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JEE Main 2019 12 Jan Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 201912 Jan, Morning shift

Physics 17Chemistry 19Mathematics 29

Physics

Q5991A particle of mass m moves in a circular orbit in a central potential field U(r) = 1/2 kr². If Bohr 's quantization conditions are applied, radii of possible…Atoms and Nuclei
Q6215A simple pendulum, made of a string of length and a bob of mass m, is released from a small angle θ ₀. It strikes a block of mass M, kept on a horizontal…Rotational Motion
Q6346A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is the modulation index ?Communication Systems
Q6426Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers…Current Electricity
Q6502An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and esistance 5 Ω. The value of R, to…Current Electricity
Q6541A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another particle B of mass ' 4 m' and charge 'q' is accelerated by a…Dual Nature of Matter and Radiation
Q6752A light wave is incident normally on a glass slab of refractive index 1.5. If 4% of light gets reflected and the amplitude of the electric field of the…Electromagnetic Waves
Q7185A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with…Gravitation
Q7258A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass 'm' at x = 0, if the mass per unit length of the…Gravitation
Q7293An ideal gas occupies a volume of 2m³ at a pressure of 3 × 10⁶ Pa. The energy of the gas is:Thermodynamics
Q7342A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner…Properties of Solids and Liquids
Q7747A proton and an α -particle (with their masses in the ratio of 1: 4 and charges in the ratio of 1: 2) are accelerated from rest through a potential difference…Magnetic Effects of Current and Magnetism
Q7815A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60^(o) with ground level. But he finds the aeroplane…Kinematics
Q7873A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of times…Kinematics
Q8091Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin cylinder…Rotational Motion
Q8331The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 μ m diameter of a wire…Experimental Skills
Q8493A travelling harmonic wave is represented by the equation y(x,t) = 10^–3sin (50t + 2x), where, x and y are in mater and t is in seconds. Which of the…Oscillations and Waves

Chemistry

Q45In the following reaction: Aldehyde + Alcohol HCl Acetal Aldehyde Alcohol HCHO t B uOH CH₃CHO MeOH The best combination isOrganic Compounds Containing Oxygen
Q200Among the following compounds most basic amino acid is -Biomolecules
Q474Decomposition of X exhibits a rate constant of 0.05 μ g/year. How many year are required for the decomposition of 5 μ g of X into 2.5 μ g?Chemical Kinetics
Q559Mn₂(CO)₁₀ is an organometallic compound due to the presence of -Coordination Compounds
Q613The pair of metal ions that can give a spin only magnetic moment of 3.9 BM for the complex [M(H₂O)₆]Cl₂, is -Coordination Compounds
Q721The metal d-orbitals that are directly facing the ligands in K₃[Co(CN)₆] are -Coordination Compounds
Q995The standard electrode potential E^(o) and its temperature coefficient (d E^(o) dT) for a cell are 2V and - 5 × 10⁻⁴ VK⁻¹ at 300 K respectively. The cell…Redox Reactions and Electrochemistry
Q1017The molecule that has minimum /no role in the formation of photochemical smog, is:Environmental Chemistry
Q1086Water samples with BOD values of 4 ppm and 18 ppm, respectively are:Environmental Chemistry
Q1130The volume of gas A is twice than that of gas B. The compressibility factor of gas A is thrice than that of gas B at same temperature. The pressures of the…Gaseous State
Q1172The correct order for acid strength of compounds: CH CH, CH₃–C CH and CH₂ = CH₂ is as followsHydrocarbons
Q1380In the Hall-Heroult process, aluminium is formed at the cathode. The cathode is made out of -Isolation of Elements
Q1648The element with Z = 120 (not yet discovered) will be an/a -Classification of Elements and Periodicity in Properties
Q1682Poly β –hydroxybutyrate-co- β -hydroxyvalerate (PHBV) is a copolymer ofPolymers
Q1791The hardness of a water sample (in terms of equivalents of CaCO₃) containing 10^–3 M CaSO₄ is (Molar mass of CaSO₄ = 136 g mol^–1)Redox Reactions and Electrochemistry
Q181050 mL of 0.5 M oxalic acid is needed to neutralize 25 mL of sodium hydroxide solution. The amount of NaOH in 50 mL of the given sodium hydroxide solution is -Redox Reactions and Electrochemistry
Q1823A metal on combustion in excess air forms X. X upon hydrolysis with water yields H₂O₂ and O₂ along with another product. The metal is:S Block Elements
Q1979Freezing point of a 4% aqueous solution of X is equal to freezing point of 12% aqueous solution of Y. If molecular weight of X is A, then molecular weight of…Solutions
Q2174What is the work function of the metal if the light of wavelength 4000 A° generates photoelectrons of velocity 6 × 10⁵ ms^–1 from it ? (Mass of electron = 9 ×…Atomic Structure

Mathematics

Q2560The perpendicular distance from the origin to the plane containing the two lines, (x + 2)/3 = (y - 2)/5 = (z + 5)/7 and (x - 1)/1 = (y - 4)/4 = (z + 4)/7, is:Three Dimensional Geometry
Q2574A tetrahedron has vertices P(1, 2, 1), Q(2, 1, 3), R(–1, 1, 2) and O(0, 0, 0). The angle between the faces OPQ and PQR is:Three Dimensional Geometry
Q2816The area (in sq. units) of the region bounded by the parabola, y = x² + 2 and the lines, y = x + 1, x = 0 and x = 3, isIntegral Calculus
Q2919A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of (2^(1/3) + 1/(2(3)^(1/3)))¹⁰ is:Binomial Theorem and Its Simple Applications
Q3094Let C₁ and C₂ be the centres of the circles x² + y² – 2x – 2y – 2 = 0 and x² + y² – 6x – 6y + 14 = 0 respectively. If P and Q are the points of intersection…Coordinate Geometry
Q3095If a variable line, 3x + 4y – λ = 0 is such that the two circles x² + y² – 2x – 2y + 1 = 0 and x² + y² – 18x – 2y + 78 = 0 are on its opposite sides, then the…Coordinate Geometry
Q3152If (z - α)/(z + α)(α R) is a purely imaginary number and | z | = 2, then a value of α is:Complex Numbers and Quadratic Equations
Q3370Let f and g be continuous functions on [0, a] such that f(x) = f(a – x) and g(x) + g(a – x) = 4, then ∫₀^(a) f(x) g(x) dx is equal to:Integral Calculus
Q3517Let y = y(x) be the solution of the differential equation, x dy/dx + y = x log e x, (x > 1). If 2y(2) = log e 4 - 1, then y(e) is equal to:Differential Equations
Q3688For x > 1, if (2x)²y = 4e²x - 2y, then (1 + log e 2x)² dy/dx is equal to:Limit, Continuity and Differentiability
Q3965If the vertices of a hyperbola be at (–2, 0) and (2, 0) and one of its foci be at (–3, 0), then which one of the following points does not lie on this…Coordinate Geometry
Q3994The integral ∫ cos(log e x) dx is equal to: (where C is a constant of integration)Integral Calculus
Q4071Considering only the principal values of inverse functions, the set A = x ≥ 0: tan⁻¹(2x) + tan⁻¹(3x) = (π)/4Trigonometry
Q4276lim x → π /4 (cot ³x - tan x)/(cos (x + (π)/4)) is:Limit, Continuity and Differentiability
Q4325The Boolean expression ((p q) (p q)) (p q) is equivalent to:Mathematical Reasoning
Q4498Let P = [ 1 0 0 3 1 0 9 3 1 ] and Q = [q i j] be two 3 × 3 matrices such that Q – P⁵ = I₃. Then (q₂₁ + q₃₁)/(q₃₂) is equal to:Matrices and Determinants
Q4563An ordered pair (α, β) for which the system of linear equations (1 + α) x + β y + z = 2 α x + (1 + β)y + z = 3 α x + β y + 2z = 2 has a unique solution, is:Matrices and Determinants
Q4718The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, y = 12 – x² such that the rectangle…Coordinate Geometry
Q4719Let P(4, –4) and Q(9, 6) be two points on the parabola, y² = 4x and let x be any point on the arc POQ of this parabola, where O is the vertex of this…Coordinate Geometry
Q4824Consider three boxes, each containing, 10 balls labelled 1, 2, …, 10. Suppose one ball is randomly drawn from each of the boxes. Denote by n i, the label of…Permutations and Combinations
Q4906In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of…Statistics and Probability
Q5135If λ be the ratio of the roots of the quadratic equation in x, 3m²x² + m(m – 4)x + 2 = 0, then the least value of m for which λ + 1/(λ) = 1, isComplex Numbers and Quadratic Equations
Q5251The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P…Sequence and Series
Q5307Let S k = (1 + 2 + 3 +.... + k)/k. If S₁² + S₂² +..... + S₁₀² = 5/12 A, then A is equal to:Sequence and Series
Q5355Let S = 1, 2, 3, …, 100. The number of non-empty subsets A of S such that the product of elements in A is even is:Sets, Relations and Functions
Q5445If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is:Statistics and Probability
Q5501If the straight line, 2x – 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, β), then β equals:Coordinate Geometry
Q5660The maximum value of 3cos θ + 5sin (θ - (π)/6) for any real value of θ is:Trigonometry
Q5722The sum of the distinct real values of μ, for which the vectors, μ i + j + k, i + μ j + k, i + j + μ k are co-planar, is:Vector Algebra