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JEE Main 2020 9 Jan Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 20209 Jan, Morning shift

Physics 16Chemistry 14Mathematics 25

Physics

Q46In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25 A to 0 in a duration…Electromagnetic Induction and Alternating Currents
Q54The distance x covered by a particle in one dimensional motion varies with time t as x² = at² + 2bt + c. If the acceleration of the particle depends on x as…Kinematics
Q55A body of mass m = 10 kg is attached to one end of a wire of length 0.3 m. The maximum angular speed (in rad s^–1) with which it can be rotated about its…Rotational Motion
Q6220Two particles of equal mass m have respective initial velocities u i and u((i + j)/2). They collide completely inelastically. The energy lost in the process is:Rotational Motion
Q6550A particle moving with kinetic energy E has de Broglie wavelength λ. If energy Δ E is added to its energy, the wavelength become λ /2. Value of Δ E, is:Dual Nature of Matter and Radiation
Q6634Radiation, with wavelength 6561 A^(o) falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of 3 ×…Dual Nature of Matter and Radiation
Q6767The electric fields of two plane electromagnetic plane waves in vacuum are given by E₁ = E₀ j cos (ω t - kx) and E₂ = E₀ k cos (ω t - ky) At t = 0, a particle…Electromagnetic Waves
Q6943An electric dipole of moment p = (- i - 3 j + 2 k) × 10⁻²⁹ C.m is at the origin (0, 0, 0). The electric field due to this dipole at r = + i + 3 j + 5 k (note…Electrostatics
Q7065The aperture diameter of a telescope is 5m. The separation between the moon and the earth is 4 × 10⁵ km. With light of wavelength of 5500 A^(o), the minimum…Optics
Q7104A vessel of depth 2h is half filled with a liquid of refractive index 2 2 and the upper half with another liquid of refractive index 2. The liquids are…Optics
Q7259A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass m/2 collides with A with a velocity which is half ((v)/2)…Gravitation
Q7300Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an…Thermodynamics
Q7659A long, straight wire of radius a carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance…Magnetic Effects of Current and Magnetism
Q8239A quantity f is given by f = h c⁵ G where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of:Units and Measurements
Q8334If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on the circular scale the least count of…Experimental Skills
Q8550Three harmonic waves having equal frequency ν and same intensity I₀, have phase angles 0, (π)/4 and - (π)/4 respectively. When they are superimposed the…Oscillations and Waves

Chemistry

Q14The molarity of HNO₃ in a sample which has density 1.4 g/mL and mass percentage of 63% is _ _ _. (Molecular Weight of HNO₃ = 63)Some Basic Concepts in Chemistry
Q15The hardness of a water sample containing 10^–3 M MgSO₄ expressed as CaCO₃ equivalents (in ppm) is _ _ _. (molar mass of MgSO₄ is 120.37 g/mol)Some Basic Concepts in Chemistry
Q368If the magnetic moment of a dioxygen species is 1.73 B.M, it may be:Chemical Bonding and Molecular Structure
Q450For the following reactions A 700K Product A 0pt catalyst ^(500K) Product it was found that E a is decreased by 30 kJ/mol in the presence of catalyst. If the…Chemical Kinetics
Q511A chemist has 4 samples of artificial sweetener A, B, C and D. To identify these samples, he performed certain experiments and noted the following…Chemistry in Everyday Life
Q623[Pd(F)(Cl)(Br)(I)]²– has n number of geometrical isomers. Then, the spin-only magnetic moment and crystal field stabilisation energy [CFSE] of [Fe(CN)₆]ⁿ–6…Coordination Compounds
Q682Complex X of composition Cr(H₂O)₆Cl n has a spin only magnetic moment of 3.83 BM. It reacts with AgNO₃ and shows geometrical isomerism. The IUPAC nomenclature…Coordination Compounds
Q1338The K s p for the following dissociation is 1.6 × 10^–5 PbC l 2(s) Pb (aq) ²⁺ + 2Cl (aq) ^(- W)hich of the following choices is correct for a mixture of 300…Equilibrium
Q1603B has a smaller first ionization enthalpy than Be. Consider the following statements: (I) It is easier to remove 2p electron than 2s electron (II) 2p electron…Classification of Elements and Periodicity in Properties
Q1633The acidic, basic and amphoteric oxides, respectively, are:Classification of Elements and Periodicity in Properties
Q1650The electronic configurations of bivalent europium and trivalent cerium are (atomic number: Xe = 54, Ce = 58, Eu = 63)Classification of Elements and Periodicity in Properties
Q1806The compound that cannot act both as oxidising and reducing agent is:Redox Reactions and Electrochemistry
Q2116The de Broglie wavelength of an electron in the 4th Bohr orbit is:Atomic Structure
Q2358If enthalpy of atomisation for Br₂(1) is x kJ/mol and bond enthalpy for Br₂ is y kJ/mol, the relation between them:Chemical Thermodynamics

Mathematics

Q18The projection of the line segment joining the points (1, –1, 3) and (2, –4, 11) on the line joining the points (–1, 2, 3) and (3, –2, 10) is _ _ _ _ _ _.Three Dimensional Geometry
Q20The coefficient of x⁴ is the expansion of (1 + x + x²)¹⁰ is _ _ _.Binomial Theorem and Its Simple Applications
Q25If for x ≥ 0, y = y(x) is the solution of the differential equation (x + 1)dy = ((x + 1)² + y – 3)dx, y(2) = 0, then y(3) is equal to _ _ _ _.Differential Equations
Q31The number of distinct solutions of the equation log 1/2 | sin x | = 2 - log 1/2 | cos x | in the interval [0, 2 π ], is _ _.Limit, Continuity and Differentiability
Q42If the vectors, p = (a + 1) i + a j + a k, q = a i + (a + 1) j + a k and r = a i + a j + (a + 1) k(a R) are coplanar and 3(p. q)² - λ | r × q |² = 0, then the…Vector Algebra
Q2745A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness the melts at a rate of 50 cm³/min. When the thickness of ice is 5 cm…Limit, Continuity and Differentiability
Q3128A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to this circle?Coordinate Geometry
Q3256Let z be complex number such that | (z - i)/(z + 2i) | = 1 and |z| = 5/2. Then the value of |z + 3i| is:Complex Numbers and Quadratic Equations
Q3390If for all real triplets (a, b, c), ƒ(x) = a + bx + cx²; then ∫₀¹ f(x)dx is equal to:Integral Calculus
Q3391The value of ∫₀^(2π) x sin ⁸ x sin ⁸x + cos ⁸x dx is equal to:Integral Calculus
Q3968If e₁ and e₂ are the eccentricities of the ellipse, (x²)/18 + (y²)/4 = 1 and the hyperbola, (x²)/9 - (y²)/4 = 1 respectively and (e₁, e₂) is a point on the…Coordinate Geometry
Q4025The integral ∫ dx/((x + 4)^(8/7)(x - 3)^(6/7)) is equal to: (where C is a constant of integration)Integral Calculus
Q4051If ƒ'(x) = tan^–1(secx + tanx), - (π)/2 < x < (π)/2, and ƒ(0) = 0, then ƒ(1) is equal to:Integral Calculus
Q4141If f(x) = \ (sin (a + 2)x + sin x)/x; x < 0 b; x = 0 ((x + 3x²)^(1/3) - x^(1/3))/(x^(4/3)); x > 0. is continuous at x = 0, then a + 2b is equal to:Limit, Continuity and Differentiability
Q4193Let ƒ be any function continuous on [a, b] and twice differentiable on (a, b). If for all x (a, b), ƒ'(x) > 0 and ƒ''(x) < 0, then for any c (a, b), (f(c)…Limit, Continuity and Differentiability
Q4411Negation of the statement: 5 is an integer or 5 is an irrational is:Mathematical Reasoning
Q4522If the matrices A = [ 1 1 2 1 3 4 1 - 1 3 ], B = adjA and C = 3A, then (| adjB |)/(| C |) is equal to:Matrices and Determinants
Q4582If for some α and β in R, the intersection of the following three places x + 4y – 2z = 1 x + 7y – 5z = b x + 5y + α z = 5 is a line in R³, then α + β is equal…Matrices and Determinants
Q4795If the number of five digit numbers with distinct digits and 2 at the 10^(t)h place is 336 k, then k is equal to:Permutations and Combinations
Q4910In a box, there are 20 cards, out of which 10 are lebelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and…Statistics and Probability
Q5044The number of real roots of the equation, e⁴x + e³x – 4e²x + eˣ + 1 = 0 is:Complex Numbers and Quadratic Equations
Q5315The product 2^(1/4).4^(1/16).8^(1/48).16^(1/128)... to ∞ is equal to:Sequence and Series
Q5457Let the observations x i (1 ≤ i ≤ 10) satisfy the equations, Σ i = 1 ¹⁰ (x₁ - 5) = 10 and Σ i = 1 ¹⁰ (x₁ - 5)² = 40. If μ and λ are the mean and the variance…Statistics and Probability
Q5534Let C be the centroid of the triangle with vertices (3, –1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y – 1 = 0 and 3x – y + 1…Coordinate Geometry
Q5652The value of cos ³((π)/8) cos ((3π)/8) + sin ³((π)/8) sin ((3π)/8) is:Trigonometry