Practice Questions

Q90.Let y = y(x) be the solution of the differential equation x+2 ) + (y + = (x + 2)dy, y(1) = 1. If the domain of y = y(x) is an open interval (α, β), + 2)e( 1))dx ((x y+1 then |α + β| is equal to ___________. JEE Main 2021 (22 Jul Shift 1) JEE Main Previous Year Paper

Q90.Let →a = ˆi + 5ˆj + αˆk, b = ˆi + 3ˆj + βˆk and →c= −ˆi + 2ˆj −3ˆk be three vectors such that, b ×→c = 5√3 and →a → 2 is ________. is perpendicular to b. Then the greatest amongst the values of →a JEE Main 2021 (27 Aug Shift 1) JEE Main Previous Year Paper

Q6. The mass density of a planet of radius R varies with the distance r from its centre as ρ(r) = ρ0(1 −r2R2 ) Then the gravitational field is maximum at: (1) (2) r = R R r = √34 (3) r = 1 R (4) R √3 r = √59

Q21.A particle of mass 200 MeV c−2 collides with a hydrogen atom at rest. Soon after the collision, the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in eV ) is N4 . The value of N is: (Given the mass of the hydrogen atom to be 1 GeV c−2 )......... → + 2ˆj + m . Then the magnitude of torque about the point N acts at a point (4ˆi + 3ˆj −ˆk)

Q21.The sum of two forces P and Q is R such that R = P . Find the angle between resultant of 2P and Q and Q , ________ JEE Main 2020 (07 Jan Shift 2) JEE Main Previous Year Paper

Q21.A block starts moving up an inclined plane of inclination 30° with an initial velocity of v0 . It comes back to its initial position with velocity v0 2 . The value of the coefficient of kinetic friction between the block and the inclined plane is close to 1 , The nearest integer to I is : 1000

Q21. ABC is a plane lamina of the shape of an equilateral triangle. D, E are mid-points of AB, AC and G is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through G and perpendicular to the plane ABC is I0 . If part ADE is removed, the moment of inertia of the remaining part about the same axis is NI0 where N is an integer. Value of N is: 16

Q22. Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its centre of mass (see figure). If the coefficient of friction is μ = 0.4 , the maximum possible value of 100 × ba for a box not to topple before moving is ________

Q22.A particle of mass m is moving along the x-axis with initial velocity uˆi. It collides elastically with a particle of mass 10m at rest and then moves with half its initial kinetic energy (see figure). If sin θ1 = √n sin θ2 then value of n is ________. JEE Main 2020 (02 Sep Shift 2) JEE Main Previous Year Paper

Q23.In a series LR circuit, power of 400 W is dissipated from a source of 250 V, 50 Hz. The power factor of the circuit is 0. 8 . In order to bring the power factor to unity, a capacitor of value C is added in series to the L and R. Taking the value of C as ( 3πn ) μF , then value of n is

Q23.Two concentric circular coils, C1 and C2 , are placed in the XY plane. C1 has 500turns, and a radius of 1 cm . C2 has 200 turns and radius of 20 cm . C2 carries a time dependent current I(t) = (5t2 −2t + 3)A where t is in s. The emf induced in C1(in mV) at the instant t = 1 s is x4 . The value of x is ..........

Q23.A wire of density 9 × 10–3 kg cm–3 is stretched between two clamps 1 m apart. The resulting strain in the wire is 4. 9 × 10–4 . The lowest frequency of the transverse vibrations in the wire (Young's modulus of wire Y = 9 × 1010 Nm–2 ), (to the nearest integer),_______

Q24.The series combination of two batteries, both of the same emf 10V, but different internal resistance of 20 Ω and 5 Ω, is connected to the parallel combination of two resistors 30 Ω and x Ω. The voltage difference across the battery of internal resistance 20 Ω is zero, the value of x (in Ω) is____ ∘

Q24.A loop ABCDEFA of straight edges has six corner points A(0, 0, 0), B(5, 0, 0), C(5, 5, 0), D(0, 5, 0), E(0, 5, 5) and F(0, 0, 5) . The magnetic field in this region is → B = + ABCDEFA (in Wb ) is _____________ (3ˆi 4ˆk)T . The quantity of flux through the loop

Q25.A beam of electromagnetic radiation of intensity 6.4 × 10−5W/cm2 is comprised of wavelength, λ = 310nm . It falls normally on a metal (work function φ = 2eV ) of surface area of 1cm2 . If one in 103 photons ejects an election, total number of electrons ejected in 1s is 10x . (hc = 1240eVnm, 1eV = 1.6 × 10−19J), then x is ___________

Q25.In the line spectra of hydrogen atom, difference between the largest and the shortest wavelengths of the Lyman ∘ ∘ series is 305 A . The corresponding difference for the Paschan series in A is:________

Q27.The variation of equilibrium constant with temperature is given below : Temperature EquilibriumConstant T1 = 25°C K1 = 10 T2 = 100°C K2 = 100 JEE Main 2020 (06 Sep Shift 1) JEE Main Previous Year Paper The values of ΔH°, ΔG° at T1 and ΔG° at T2 (in kJ mol−1 ) respectively, are close to [use R = 8. 314 JK−1 mol−1 ] (1) 28. 4, −7. 14 and −5. 71 (2) 0. 64, −7. 14 and −5. 71 (3) 28. 4, −5. 71 and −14. 29 (4) 0. 64, −5. 71 and −14. 29

Q46.The ratio of the mass percentages of ' C & H ' and ' C & O' of a saturated acyclic organic compound ' X ' are 4 : 1 and 3 : 4 respectively. Then, the moles of oxygen gas required for complete combustion of two moles of organic compound ' X' is_______

Q46.A soft drink was bottled with a partial pressure of CO2 of 3 bar over the liquid at room temperature. The partial pressure of CO2 over the solution approaches a value of 30 bar when 44 g of CO2 is dissolved in 1 kg of water at room temperature. The approximate pH of the soft drink is ___________ ×10−1 . (First dissociation constant of H2 CO3 = 4. 0 × 10−7; log 2 = 0. 3; density of the soft drink = 1 g mL−1 ) JEE Main 2020 (05 Sep Shift 1) JEE Main Previous Year Paper

Q48.Consider the following reactions: NaCl + K2Cr2O7 + H2SO4 →(A)+ side products (Conc.) (A) + NaOH →(B)+ side products (B) + H2SO4 + H2O2 →(C)+ side products (dilute) The sum of the total number of atoms in one molecule each of (A), (B) and (C) is ________

Q48.The total number of monohalogenated organic products in the following (including stereoisomers) reaction is (i) H2/ Ni /Δ −A → (Simplest optically active alkene) (ii) X2/Δ

Q48.The elevation of boiling point of 0. 10m aqueous CrCl3. xNH3 solution is two times that of 0. 05 m aqueous CaCl2 solution. The value of x is … … … … . . [Assume 100% ionisation of the complex and CaCl2, coordination number of Cr as 6, and that all NH3 molecules are present inside the coordination sphere]

Q49.Chlorine reacts with hot and concentrated NaOH and produces compounds (X) and (Y). Compound (X) gives white precipitate with silver nitrate solution. The average bond order between Cl and O atoms in (Y) is _______________.

Q50.Complexes (ML5) of metals Ni and Fe have ideal square pyramidal and trigonal bipyramidal geometries, respectively. The sum of the 90o, 120o and 180o L −M −L angles in the two complexes is_______

Q70.Let x0 be the point of local maxima of f(x) =→a⋅(→ ×→c), →c= 7ˆi −2ˆj + xˆk. Then the value of →a⋅→b +→b ⋅→c+→c⋅→a at x = x0 is: (1) −4 (2) −30 (3) 14 (4) −22 is equal to ______