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

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JEE Main 201912 Jan, Evening shift

Physics 19Chemistry 17Mathematics 29

Physics

Q6093In a radioactive decay chain, the initial nucleus is ₉₀²³² Th. At the end there are 6 α -particles and 4 β -particles which are emitted. If the end nucleus is…Atoms and Nuclei
Q6184A parallel plate capacitor with plates of area 1 m² each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of…Electrostatics
Q6214An alpha-particle of mass m suffers 1-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of…Rotational Motion
Q6307To double the covering range of a TV transmittion tower, its height should be multiplied by:Communication Systems
Q6461A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of 4 × 10^–4 A passes through it, its needle (pointer) deflects by one…Current Electricity
Q6597In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons…Dual Nature of Matter and Radiation
Q6628When a certain photosensitive surface is illuminated with monochromatic light of frequency v, the stopping potential for the current is –V₀/2. When the…Dual Nature of Matter and Radiation
Q6720A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0 ms^–1, at right angles to the horizontal component of the…Electromagnetic Induction and Alternating Currents
Q6759The mean intensity of radiation on the surface of the Sun is about 10⁸ W/m². The rms value of the corresponding magnetic field is closet to:Electromagnetic Waves
Q7035A plano-convex lens (focal length f₂, refractive index μ ₂, radius of curvature R) fits exactly into a plano-concave lens (focal length f₁, refractive index μ…Optics
Q7184Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth…Gravitation
Q7369A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the…Thermodynamics
Q7370An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature 300 K. The mean time between two successive collisions is 6 × 10^–8 s. If the…Thermodynamics
Q7639A paramagnetic material has 10²⁸ atoms/m³. Its magnetic susceptibility at temperature 350 K is 2.8 × 10^–4. Its susceptibility at 300 K is:Magnetic Effects of Current and Magnetism
Q7931A load of mass M kg is suspended from a steel wire of length 2m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the…Properties of Solids and Liquids
Q7980A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the…Properties of Solids and Liquids
Q8150A simple harmonic motion is represented by: y = 5 (sin 3 π t + 3 cos 3 π t) cm The amplitude and time period of the motion are:Oscillations and Waves
Q8229Let, r, C and V represent inductance, resistance, capacitance and voltage, respectively. The dimension of ()/rCV in SI units will be:Units and Measurements
Q8549A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz…Oscillations and Waves

Chemistry

Q199The correct statement (s) among I to III with respect to potassium ions that are abundant within the cell fluid is /are I. They activate many enzymes II. They…Biomolecules
Q723The magnetic moment of an octahedral homoleptic Mn(II) complex is 5.9 BM. The suitable ligand for this complex is -Coordination Compounds
Q812The correct order of atomic radii is:d- and f-Block Elements
Q940m° for NaCl, HCl and NaA are 126.4, 425.9 and 100.5 S cm² mol^–1, respectively. If the conductivity of 0.001 M HA is- 5 × 10^–5 S cm^–1, degree of…Redox Reactions and Electrochemistry
Q1114An open vessel at 27^(o)C is heated until two fifth of the air (assumed as an ideal gas) it has escaped from the vessel assuming that the volume of the vessel…Gaseous State
Q1214The volume strength of 1M H₂O₂ is: (Molar mass of H₂O₂ = 34 g mol^–1)Hydrogen
Q1336If K s p of Ag₂CO₃ is 8 × 10^–12, the molar solubility of Ag₂CO₃ in 0.1 M AgNO₃ is -Equilibrium
Q1381The pair that does NOT require calcination is -Isolation of Elements
Q1470The element that does NOT show catenation is:p-Block Elements
Q1471The element that shows greater ability to form p π -p π multiple bonds, is:p-Block Elements
Q1683The two monomers for the synthesis of Nylon 6, 6 arePolymers
Q1963Molecules of benzoic acid (C₆H₅COOH) dimerise in benzene. 'w' g of the acid dissolved in 30 g of benzene shows a depression in freezing point equal to 2K. If…Solutions
Q20358 g of NaOH is dissolved in 18g of H₂O. Mole fraction of NaOH in solution and molality (in mol kg^–1) of the solution respectively are -Some Basic Concepts in Chemistry
Q2175The upper stratosphere consisting of the ozone layer protects us from sun's radiation that falls in the wavelength region of -Atomic Structure
Q2181If the de Broglie wavelength of the electron in n^(t)h Bohr orbit in a hydrogenic atom is equal to 1.5 π a₀ (a₀ is Bohr radius), then the value of n/z is -Atomic Structure
Q2242Among the following the false statement is -Surface Chemistry
Q2352Given (i) C (graphite) + O₂(g) → CO₂(g); Δ rH ^Θ = x kJ mol⁻¹ (ii) C(graphite) + 1/2 O₂(g) → CO(g); Δ rH ^Θ = y kJ mol⁻¹ (iii) CO(g) + 1/2 O₂(g) → CO₂(g); Δ…Chemical Thermodynamics

Mathematics

Q2413If an angle between the line, (x + 1)/2 = (y - 2)/1 = (z - 3)/(- 2) and the plane, x - 2y - kz = 3 is cos ⁻¹((2 2)/3), then a value of k is:Three Dimensional Geometry
Q2567Let S be the set of all real values of λ such that a plane passing through the points (– λ ², 1, 1), (1, – λ ², 1) and (1, 1, – λ ²) also passes through the…Three Dimensional Geometry
Q2709If the function f given by f(x) = x³ – 3(a – 2)x² + 3ax + 7, for some a R is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, (f(x)…Limit, Continuity and Differentiability
Q2767The tangent to the curve y = x² – 5x + 5, parallel to the line 2y = 4x + 1, also passes through the point:Limit, Continuity and Differentiability
Q2913The total number of irrational terms in the binomial expansion of (7¹/5 – 3¹/10)⁶⁰ is:Binomial Theorem and Its Simple Applications
Q3080If a circle of radius R passes through the origin O and intersects the coordinates axes at A and B, then the locus of the foot of perpendicular from O on AB is:Coordinate Geometry
Q3255Let z₁ and z₂ be two complex numbers satisfying | z₁ | = 9 and | z₂ – 3 – 4i | = 4. Then the minimum value of | z₁ – z₂ | is:Complex Numbers and Quadratic Equations
Q3285lim x → ∞ (n/(n² + 1²) + n/(n² + 2²) + n/(n² + 3²) +..... + 1/5n) is equal to:Integral Calculus
Q3377The integral ∫₁^(e) (x/e)²ˣ - (e/x)ˣ log e x dx is equal to:Integral Calculus
Q3518If a curve passes through the point (1, –2) and has slope of the tangent at any point (x, y) on it as (x² - 2y)/x, then the curve also passes through the point:Differential Equations
Q3752Let S and S' be the foci of an ellipse and B be any one of the extremities of its minor axis. If Δ S'BS is a right angled triangle with right angle at B and…Coordinate Geometry
Q3917If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30^(o) and the angle of depression of reflection of the cloud in the lake…Height and Distance
Q4015The integral ∫ (3x¹³ + 2x¹¹)/((2x⁴ + 3x² + 1)⁴) dx is equal to: (where C is a constant of integration)Integral Calculus
Q4187Let f be a differentiable function such that f(1) = 2 and f '(x) = f(x) for all x R R. If h(x) = f(f(x)), then h'(1) is equal to:Limit, Continuity and Differentiability
Q4275lim x → 1^ - (π - √(2 sin ⁻¹x))/(√(1 - x)) is equal to:Limit, Continuity and Differentiability
Q4453If A = [ 1 sin θ 1 - sin θ 1 sin θ - 1 - sin θ 1 ]; then for all θ ((3π)/4,(5π)/4), det (A) lies in the interval:Matrices and Determinants
Q4568The set of all values of λ for which the system of linear equations x – 2y – 2z = λ x x + 2y + z = λ y – x – y = λ z has a non-trivial solutions:Matrices and Determinants
Q4737The equation of a tangent to the parabola, x² = 8y, which makes an angle θ with the positive directions of x-axis, is:Coordinate Geometry
Q4825There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games…Permutations and Combinations
Q4907In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the…Statistics and Probability
Q5017In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the…Statistics and Probability
Q5108The number of integral values of m for which the quadratic expression, (1 + 2m)x² – 2(1 + 3m)x + 4(1 + m), x R, is always positive, is:Complex Numbers and Quadratic Equations
Q5178If sin⁴ α + 4 cos⁴ β + 2 = 4 2 sin α cos β; α, β [0, π ], then cos(α + β) - cos(α - β) is equal to:Sequence and Series
Q5205If ⁿC₄, ⁿC₅ and ⁿC₆ are in A.P., then n can be:Sequence and Series
Q5306If the sum of the first 15 terms of the series (3/4)³ + (11/2)³ + (21/4)³ + 3³ + (33/4)³ +.... is equal to 225 k, then k is equal to:Sequence and Series
Q5356Let Z be the set of integers. If A = x Z: 2(x + 2) (x² - 5x + 6) = 1 and B = x Z: - 3 < 2x - 1 < 9, then the number of subsets of the set A × B, isSets, Relations and Functions
Q5444The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then the absolute value of the…Statistics and Probability
Q5607If a straight line passing through the point P(–3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is:Coordinate Geometry
Q5719Let a, b and c be three unit vectors, out of which vectors b and c are non-parallel. If α and β are the angles which vector a makes with vectors b and c…Vector Algebra