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JEE Main 2019 10 Apr Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 201910 Apr, Morning shift

Physics 22Chemistry 19Mathematics 30

Physics

Q5940A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2 kW. If the current in the secondary coil is 10A…Electromagnetic Induction and Alternating Currents
Q6092Two radioactive materials A and B have decay constants 10 λ and λ, respectively. It initially they have the same number of nuclei, then the ratio of the…Atoms and Nuclei
Q6311Given below in the the left column are different modes of communication using the kinds of waves given the right column. A Optical Fibre communication P…Communication Systems
Q6348A message signal of frequency 100 MHz and peak voltage 100 V is used to execute amplitude modulation on a carrier wave of frequency 300 GHz and peak voltage…Communication Systems
Q6459A moving coil galvanometer allows a full scale current of 10^–4 A. A series resistance of 2 M Ω is required to convert the above galvanometer into a voltmeter…Current Electricity
Q6513A current of 5 A passes through a copper conductor (resistivity = 1.7 × 10^–8 Ω m) of radius of cross-section 5 mm. Find the mobility of the charges if their…Current Electricity
Q6627In a photoelectric effect experiment the threshold wavelength of the light is 380 nm. If the wavelentgh of incident light is 260 nm, the maximum kinetic…Dual Nature of Matter and Radiation
Q6747The electric field of a plane electromagnetic wave is given by E = E₀ i cos (kz)cos(ω t) The corresponding magnetic field B is then given byElectromagnetic Waves
Q6902An n-p-n transistor operates as a common emitter amplifier, with a power gain of 60 dB. The input circuit resistance is 100 Ω and the output load resistance…Electronic Devices
Q7008A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centred at origin. A point charge q is moving towards the ring along the z-axis…Electrostatics
Q7134The value of acceleration due to gravity at Earth's surface is 9.8 ms^–2. The altitude above its surface at which the acceleration due to gravity decreases to…Gravitation
Q7366A 25 × 10^–3 m³ volume cylinder is filled with 1 mol of O₂ gas at room temperature (300K). The molecular diameter of O₂, and its root mean square speed, are…Kinetic Theory of Gases
Q7477n moles of an ideal gas with constant volume heat capcity C V undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to…Thermodynamics
Q7532A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20°C is: [Given that R…Thermodynamics
Q7580A ball is thrown upward with an initial velocity V₀ from the surface of the earth. The motion of the ball is affected by a drag force equal to m γ u² (where m…Laws of Motion
Q7748A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicualr to the plane…Magnetic Effects of Current and Magnetism
Q8010The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of thier densities is 13.6. Their contact angles, with glass, are close…Properties of Solids and Liquids
Q8086Two coaxial discs, having moments of inertia I₁ and I₁/2, are rotating with respective angular velocities ω ₁ and ω ₁/2, about their common axis. They are…Rotational Motion
Q8087A thin disc of mass M and radius R has mass per unit area σ (r) = kr² where r is the distance from its centre. Its moment of inertia about an axis going…Rotational Motion
Q8108A particle of mass m is moving along a trajectory given by x = x₀ + a cos ω ₁t y = y₀ + b sin ω ₂t The torque, acting on the particle about the origin, at t =…Rotational Motion
Q8121The displacement of a damped harmonic oscillator is given by x(t) = e^–0.1t cos (10 π t + f). Here t is in seconds. The time taken for its amplitude of…Oscillations and Waves
Q8525A stationary source emits sound waves of frequency 500 Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480…Oscillations and Waves

Chemistry

Q120The principle of column chromatography is:Some Basic Principles of Organic Chemistry
Q158Amylopectin is compound of:Biomolecules
Q292The oxoacid of sulphur that does not contain bond between sulphur atoms isChemical Bonding and Molecular Structure
Q361During the change of O₂ to O₂⁻, the incoming electron goes to the orbital:Chemical Bonding and Molecular Structure
Q526Ethylamine (C₂H₅NH₂) can be obtained from N-ethylphatalimide on treatment with:Organic Compounds Containing Nitrogen
Q610Three complexes, [CoCl(NH₃)₅] ²⁺(I), [Co(NH₃)₅H₂O]³⁺ (II) and [Co(NH₃)₆] ³⁺(III) absorb light in the visible region. The correct order of the wavelength of…Coordination Compounds
Q870Consider the hydrated ions of Ti²⁺, V²⁺, Ti³⁺, and Sc³⁺. The correct order of their spin-only magnetic moments is:d- and f-Block Elements
Q939Consider the statements S1 and S2 S1: Conductivity always increases with decrease in the concentration of electrolyte. S2: Molar conductivity always increases…Redox Reactions and Electrochemistry
Q1060The regions of the atmosphere, where clouds form and where we live, respectively, are:Environmental Chemistry
Q1128Consider the following table: Gas a/(k Pa dm⁶ mol⁻¹) b/(dm³ mol⁻¹) A 642.32 0.05196 B 155.21 0.04136 C 431.91 0.05196 D 155.21 0.4382 a and b are vander Waals…Gaseous State
Q1268The synonym for water gas when used in the production of methanol is:Hydrogen
Q1303Consider the following statements (a) The pH of a mixture containing 400 mL of 0.1 M H₂SO₄ and 400 mL of 0.1 M NaOH will be approximately 1.3 (b) Ionic…Equilibrium
Q1435Match the refining methods (Column I) with metals (Column II). Column I (Refining Methods) Column II (Metals) (I) Liquation (a) Zr (II) Zone Refining (b) Ni…Isolation of Elements
Q1681Which of the following is a condensation polymer?Polymers
Q1876The alloy used in the construction of aircrafts is:S Block Elements
Q2011At room temperature, a dilute solution of urea is prepared by dissolving 0.60 of urea in 360 g of water. If the vapour pressure of pure water at this…Solutions
Q2094At 300 K and 1 atmospheric pressure, 10 mL of a hydrocarbon required 55 mL of O₂ for complete combustion, and 40 mL of CO₂ is formed. The formula of the…Some Basic Concepts in Chemistry
Q2139The isoelectronic set of ions is:Atomic Structure
Q2304A process will be spontaneous at all temperatures if:Chemical Thermodynamics

Mathematics

Q2488If the length of the perpendicular from the point (β, 0, β) (β ≠ 0) to the line, x/1 = (y - 1)/0 = (z + 1)/(- 1) is √(3/2), then β is equal to:Three Dimensional Geometry
Q2563If Q(0, –1, –3) is the image of the point P in the plane 3x – y + 4z = 2 and R is the point (3, –1, –2), then the area (in sq. units) of Δ PQR is:Three Dimensional Geometry
Q2980If the coefficients of x² and x³ are both zero, in the expansion of the expression (1 + ax + bx²) (1 – 3x)¹⁵ in powers of x, then the ordered pair (a,b) is…Binomial Theorem and Its Simple Applications
Q3092If the circles x² + y² + 5Kx + 2y + K = 0 and 2(x² + y²) + 2Kx + 3y –1 = 0, (K R), intersect at the points P and Q, then the line 4x + 5y – K = 0 passes…Coordinate Geometry
Q3125The line x = y touches a circle at the point (1,1). If the circle also passes through the point (1, – 3), then its radius is:Coordinate Geometry
Q3220If a > 0 and z = ((1 + i)²)/(a - i), has magnitude √(2/5), then z is equal to:Complex Numbers and Quadratic Equations
Q3286lim n → ∞ (((n + 1)^(1/3))/(n^(4/3)) + ((n + 2)^(1/3))/(n^(4/3)) +....... + ((2n)^(1/3))/(n^(4/3))) is equal to:Integral Calculus
Q3366The value of ∫₀^(2π) [ sin 2x(1 + cos 3x) ] dx, where [t] denotes the greatest integer function is:Integral Calculus
Q3521If y = y(x) is the solution of the differential equation dy/dx = (tan x - y) sec ²x, x (- (π)/2,(π)/2), such that y (0) = 0, then y(- (π)/4) is equal to:Differential Equations
Q3776If the line x – 2y = 12 is tangent to the ellipse (x²)/(a²) + (y²)/(b²) = 1 at the point (3, - 9/2), then the length of the latus rectum of the ellipse is:Coordinate Geometry
Q3817Let f(x) = x², x R. For any A R, define g (A) = x R: f(x) A. If S = [0,4], then which one of the following statements is not true ?Sets, Relations and Functions
Q3818Let f(x) = eˣ – x and g(x) = x² – x, x R. Then the set of all x R, where the function h(x) = (fog) (x) is increasing, is:Sets, Relations and Functions
Q3914ABC is a triangular park with AB = AC = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at…Height and Distance
Q3966If a directrix of a hyperbola centred at the origin and passing through the point (4, –2 3) is 5x = 4 5 and its eccentricity is e, then:Coordinate Geometry
Q4012If ∫ dx/((x² - 2x + 10)²) = A(tan ⁻¹((x - 1)/3) + (f(x))/(x² - 2x + 10)) + C where C is a constant of integration then:Integral Calculus
Q4138If f(x) = \ (sin (p + 1)x + sin x)/x,x < 0 q,x = 0 √(x + x²) - x x^ 0.5ex 3 -0.1em/ -0.15em 0.25ex 2,x > 0. is continuous at x = 0, then the ordered pair (p…Limit, Continuity and Differentiability
Q4185Let f: R → R be differentiable at c R and f(c) = 0. If g(x) = |f(x)|, then at x = c, g is:Limit, Continuity and Differentiability
Q4228If lim x → 1 (x⁴ - 1)/(x - 1) = lim x → k (x³ - k³)/(x² - k²), then k is:Limit, Continuity and Differentiability
Q4321Which one of the following Boolean expressions is a tautology?Mathematical Reasoning
Q4450If Δ ₁ = | x sin θ cos θ - sin θ - x 1 cos θ 1 x | and Δ ₂ = | x sin 2θ cos 2θ - sin 2θ - x 1 cos 2θ 1 x |, x ≠ 0; then for all θ (0,(π)/2):Matrices and Determinants
Q4565If the system of linear equations x + y + z = 5 x + 2y + 2z = 6 x + 3y + λ z = μ, (λ, μ R), has infinitely many solutions, then the value of λ + μ is:Matrices and Determinants
Q4793The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated is:Permutations and Combinations
Q4952Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all…Statistics and Probability
Q5067All the pairs (x, y) that satisfy the inequality 2^(√(sin ²x - 2 sin x + 5)).1/(4^(sin ²y)) ≤ 1 also satisfy the equationComplex Numbers and Quadratic Equations
Q5137If α and β are the roots of the quadratic equation, x² + x sin θ - 2 sin θ = 0, θ (0,(π)/2), then (α ¹² + β ¹²)/((α ⁻¹² + β ⁻¹²).(α - β)²⁴) is equal to:Complex Numbers and Quadratic Equations
Q5199If a₁, a₂, a₃,............... a n are in A.P. and a₁ + a₄ + a₇ +........... + a₁₆ = 114, then a₁ + a₆ + a₁₁ + a₁₆ is equal to:Sequence and Series
Q5303The sum (3 × 1³)/(1³) + (5 × (1³ + 2³))/(1² + 2²) + (7 × (1³ + 2³ + 3³))/(1² + 2² + 3²) +..... upto 10 terms is:Sequence and Series
Q5417If for some x R, the frequency distribution of the marks obtained by 20 students in a test is: Marks 2 3 5 7 Frequency (x + 1)² 2x - 5 x² - 3x x then the mean…Statistics and Probability
Q5604The region represented by| x – y | ≤ 2 and | x + y| ≤ 2 is bounded by a:Coordinate Geometry
Q5768Let A (3, 0, –1), B(2, 10, 6) and C(1, 2, 1) be the vertices of a triangle and M be the midpoint of AC. If G divides BM in the ratio, 2: 1, then cos (GOA) (O…Vector Algebra