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JEE Main 2013 Session Shift 1 Question Paper with Solutions | JEE Arc

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JEE Main 2013Session, Shift 1

Physics 20Chemistry 20Mathematics 29

Physics

Q5974In a hydrogen like atom electron make transition from an energy level with quantum number n to another with quantum number (n - 1). If n > > 1, the frequency…Atoms and Nuclei
Q6166Two capacitors C₁ and C₂ are charged to 120 V and 200 V respectively. It is found that connecting them together the potential on each one can be made zero. ThenElectrostatics
Q6204This question has statement I and statement I I. Of the four choices given after the statements, choose the one that best describes the two statements…Rotational Motion
Q6418The supply voltage to room is 120V. The resistance of the lead wires is 6Ω. A 60 W bulb is already switched on. What is the decrease of voltage across the…Current Electricity
Q6451This questions has Statement - I and Statement - I I. Of the four choices given after the Statements, choose the one that best describes into two Statements…Current Electricity
Q6696A circular loop of radius 0.3 cm lies center of the small loop is on the axis of the bigger loop. The distance between their centers is 15 cm. If a current of…Electromagnetic Induction and Alternating Currents
Q6733The magnetic field in a travelling electromagnetic wave has a peak value of 20 n T. The peak value of electric field strength is:Electromagnetic Waves
Q6918Two charges, each equals to q, are kept at x=-a and x=a on the x -axis. A particle of mass m and charge q₀ = q/2 is placed at the origin. If charge q₀ is…Electrostatics
Q7029Diameter of a plano-convex lens is 6 cm and thickness at the center is 3mm. If speed of light in material of lens is 2 × 10⁸ m/s, the focal length of the lens…Optics
Q7180What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of…Gravitation
Q7443Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of…Properties of Solids and Liquids
Q7610Two short bar magnets of length 1 cm each have magnetic moments 1.20 A m² and 1.00 A m² respectively. They are placed on a horizontal table parallel to each…Magnetic Effects of Current and Magnetism
Q7778A projectile is given an initial velocity of (i + 2 j) m/s, where i is along the ground and j is along the vertical. If g = 10 m/s², the equation of its…Kinematics
Q7976A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a mass-less spring such…Properties of Solids and Liquids
Q8044A hoop of radius r and mass m rotating with an angular velocity ω ₀ is placed on a rough horizontal surface. The initial velocity of the center of the hoop is…Rotational Motion
Q8116The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10s it will decrease to α times its original magnitude…Oscillations and Waves
Q8186An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and the cylinder have equal cross sectional…Oscillations and Waves
Q8220Let [ ε ₀ ] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then:Units and Measurements
Q8457A beam of unpolarised light of intensity I₀ is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane…Optics
Q8482A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1%. What is the fundamental frequency of steel if density…Oscillations and Waves

Chemistry

Q5An unknown alcohol is treated with the “Lucas reagent” to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by…Organic Compounds Containing Oxygen
Q194Synthesis of each molecule of glucose in photosynthesis involves:Biomolecules
Q354In which of the following pairs of molecules/ions, both the species are not likely to exist?Chemical Bonding and Molecular Structure
Q355Stability of the species Li₂, Li₂^− and Li₂⁺ increases in the order of:Chemical Bonding and Molecular Structure
Q442The rate of a reaction doubles when its temperature changes from 300K to 310K. Activation energy of such a reaction will be:(R = 8.314 JK^–1 mol^–1 and log 2…Chemical Kinetics
Q670Which of the following complex species is not expected to exhibit optical isomerism?Coordination Compounds
Q854Which of the following arrangements does not represent the correct order of the property stated against it?d- and f-Block Elements
Q978Given E_ C r²⁺ /Cr ^(o) = -0.74 V; E_ MnO₄^ - /M n²⁺ ^(o) = 1.51 V E_ C r₂ O₇²⁻/C r³⁺ ^(o) = 1.33 V; E_ Cl/C l^ - ^(o) = 1.36 V Based on the data given above…Redox Reactions and Electrochemistry
Q1120For gaseous state, if most probable speed is denoted by C, average speed by C^(__) and mean square speed by C, then for a large number of molecules the ratios…Gaseous State
Q1296How many litres of water must be added to 1 litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2?Equilibrium
Q1595The first ionization potential of Na is 5.1 eV. The value of electron gain enthalpy of Na+ will be:Classification of Elements and Periodicity in Properties
Q1596Which of the following represents the correct order of increasing first ionization enthalpy for Ca, Ba, S, Se and Ar?Classification of Elements and Periodicity in Properties
Q1786Consider the following reaction: xMnO₄⁻⁺ yC₂O₄²⁻ + zH⁺ → xMn²⁺ + 2yCO₂ + z/2H₂O The value's of x, y and z in the reaction are, respectively:Redox Reactions and Electrochemistry
Q1944Which of the following exists as covalent crystals in the solid state?Solid State
Q2029The molarity of a solution obtained by mixing 750 mL of 0.5 (M) HCl with 250 mL of 2(M) HCl will be:Some Basic Concepts in Chemistry
Q2087A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g of CO₂. The empirical formula of the hydrocarbon isSome Basic Concepts in Chemistry
Q2088Experimentally it was found that a metal oxide has formula M₀.98O. Metal M, present as M²⁺ and M³⁺ in its oxide. Fraction of the metal which exists as M³⁺…Some Basic Concepts in Chemistry
Q2156Energy of an electron is given by E = - 2.178 × 10⁻¹⁸J((Z²)/(n²)). Wavelength of light required to excite an electron in an hydrogen atom from level n = 1 to…Atomic Structure
Q2231The coagulating power of electrolytes having ions Na⁺, Al³⁺ and Ba²⁺ for arsenic sulphide sol increases in the order:Surface Chemistry
Q2313A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant temperature of 37.0^(o)C. As it does so, it absorbs 208J…Chemical Thermodynamics

Mathematics

Q2485If the lines (x - 2)/1 = (y - 3)/1 = (z - 4)/(- k) and (x - 1)/k = (y - 4)/2 = (z - 5)/1 are coplanar, then k can have:Three Dimensional Geometry
Q2552Distance between two parallel planes 2x+y+2z=8 and 4x+2y+4z+5=0 is:Three Dimensional Geometry
Q2757The intercepts on x -axis made by tangents to the curve, y = ∫₀ˣ | t |dt,x R, which are parallel to the line y=2x, are equal to:Limit, Continuity and Differentiability
Q2802The area (in square units) bounded by the curves y = √(x,) 2y - x + 3 = 0, x -axis, and lying in the first quadrant is:Integral Calculus
Q2909The term independent of x in expansion of ((x + 1)/(x^(2/3) - x^(1/3) + 1) - (x - 1)/(x - x^(1/2)))¹⁰ isBinomial Theorem and Its Simple Applications
Q3118The circle passing through (1, -2) and touching the axis of x at (3, 0) also passes through the point:Coordinate Geometry
Q3209If z is a complex number of unit modulus and argument θ, then arg ((1 + z)/(1 + z)) equals:Complex Numbers and Quadratic Equations
Q3349Statement-1: The value of the integral ∫ π /6 ^(π /3) dx/(1 + √(tan x)) is equal to π /6 Statement-2: ∫ a ^(b) f(x) dx = ∫ a ^(b) f(a + b - x) dx.Integral Calculus
Q3582At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by…Differential Equations
Q3675If y = sec (tan ⁻¹x), then dy/dx at x=1 is equal to:Limit, Continuity and Differentiability
Q3735The equation of the circle passing through the foci of the ellipse (x²)/16 + (y²)/9 = 1, and having centre at (0,3) is:Coordinate Geometry
Q3902ABCD is a trapezium such that AB and CD are parallel and BC CD. If ADB = θ, BC = p and CD = q, then AB is equal to:Height and Distance
Q4001If ∫ f(x)dx = ψ (x), then ∫ x⁵f(x³)dx is equal toIntegral Calculus
Q4087If x, y, z are in A.P. and tan ⁻¹x, tan ⁻¹y and tan ⁻¹z are also in A.P., then:Trigonometry
Q4267lim x → 0 ((1 - cos 2x)(3 + cos x))/(x tan 4x) is equal toLimit, Continuity and Differentiability
Q4310Consider: Statement − I: (p q) (p q) is a fallacy. Statement − II: (p → q) (q → p) is a tautology.Mathematical Reasoning
Q4519If P = [ 1 α 3 1 3 3 2 4 4 ] is the adjoint of a 3 × 3 matrix A and | A | = 4, then α is equal to:Matrices and Determinants
Q4554The number of values of k, for which the system of equations: (k + 1)x + 8y = 4k kx + (k + 3)y = 3k - 1 has no solution, isMatrices and Determinants
Q4678Given: A circle, 2x² + 2y² = 5 and a parabola, y² = 4 5 x. Statement-1: An equation of a common tangent to these curves is y = x + 5. Statement-2: If the…Coordinate Geometry
Q4818Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is:Permutations and Combinations
Q4819Let T n be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If T n + 1 - T n = 10, then the value of n is:Permutations and Combinations
Q4873A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student…Statistics and Probability
Q5053If the equations x² + 2x + 3 = 0 and a x² + bx + c = 0, a, b, c R, have a common root, then a:b:c isComplex Numbers and Quadratic Equations
Q5290The sum of first 20 terms of the sequence 0.7, 0.77, 0.777,........,isSequence and Series
Q5430All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following…Statistics and Probability
Q5499A ray of light along x + 3 y = 3 gets reflected upon reaching X -axis, the equation of the reflected ray is:Coordinate Geometry
Q5528The x -coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1) (1, 1) and (1, 0) is:Coordinate Geometry
Q5643The expression (tan A)/(1 - cot A) + (cot A)/(1 - tan A) can be written as:Trigonometry
Q5686If the vectors AB = 3 i + 4 k and AC = 5 i - 2 j + 4 k are the sides of a triangle ABC, then the length of the median through A is:Vector Algebra