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JEE Main 2010 Annual Paper 1 Question Paper with Solutions | JEE Arc

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JEE Main 2010Annual, Paper 1

Physics 19Chemistry 27Mathematics 30

Physics

Q5871In a series LCR circuit R = 200Ω and the voltage and the frequency of the main supply is 220V and 50 Hz respectively. On taking out the capacitance from the…Electromagnetic Induction and Alternating Currents
Q6041A nucleus of mass M+ Δ m is at rest and decays into two daughter nuclei of equal mass M/2 each. Speed of light is c. The binding energy per nucleon for the…Atoms and Nuclei
Q6042A nucleus of mass M+ Δ m is at rest and decays into two daughter nuclei of equal mass M/2 each. Speed of light is c. The speed of daughter nuclei isAtoms and Nuclei
Q6082A radioactive nucleus (initial mass number A and atomic number Z emits 3 α - particles and 2 positrons. The ratio of number of neutrons to that of protons in…Atoms and Nuclei
Q6191Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t₁ is the time taken for the energy stored in the capacitor to reduce to…Electrostatics
Q6203Statement - 1: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement - 2: Principle of…Rotational Motion
Q6262For a particle in uniform circular motion the acceleration a at a point P(R, θ) on the circle of radius R is (here θ is measured from the x–axis)Kinematics
Q6416Two conductors have the same resistance at 0° C but their temperature coefficients of resistance are α ₁ and α ₂. The respective temperature coefficients of…Current Electricity
Q6595If a source of power 4kW produces 10²⁰ photons/second, the radiation belongs to a part of the spectrum calledDual Nature of Matter and Radiation
Q6620Statement - 1: When ultraviolet light is incident on a photocell, its stopping potential is V₀ and the maximum kinetic energy of the photoelectrons is K max…Dual Nature of Matter and Radiation
Q6916Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° with each other. When suspended in a liquid of…Electrostatics
Q6956Let there be a spherically symmetric charge distribution with charge density varying as ρ (r) = ρ ₀(5/4 - r/R) upto r=R, and ρ (r) = 0 for r>R, where r is the…Electrostatics
Q7093An initially parallel cylindrical beam travels in a medium of refractive index μ (I) = μ ₀ + μ ₂ I, where μ ₀ and μ ₂ are positive constants and I is the…Optics
Q7094An initially parallel cylindrical beam travels in a medium of refractive index μ (I) = μ ₀ + μ ₂ I, where μ ₀ and μ ₂ are positive constants and I is the…Optics
Q7775A particle is moving with velocity v = k(y i + x j), where K is a constant. The general equation for its path isKinematics
Q8288The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 × 10^–3 areUnits and Measurements
Q8413An initially parallel cylindrical beam travels in a medium of refractive index μ (I) = μ ₀ + μ ₂ I, where μ ₀ and μ ₂ are positive constants and I is the…Optics
Q8479The equation of a wave on a string of linear mass density 0.04 kg m⁻¹ is given by y = 0.02(m) sin [ 2π (t/(0.04(s)) - x/(0.50(m))) ]. The tension in the…Oscillations and Waves
Q8573The potential energy function for the force between two atoms in a diatomic molecule is approximately given by U(x) = a/(x¹²) - b/(x⁶), where a and b are…Work, Energy and Power

Chemistry

Q4From amongst the following alcohols the one that would react fastest with conc. HCl and anhydrous ZnCl₂, isOrganic Compounds Containing Oxygen
Q51One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of 44 u. The alkene isOrganic Compounds Containing Oxygen
Q68The correct order of increasing basicity of the given conjugate bases (R = CH₃) isSome Basic Principles of Organic Chemistry
Q100Out of the following, the alkene that exhibits optical isomerism isSome Basic Principles of Organic Chemistry
Q192Biuret test is not given byBiomolecules
Q401In aqueous solution the ionization constants for carbonic acid are K₁ = 4.2 x 10^–7 and K₂ = 4.8 x 10^–11 Select the correct statement for a saturated 0.034 M…Equilibrium
Q466The time for half life period of a certain reaction A → products is 1 hour. When the initial concentration of the reactant ‘A’, is 2.0 mol L^–1, how much time…Chemical Kinetics
Q494Consider the reaction: Cl₂(aq) + H₂S(aq) → S(s) + 2H⁺ (aq) + 2Cl^– (aq) The rate equation for this reaction is rate = k [Cl₂] [H₂S] Which of these mechanisms…Chemical Kinetics
Q585A solution containing 2.675g of CoCl₃. 6NH₃ (molar mass = 267.5 g mol^–1) is passed through a cation exchanger. The chloride ions obtained in solution were…Coordination Compounds
Q669Which one of the following has an optical isomer ? (en = ethylenediamine)Coordination Compounds
Q974The correct order of E M²⁺/M ^(o) values with negative sign for the four successive elements Cr, Mn, Fe and Co is:Redox Reactions and Electrochemistry
Q975The Gibbs energy for the decomposition of Al₂O₃ at 500^(o)C is as follows: 2/3A l₂ O₃ → 4/3Al + O₂, Δ r G = + 966 kJ mol^–1 The potential difference needed…Redox Reactions and Electrochemistry
Q1110If 10^–4 dm³ of water is introduced into a 1.0 dm³ flask to 300 K, how many moles of water are in the vapour phase when equilibrium is established ? (Given…Gaseous State
Q1281Three reactions involving H₂PO₄^− are given below: (i) H₃PO₄ + H₂O → H₃O⁺ + H₂PO₄^− (ii) H₂PO₄^− + H₂O → HPO₄^(2−) + H₃O⁺ (iii) H₂PO₄^− + OH⁻ → H₃PO₄ + O²⁻ In…Equilibrium
Q1294At 25°C, the solubility product of Mg(OH)₂ is 1.0 × 10^–11. At which pH, will Mg²⁺ ions start precipitating in the form of Mg(OH)₂ from a solution of 0.001 M…Equilibrium
Q1330Solubility product of silver bromide is 5.0 × 10^–13. The quantity of potassium bromide (molar mass taken as 120g of mol^–1) to be added to 1 litre of 0.05 M…Equilibrium
Q1548The correct sequence which shows decreasing order of the ionic radii of the elements isClassification of Elements and Periodicity in Properties
Q1672The polymer containing strong intermolecular forces e.g. hydrogen bonding, isPolymers
Q172329.5 mg of an organic compound containing nitrogen was digested according to Kjeldahl’s method and the evolved ammonia was absorbed in 20 mL of 0.1 M HCl…Purification and Characterisation of Organic Compounds
Q1908Percentages of free space in cubic close packed structure and in body centred packed structure are respectively:Solid State
Q1941The edge length of a face centered cubic cell of an ionic substance is 508 pm. If the radius of the cation is 110 pm, the radius of the anion is:Solid State
Q1955If sodium sulphate is considered to be completely dissociated into cations and anions in aqueous solution, the change in freezing point of water (∆T f), when…Solutions
Q2005On mixing, heptane and octane form an ideal solution. At 373 K, the vapour pressures of the two liquid components (heptane and octane) are 105 kPa and 45 kPa…Solutions
Q2111Ionisation energy of He⁺ is 19.6 x 10^–18 J atom^–1. The energy of the first stationary state (n = 1) of Li²⁺ isAtomic Structure
Q2130The energy required to break one mole of Cl–Cl bonds in Cl₂ is 242 kJ mol^–1. The longest wavelength of light capable of breaking a single Cl – Cl bond is (c…Atomic Structure
Q2289For a particular reversible reaction at temperature T, ∆H and ∆S were found to be both +ve. If T e is the temperature at equilibrium, the reaction would be…Chemical Thermodynamics
Q2344The standard enthalpy of formation of NH₃ is –46.0 kJ mol^–1. If the enthalpy of formation of H₂ from its atoms is –436 kJ mol^–1 and that of N2 is –712 kJ…Chemical Thermodynamics

Mathematics

Q2373A line AB in three-dimensional space makes angles 45° and 120° with the positive x -axis and the positive y -axis respectively. If AB makes an acute angle θ…Three Dimensional Geometry
Q2550Statement-1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x-y+z=5. Statement-2: The plane x-y+z=5 bisects the line segment…Three Dimensional Geometry
Q2626Let f:R → R be defined by f(x) = \ k - 2x, if x ≤ - 1 2x + 3, if x > - 1. If f has a local minimum at x=-1, then a possible value of k isLimit, Continuity and Differentiability
Q2627Let f:R → R be a continuous function defined by f(x) = 1/(eˣ + 2e⁻ˣ) Statement - 1: f(c) = 1/3, for some c R. Statement - 2: 0 < f(x) ≤ 1/(2 2), for all x RLimit, Continuity and Differentiability
Q2755The equation of the tangent to the curve y = x + 4/(x²), that is parallel to the x -axis, isLimit, Continuity and Differentiability
Q2799The area bounded by the curves y = cos x and y = sin x between the ordinates x=0 and x = (3π)/2 isIntegral Calculus
Q2971Let s₁ = Σ j = 1 ¹⁰ j(j - 1)¹⁰ C j, s₂ = Σ j = 1 ¹⁰ j.¹⁰C j and s₃ = Σ j = 1 ¹⁰ j².¹⁰C j. Statement-1: S₃ = 55 × 2⁹. Statement-2: S₁ = 90 × 2⁸ and S₂ = 10 × 2⁸.Binomial Theorem and Its Simple Applications
Q3076The circle x² + y² = 4x + 8y + 5 intersects the line 3x - 4y = m at two distinct points if:Coordinate Geometry
Q3249The number of complex numbers z such that | z - 1 | = | z + 1 | = | z - i | equals:Complex Numbers and Quadratic Equations
Q3347Let p(x) be a function defined on R such that p'(x)=p'(1-x), for all x [ 0,1 ],p(0) = 1 and p(1)=41. Then ∫₀¹ p(x)dx equals:Integral Calculus
Q3579Solution of the differential equation cos x dy = y(sin x - y)dx, 0 < x <(π)/2 is:Differential Equations
Q3655Let f:(- 1,1) → R be a differentiable function with f(0) = - 1 and f'(0) = 1. Let g(x) = [ f(2f(x) + 2) ]². Then g'(0) =Limit, Continuity and Differentiability
Q4222Let f:R → R be a positive increasing function with lim x → ∞ (f(3x))/(f(x)) = 1. Then lim x → ∞ (f(2x))/(f(x)) =Limit, Continuity and Differentiability
Q4400Let S be a non-empty subset of R. Consider the following statement: P: There is a rational number x ∈ S such that x > 0. Which of the following statements is…Mathematical Reasoning
Q4432The number of 3 × 3 non-singular matrices, with four entries as 1 and all other entries as 0, is:Matrices and Determinants
Q4552Consider the system of linear equations; x₁ + 2x₂ + x₃ = 3 2x₁ + 3x₂ + x₃ = 3 3x₁ + 5x₂ + 2x₃ = 1 The system has:Matrices and Determinants
Q4652Let A be a 2 × 2 matrix with non-zero entries and let A² = I, where I is 2 × 2 identity matrix. Define Tr (A)= sum of diagonal elements of A and | A | =…Matrices and Determinants
Q4694If two tangents drawn from a point P to the parabola y² = 4x are at right angles, then the locus of P isCoordinate Geometry
Q4814There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred…Permutations and Combinations
Q4970An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The…Statistics and Probability
Q4971Four numbers are chosen at random (without replacement) from the set 1,2,3,....20 \. Statement - 1: The probability that the chosen numbers when arranged in…Statistics and Probability
Q5036For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is:Properties of Triangle
Q5121If α and β are the roots of the equation x² - x + 1 = 0, then α ²⁰⁰⁹ + β ²⁰⁰⁹ =Complex Numbers and Quadratic Equations
Q5192A person is to count 4500 currency notes. Let a n denote the number of notes he counts in the n^(th) minute. If a₁ = a₂ =....= a₁₀ = 150 and a₁₀, a₁₁,.... are…Sequence and Series
Q5371Consider the following relations R=\(x, y) x, y are real numbers and x=w y for some rational number w; S=\(m/n, p/q) m, n, p. and q are integers such that n…Sets, Relations and Functions
Q5427For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of…Statistics and Probability
Q5550The line L given by x/5 + y/b = 1 passes through the point (13,32). The line K is parrallel to L and has the equation x/c + y/3 = 1. Then the distance between…Coordinate Geometry
Q5634Let cos (α + β) = 4/5 and sin (α - β) = 5/13, where 0 ≤ α, β ≤ (π)/4. Then tan 2α =Trigonometry
Q5714Let a = j - k and c = i - j - k. Then the vector b satisfying a × b + c = 0 and a. b = 3:Vector Algebra
Q5762If the vectors a = i - j + 2 k, b = 2 i + 4 j + k and c = λ i + j + μ k are mutually orthogonal, then (λ,μ) is equal to:Vector Algebra