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JEE Main 2015 Session Shift 1 Question Paper with Solutions | JEE Arc

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JEE Main 2015Session, Shift 1

Physics 15Chemistry 24Mathematics 29

Physics

Q5977As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion:Atoms and Nuclei
Q6197Distance of the center of mass of a solid uniform cone from its vertex is z ₀. If the radius of its base is R and its height is h then z ₀ is equal to:Rotational Motion
Q6205A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is…Rotational Motion
Q6335A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant signal is/are:Communication Systems
Q6495When 5V potential difference is applied across a wire of length 0.1 m, the drift speed of electrons is 2.5 × 10⁻⁴ m s⁻¹. If the electron density in the wire…Current Electricity
Q6679Two coaxial solenoids of different radius carry current I in the same direction. F₁ be the magnetic force on the inner solenoid due to the outer one and F₂ be…Electromagnetic Induction and Alternating Currents
Q6864A red LED emits light at 0.1 watt uniformly around it. The amplitude of the electric field of the light at a distance of 1 m from the diode is:Electronic Devices
Q7330A solid body of constant heat capacity 1 J/° C is being heated by keeping it in contact with reservoirs in two ways: (i) Sequentially keeping in contact with…Thermodynamics
Q7357Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules…Thermodynamics
Q7471Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy…Properties of Solids and Liquids
Q8084From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and…Rotational Motion
Q8187A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to T M…Oscillations and Waves
Q8188The period of oscillation of a simple pendulum is T = 2π √(L/g). Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the…Oscillations and Waves
Q8390Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm, the minimum separation between two objects that human eye can…Optics
Q8517A train is moving on a straight track with speed 20 m s⁻¹. It is blowing its whistle at the frequency of 1000 Hz. The percentage change in the frequency heard…Oscillations and Waves

Chemistry

Q101Which of the following compounds will exhibit geometrical isomerism?Some Basic Principles of Organic Chemistry
Q113In Carius method of estimation of halogens, 250 mg of an organic compound gave 141 mg of AgBr. The percentage of bromine in the compound is: (at. Mass Ag =…Some Basic Principles of Organic Chemistry
Q230Which of the vitamins given below is water soluble?Biomolecules
Q332The intermolecular interaction that is dependent on the inverse cube of distance between the molecule is:Chemical Bonding and Molecular Structure
Q405The standard Gibbs energy change at 300 K for the reaction 2A B + C is 2494.2 J. At a given time, the composition of the reaction mixture is [A] = 1/2, [B] =…Equilibrium
Q468Higher order (>3) reactions are rare due toChemical Kinetics
Q606Which of the following compounds is not colored yellow?Coordination Compounds
Q671The number of geometric isomers that can exist for square planar [Pt (Cl) (py) (NH₃) (NH₂OH)]+ is (py = pyridine):Coordination Compounds
Q759The colour of KMnO₄ is due to:d- and f-Block Elements
Q856Match the catalysts to the correct processes: Catalyst Process (A) TiCl₃ (i) Wacker process (B) PdCl₂ (ii) Ziegler - Natta polymerization (C) CuCl₂ (iii)…d- and f-Block Elements
Q934Two Faraday of electricity is passed through a solution of CuSO₄. The mass of copper deposited at the cathode is: (at. mass of Cu = 63.5 amu)Redox Reactions and Electrochemistry
Q1142The synthesis of alkyl fluorides is best accomplished by:Organic Compounds Containing Halogens
Q1210From the following statements regarding H₂O₂, choose the incorrect statement:Hydrogen
Q1432In the context of the Hall-Heroult process for the extraction of Al, which of the following statements is false?Isolation of Elements
Q1505Assertion: Nitrogen and Oxygen are the main components in the atmosphere but these do not react to form oxides of nitrogen. Reason: The reaction between…p-Block Elements
Q1539Which one has the highest boiling point?p-Block Elements
Q1550The ionic radii (in Å) of N³–, O²– and F^– are respectively:Classification of Elements and Periodicity in Properties
Q1716Which polymer is used in the manufacture of paints and lacquers?Polymers
Q1872Which one of the following alkaline earth metal sulphates has its hydration enthalpy greater than its lattice enthalpy?S Block Elements
Q1917Sodium metal crystallizes in a body centred cubic lattice with a unit cell edge of 4.29 Å. The radius of sodium atom is approximately:Solid State
Q2006The vapour pressure of acetone at 20^(o)C is 185 torr. When 1.2 g of a non-volatile substance was dissolved in 100 g of acetone at 20^(o)C, its vapour…Solutions
Q2065The molecular formula of a commercial resin used for exchanging ions in water softening is C₈H₇SO₃Na (Mol. Wt. 206). What would be the maximum uptake of Ca²⁺…Some Basic Concepts in Chemistry
Q2112Which of the following is the energy of a possible excited state of hydrogen?Atomic Structure
Q2292The following reaction is performed at 298 K 2NO(g) + O₂ (g) 2NO₂ (g) The standard free energy of formation of NO(g) is 86.6 kJ/mol at 298 K. What is the…Chemical Thermodynamics

Mathematics

Q2394The equation of the plane containing the line 2x-5y+z=3; x+y+4z=5, and parallel to the plane, x+3y+6z=1, is:Three Dimensional Geometry
Q2395The distance of the point (1, 0, 2) from the point of intersection of the line (x - 2)/3 = (y + 1)/4 = (z - 2)/12 and the plane x - y + z = 16, is:Three Dimensional Geometry
Q2632Let f(x) be a polynomial of degree four having extreme values at x=1 and x=2. If lim x → 0 [ 1 + (f(x))/(x²) ] = 3, then f (2) is equal to:Limit, Continuity and Differentiability
Q2758The normal to the curve, x² + 2xy - 3y² = 0, at (1,1)Limit, Continuity and Differentiability
Q2804The area (in sq. units) of the region described by (x,y):y² ≤ 2x. and. y ≥ 4x - 1 is:Integral Calculus
Q2974The sum of coefficients of integral power of x in the binomial expansion (1 - 2 x)⁵⁰ is:Binomial Theorem and Its Simple Applications
Q3020Locus of the image of the point (2, 3) in the line (2x - 3y + 4) + k(x - 2y + 3) = 0, k R, is a:Coordinate Geometry
Q3091The number of common tangents to the circles x² + y² - 4x - 6x - 12 = 0 and x² + y² + 6x + 18y + 26 = 0, is:Coordinate Geometry
Q3251A complex number z is said to be unimodular if | z | = 1. Suppose z₁ and z₂ are complex numbers such that (z₁ - 2z₂)/(2 - z₁ z₂) is unimodular and z₂ is not…Complex Numbers and Quadratic Equations
Q3351The integral ∫₂⁴ (log x²)/(log x² + log (36 - 12x + x²))dx is equal to:Integral Calculus
Q3508Let y(x) be the solution of the differential equation (x log x)dy/dx + y = 2x log x,(x ≥ 1). Then y(e) is equal to:Differential Equations
Q3772The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse (x²)/9 + (y²)/5 = 1, is:Coordinate Geometry
Q3904If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the tower, are 30°, 45° and 60°…Height and Distance
Q4002The integral ∫ dx/(x²(x⁴ + 1)^(3/4)) equals:Integral Calculus
Q4088Let tan ⁻¹y = tan ⁻¹x + tan ⁻¹(2x/(1 - x²)), where | x | < 1/(3). Then a value of y is:Trigonometry
Q4179If the function. g(x) = \ k√(x + 1), 0 ≤ x ≤ 3 m x + 2, 3 < x ≤ 5. is differentiable, then the value of k+m is:Limit, Continuity and Differentiability
Q4312The negation of s (r s) is equivalent to:Mathematical Reasoning
Q4555The set of all values of λ for which the system of linear equations: 2x₁ - 2x₂ + x₃ = λ x₁ 2x₁ - 3x₂ + 2x₃ = λ x₂ - x₁ + 2x₂ = λ x₃ has a non-trivial solutionMatrices and Determinants
Q4657If A = [ 1 2 2 2 1 - 2 a 2 b ] is a matrix satisfying the equation A A^(T) = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to:Matrices and Determinants
Q4695Let O be the vertex and Q be any point on the parabola, x² = 8y. If the point P divides the line segment OQ internally in the ratio 1:3, then locus of P is:Coordinate Geometry
Q4840The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is:Permutations and Combinations
Q4972If 12 different balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is:Statistics and Probability
Q5123Let α and β be the roots of equation x² - 6x - 2 = 0. If a n = α ⁿ - β ⁿ, for n ≥ 1, then the value of (a₁₀ - 2a₈)/2a₉ is equal to:Complex Numbers and Quadratic Equations
Q5173If m is the A.M. of two distinct real numbers l and n (l,n > 1) and G₁,G₂ and G₃ are three geometric means between l and n, then G₁⁴ + 2G₂⁴ + G₃⁴ equals:Sequence and Series
Q5292The sum of first 9 terms of the series. (1³)/1 + (1³ + 2³)/(1 + 3) + (1³ + 2³ + 3³)/(1 + 3 + 5) +......Sequence and Series
Q5352Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A × B, each having atleast three elements areSets, Relations and Functions
Q5413The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are…Statistics and Probability
Q5514The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0) (0, 41) and (41, 0) is:Coordinate Geometry
Q5717Let a, b and c be three non-zero vectors such that no two of them are collinear and (a × b) × c = 1/3| b || c | a. If θ is the angle between vectors b and c…Vector Algebra