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JEE Main 2009 Annual Paper 1 Question Paper with Solutions | JEE Arc

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JEE Main 2009Annual, Paper 1

Physics 18Chemistry 19Mathematics 29

Physics

Q5970The transition from the state n=4 to n=3 in a hydrogen like atom result in ultra violet radiation. Infrared radiation will be obtained in the transition from:Atoms and Nuclei
Q6619The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of…Dual Nature of Matter and Radiation
Q6915A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is…Electrostatics
Q6955Let P(r) = Q/(π R⁴)r be the change density distribution for a solid sphere of radius R and total charge Q. For a point 'p' inside the sphere at distance r₁…Electrostatics
Q6998(This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.)…Electrostatics
Q6999Two points P and Q are maintained at the potentials of 10 V and -4 V, respectively. The work done in moving 100 electrons from P to Q is:Electrostatics
Q7027In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted…Optics
Q7131The height at which the acceleration due to gravity becomes g/9 (where g= the acceleration due to gravity on the surface of the earth) in terms of R, the…Gravitation
Q7288One kg of a diatomic gas is at a pressure of 8 × 10⁴ N/m². The density of the gas is 4kg/m³. What is the energy of the gas due to its thermal motion ?Thermodynamics
Q7508Statement - 1: The temperature dependence of resistance is usually given as R = R₀(1 + α Δ t). The resistance of wire changes from 100Ω to 150Ω when its…Thermodynamics
Q7812A particle has an initial velocity 3 i + 4 j and an acceleration of 0.4 i + 0.3 j. Its speed after 10 s is:Kinematics
Q7926Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area A and wire 2 has cross-sectional area 3A. If the…Properties of Solids and Liquids
Q8083A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ω. Its center of…Rotational Motion
Q8138If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the…Oscillations and Waves
Q8351In an experiment the angles are required to be measured using an instrument, 29 divisions of the main scale exactly coincide with the 30 divisions of the…Experimental Skills
Q8412A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference…Optics
Q8516A motor cycle starts from rest and accelerates along a straight path at 2m/s². At the starting point of the motor cycle there is a stationary electric siren…Oscillations and Waves
Q8543Three sound waves of equal amplitudes have frequencies (v - 1), v, (v + 1). They superpose to give beats. The number of beats produced per second will be:Oscillations and Waves

Chemistry

Q55A liquid was mixed with ethanol and a drop of concentrated H₂SO₄ was added. A compound with a fruity smell was formed. The liquid was:Organic Compounds Containing Oxygen
Q99The number of stereoisomers possible for a compound of the molecular formula CH₃ - CH = CH - CH(OH) - Me is:Some Basic Principles of Organic Chemistry
Q149The two functional groups present in a typical carbohydrate areBiomolecules
Q353Using MO theory, predict which of the following species has the shortest bond length?Chemical Bonding and Molecular Structure
Q465The half life period of a first order chemical reaction is 6.93 minutes. The time required for the completion of 99% of the chemical reaction will be (log…Chemical Kinetics
Q668Which of the following pairs represents linkage isomers ?Coordination Compounds
Q806Knowing that the Chemistry of lanthanoids (Ln) is dominated by its +3 oxidation state, which of the following statements is incorrect?d- and f-Block Elements
Q852In context with the transition elements, which of the following statements is incorrect ?d- and f-Block Elements
Q913In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is CH₃OH(l) + 3/2O₂ → CO₂ (g) + 2H₂O (l) At 298K standard Gibb’s…Redox Reactions and Electrochemistry
Q973Given: E_ F e³⁺ /Fe ^(o) = -0.036V; E_ F e²⁺ /Fe ^(o) = -0.439 V The value of standard electrode potential for the change, Fe³⁺ (aq) + e⁻ → Fe²⁺ (aq) will beRedox Reactions and Electrochemistry
Q1329Solid Ba(NO₃)₂ is gradually dissolved in a 1.0 × 10⁻⁴ M Na₂CO₃ solution. At what concentration of Ba²⁺ will a precipitate begin to form ? (K s p for BaCO₃ =…Equilibrium
Q1547The set representing the correct order of ionic radius is:Classification of Elements and Periodicity in Properties
Q1630In which of the following arrangements, the sequence is not strictly according to the property written against itClassification of Elements and Periodicity in Properties
Q1914Copper crystallizes in fcc with a unit cell length of 361 pm. What is the radius of copper atom?Solid State
Q2003A binary liquid solution is prepared by mixing n-heptane and ethanol. Which one of the following statements is correct regarding the behaviour of the solution ?Solutions
Q2004Two liquids X and Y form an ideal solution. At 300K, vapour pressure of the solution containing 1 mol of X and 3 mol of Y is 550 mm Hg. At the same…Solutions
Q2129Calculate the wavelength (in nanometer) associated with a proton moving at 1.0 x 10³ ms^−1 (Mass of proton = 1.67 × 10⁻²⁷ kg and h = 6.63 × 10⁻³⁴ Js):Atomic Structure
Q2153In an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005%. Certainity with which the position of the electron can be located is (h…Atomic Structure
Q2343On the basis of the following thermochemical data: (Δ f G^(o)H⁺ (aq) = 0) H₂O(l) → H⁺(aq) + OH⁻(aq); Δ H = 57.32 kJ H₂(g) + 1/2 O₂(g) → H₂O(l); Δ H = -286.20…Chemical Thermodynamics

Mathematics

Q2372The projections of a vector on the three coordinate axis are 6,-3,2 respectively. The direction cosines of the vector are:Three Dimensional Geometry
Q2391Let the line (x - 2)/3 = (y - 1)/(- 5) = (z + 2)/2 lie in the plane x + 3y - α z + β = 0. Then (α,β) equalsThree Dimensional Geometry
Q2625Given P(x) = x⁴ + a x³ + b x² + cx + d such that x=0 is the only real root of P' (x) = 0. If P(- 1) < P(1), then in the interval [ - 1,1 ]:Limit, Continuity and Differentiability
Q2798The area of the region bounded by the parabola (y - 2)² = x - 1, the tangent of the parabola at the point (2, 3) and the x -axis is:Integral Calculus
Q2890The remainder left out when 8²ⁿ - (62)²ⁿ⁺¹ is divided by 9 is:Binomial Theorem and Its Simple Applications
Q3019Three distinct points A, B and C are given in the 2 -dimensional coordinates plane such that the ratio of the distance of any one of them from the point (1…Coordinate Geometry
Q3065If P and Q are the points of intersection of the circles x² + y² + 3x + 7y + 2p - 5 = 0 and x² + y² + 2x + 2y - p² = 0 then there is a circle passing through…Coordinate Geometry
Q3146If | z - 4/z | = 2, then the maximum value of | z | is equal to:Complex Numbers and Quadratic Equations
Q3346∫₀^π [ cot x ]dx, where [. ] denotes the greatest integer function, is equal to:Integral Calculus
Q3491The differential equation which represents the family of curves y = c₁e^(c₂x), where c₁, and c₂ are arbitrary constants, isDifferential Equations
Q3664Let y be an implicit function of x defined by x²ˣ - 2xˣ cot y - 1 = 0. Then y'(1) equalsLimit, Continuity and Differentiability
Q3744The ellipse x² + 4y² = 4 is inscribed in a rectangle aligned with the coordinate axex, which in turn is inscribed in another ellipse that passes through the…Coordinate Geometry
Q3793Let f(x) = (x + 1)² - 1,x ≥ - 1 Statement - 1: The set x:f(x) = f⁻¹(x) = 0, - 1. Statement - 2: f is a bijection.Sets, Relations and Functions
Q3794For real x, let f(x) = x³ + 5x + 1, thenSets, Relations and Functions
Q4177Let f(x) = x| x | and g(x) = sin x. Statement-1: gof is differentiable at x=0 and its derivative is continuous at that point. Statement-2: gof is twice…Limit, Continuity and Differentiability
Q4309Statement-1: (p q) is equivalent to p q. Statement-2: (p q) is a tautology.Mathematical Reasoning
Q4439Let a, b, c be such that b(a + c) ≠ 0 if | a a + 1 a - 1 - b b + 1 b - 1 c c - 1 c + 1 | + | a + 1 b + 1 c - 1 a - 1 b - 1 c + 1 (- 1)ⁿ⁺²a (- 1)ⁿ⁺¹b (- 1)ⁿc |…Matrices and Determinants
Q4516Let A be a 2 × 2 matrix Statement - 1: adj(adj A) = A Statement - 2: | adj A | = | A |Matrices and Determinants
Q4839From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is…Permutations and Combinations
Q4871In a binomial distribution B(n,p = 1/4), if the probability of at least one success is greater than or equal to 9/10, then n is greater than:Statistics and Probability
Q4938One ticket is selected at random from 50 tickets numbered 00, 01, 02,...., 49. Then the probability that the sum of the digits on the selected ticket is 8…Statistics and Probability
Q5090If the roots of the equation b x² + cx + a = 0 imaginary, then for all real values of x, the expression 3b²x² + 6bcx + 2c² is:Complex Numbers and Quadratic Equations
Q5288The sum to infinite term of the series 1 + 2/3 + 6/(3²) + 10/(3³) + 14/(3⁴) +..... isSequence and Series
Q5399If A, B and C are three sets such that A B=A C and A B=A C, then:Sets, Relations and Functions
Q5425Statement - 1: The variance of first n even natural numbers is (n² - 1)/4 Statement - 2: The sum of first n natural numbers is (n(n + 1))/2 and the sum of…Statistics and Probability
Q5426If the mean deviation of number 1, 1 + d, 1 + 2d,........, 1 + 100d from their mean is 255, then the d is equal toStatistics and Probability
Q5498The lines p(p² + 1)x - y + q = 0 and (p² + 1)²x + (p² + 1)y + 2q =0 are perpendicular to a common line for:Coordinate Geometry
Q5549The shortest distance between the line y - x = 1 and the curve x = y² is:Coordinate Geometry
Q5713If u, v, w are non-coplanar vectors and p,q are real numbers, then the equality [ 3 u p v p w ] - [ p v w q u ] - [ 2 w q v q u ] = 0 holds for:Vector Algebra