previous Year Paper

Q51.Frequency of the de-Broglie wave of electron in Bohr's first orbit of hydrogen atom is _______ ×1013 Hz [Given : RH( Rydberg constant ) = 2.18 × 10−18 J, h (Plank's (nearest integer). constant ) = 6.6 × 10−34 J.s.]

Q51.Consider the following reactions NiS + HNO3 + HCl →A + NO + S + H2O A + NH4OH + H3C −C = N −OH | →B + NH4Cl + H2O The number of protons that do not involve in H3C −C = N −OH hydrogen bonding in the product B is ______.

Q52.The number of species from the following which are paramagnetic and with bond order equal to one is H2, He+2 , O+2 , N2−2 , O2−2 , F2, Ne+2 , B2

Q53.An ideal gas, Cv = 2 R, is expanded adiabatically against a constant pressure of 1 atm untill it doubles in volume. If the initial temperature and pressure is 298 K and 5 atm, respectively then the final temperature is – _______ K (nearest integer). [ Cv is the molar heat capacity at constant volume] JEE Main 2024 (06 Apr Shift 1) JEE Main Previous Year Paper ′′ −

Q55.Consider the dissociation of the weak acid HX as given below HX(aq) ⇌H+(aq) + X−(aq), Ka = 1.2 × 10−5 [Ka : dissociation constant ] The osmotic pressure of 0.03M aqueous solution of HX at 300 K is _______ ×10−2 bar (nearest integer). [Given : R = 0.083 Lbarmol−1 K−1 ]

Q55.Considering acetic acid dissociates in water, its dissociation constant is 6.25 × 10−5 . If 5 mL of acetic acid is dissolved in 1 litre water, the solution will freeze at −x × 10−2∘C, provided pure water freezes at 0∘C. x = (Kf)water = 1.86 K kg mol−1. density of acetic acid is 1.2 g mol−1. ______ . (Nearest integer) Given : molar mass of water = 18 g mol−1. Acetic acid dissociates as molar mass of acetic acid=60 gmol−1. density of water = 1 g cm−3 CH3COOH ⇌CH3COO⊖+ H⊕

Q55.How many compounds among the following compounds show inductive, mesomeric as well as hyperconjugation effects?

Q55.Total number of aromatic compounds among the following compounds is ______.

Q57.The fusion of chromite ore with sodium carbonate in the presence of air leads to the formation of products A and B along with the evolution of CO2 . The sum of spin-only magnetic moment values of A and B is ______ B.M. (Nearest integer) [Given atomic number : C : 6, Na : 11, O : 8, Fe : 26, Cr : 24]