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JEE Main 2007 Annual Paper 1 Question Paper with Solutions | JEE Arc

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JEE Main 2007Annual, Paper 1

Physics 33Chemistry 35Mathematics 37

Physics

Q5870In an a.c. circuit the voltage applied is E = E₀ sin ω t. The resulting current in the circuit is I = I₀ sin (ω t - (π)/2). The power consumption in the…Electromagnetic Induction and Alternating Currents
Q5968Which of the following transitions in hydrogen atoms emit photons of highest frequency ?Atoms and Nuclei
Q6039If M O is the mass of an oxygen isotope ₈O¹⁷, M p and M N are the masses of a proton and neutron respectively, the nuclear binding energy of the isotope isAtoms and Nuclei
Q6080In gamma ray emission from a nucleusAtoms and Nuclei
Q6081The half-life period of a ratio-active element X is same as the mean life time of another ratio-active element Y. Initially they have the same number of…Atoms and Nuclei
Q6175A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the…Electrostatics
Q6182A parallel plate condenser with a dielectric of dielectric constant K between the plates has a capacity C and is charged to a potential V volt. The dielectric…Electrostatics
Q6195A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The center of mass of the…Rotational Motion
Q6415The resistance of a wire is 5 ohm at 50° C and 6 ohm at 100° C. The resistance of the wire at 0° C will beCurrent Electricity
Q6594Photon of frequency v has a momentum associated with it. If c is the velocity of light, the momentum isDual Nature of Matter and Radiation
Q6677An ideal coil of 10H is connected in series with a resistance of 5Ω and a battery of 5V. 2 second after the connection is made, the current flowing in ampere…Electromagnetic Induction and Alternating Currents
Q6862Carbon, silicon and germanium have four valence electrons each. At room temperature which one of the following statements is most appropriate ?Electronic Devices
Q6996An electric charge 10⁻³ μ C is placed at the origin (0,0) of X-Y co-ordinate system. Two points A and B are situated at (2, 2) and (2,0) respectively. The…Electrostatics
Q6997The potential at a point x (measured in μ m) due to some charges situated on the x -axis is given by V(x) = 20/(x² - 4) volt The electric field E at x = 4 μ m…Electrostatics
Q7026Two lenses of power -15 D and +5 D are in contact with each other. The focal length of the combination isOptics
Q7130If g E and g M are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be…Gravitation
Q7355If C p and C v denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, thenThermodynamics
Q7605A block of mass m is connected to another block of mass M by a spring (massless) of spring constant k. The block are kept on a smooth horizontal plane…Laws of Motion
Q7657A current I flows along the length of an infinitely long, straight, thin walled pipe. ThenMagnetic Effects of Current and Magnetism
Q7658A long straight wire of radius a carries a steady current i. The current is uniformly distributed across its cross section. The ratio of the magnetic field at…Magnetic Effects of Current and Magnetism
Q7670Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current I₁ and COD carries a current I₂…Magnetic Effects of Current and Magnetism
Q7738A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields E and B with a velocity v perpendicular to both E and B…Magnetic Effects of Current and Magnetism
Q7739A charged particle moves through a magnetic field perpendicular to its direction. ThenMagnetic Effects of Current and Magnetism
Q7882The velocity of a particle is v = v₀ + gt + ft². If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) isKinematics
Q8042Angular momentum of the particle rotating with a central force is constant due toRotational Motion
Q8065A round uniform body of radius R, mass M and moment of inertia I rolls down (without slipping) an inclined plane making an angle θ with the horizontal. Then…Rotational Motion
Q8135A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of…Oscillations and Waves
Q8136A point mass oscillates along the x -axis according to the law x = x₀ cos (ω t - π /4). If the acceleration of the particle is written as a = A cos (ω t + δ)…Oscillations and Waves
Q8137The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2 × 10⁻² cos π t metre. The time at which the maximum…Oscillations and Waves
Q8411In a Young's double slit experiment the intensity at a point where the path difference is (λ)/6 (λ being the wavelength of light used) is I. If I₀ denotes the…Optics
Q8477A sound absorber attenuates the sound level by 20 dB. The intensity decreases by a factor ofOscillations and Waves
Q8570A particle is projected at 60° to the horizontal with a kinetic energy K. The kinetic energy at the highest point isWork, Energy and Power
Q8571A 2 kg block slides on a horizontal floor with a speed of 4m/s. It strikes a uncompressed spring, and compress it till the block is motionless. The kinetic…Work, Energy and Power

Chemistry

Q54The compound formed as a result of oxidation of ethyl benzene by KMnO₄ is:Organic Compounds Containing Oxygen
Q81Presence of a nitro group in a benzene ringSome Basic Principles of Organic Chemistry
Q98Which one of the following conformation of cyclohexane is chiral?Some Basic Principles of Organic Chemistry
Q191The secondary structure of a protein refers toBiomolecules
Q331Which of the following hydrogen bonds is the strongest?Chemical Bonding and Molecular Structure
Q340The charge/size ratio of a cation determines its polarizing power. Which one of the following sequences represents the increasing order of the polarizinig…Chemical Bonding and Molecular Structure
Q350Which of the following species exhibits the diamagnetic behaviour?Chemical Bonding and Molecular Structure
Q351In which of the following ionization processes, the bond order has increased and the magnetic behaviour has changed?Chemical Bonding and Molecular Structure
Q441The energies of activation for forward and reverse reactions for A₂ + B₂ 2AB are 180 kJ mol^−1 and 200 kJ mol^−1 respectively. The presence of catalyst lowers…Chemical Kinetics
Q451Consider the reaction, 2A + B → products. When concentration of B alone was doubled, the half-life did not change. When the concentration of A alone was…Chemical Kinetics
Q487A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial activity is ten times the permissible value…Nuclear Chemistry (historical)
Q488Which of the following nuclear reactions will generate an isotope?Nuclear Chemistry (historical)
Q522Which one of the following is the strongest base in aqueous solution?Organic Compounds Containing Nitrogen
Q710Which one of the following has a square planar geometry?Coordination Compounds
Q803Identify the incorrect statement among the following:d- and f-Block Elements
Q804The actinoids exhibits more number of oxidation states in general than the lanthanoids. This is because:d- and f-Block Elements
Q931The equivalent conductances of two strong electrolytes at infinite dilution in H₂O (where ions move freely through a solution) at 25^(o)C are given below: _ C…Redox Reactions and Electrochemistry
Q971The cell, Zn | Zn²⁺ (1M) || Cu²⁺ (1M) | Cu(E cell ^(o) = 1.10V) was allowed to be completely discharged at 298 K. The relative concentration of Zn²⁺ to Cu²⁺ […Redox Reactions and Electrochemistry
Q1106Equal masses of methane and oxygen are mixed in an empty container at 25^(o)C. The fraction of the total pressure exerted by oxygen isGaseous State
Q1138Which of the following is the correct order of decreasing S N 2 reactivity?Organic Compounds Containing Halogens
Q1163The reaction of toluene with Cl₂ in presence of FeCl₃ gives predominantlyHydrocarbons
Q1187Which of the following reactions will yield 2, 2-dibromopropane?Hydrocarbons
Q1279The first and second dissociation constants of an acid H₂A are 1.0 × 10^−5 and 5.0 × 10^−10 respectively. The overall dissociation constant of the acid will be:Equilibrium
Q1292The pK a of a weak acid (HA) is 4.5. The pOH of an aqueous buffered solution of HA in which 50% of the acid is ionized is:Equilibrium
Q1328In a sautrated solution of the sparingly soluble strong electrolyte AgIO₃ (Molecular mass = 283) the equilibrium which sets in is AgIO₃(s) Ag⁺(aq) + IO₃^(…Equilibrium
Q1467The stability of dihalides of Si,Ge,Sn and Pb increases steadily in the sequence:p-Block Elements
Q1503Regular use of which of the following fertilizer increases the acidity of soil?p-Block Elements
Q1991A 5.25% solution of a substance is isotonic with a 1.5% solution of urea (molar mass = 60 g mol^−1) in the same solvent. If the densities of both the…Solutions
Q2000A mixture of ethyl alcohol and propyl alcohol has a vapour pressure of 290 mm at 300 K. The vapour pressure of propyl alcohol is 200 mm. If the mole fraction…Solutions
Q2026The density (in g mL⁻¹) of a 3.60 M sulphuric acid solution that is 29% H₂SO₄ (molar mass = 98 g mol⁻¹) by mass will beSome Basic Concepts in Chemistry
Q2064In the reaction 2Al(s) + 6HCl(aq) → 2Al³⁺ (aq) + 6Cl⁻(aq) + 3H₂(g)Some Basic Concepts in Chemistry
Q2192Which of the following sets of quantum numbers represents the highest energy of an atom?Atomic Structure
Q2287In conversion of lime-stone to lime, CaCO₃(s) → CaO(s) + CO₂ (g) the vales of ∆H° and ∆S° are +179.1 kJ mol−1 and 160.2 J/K respectively at 298 K and 1 bar…Chemical Thermodynamics
Q2341Assuming that water vapour is an ideal gas, the internal energy change (Δ U) when 1 mol of water is vapourised at 1 bar pressure and 100° C (Given: molar…Chemical Thermodynamics
Q2363Identify the correct statement regarding a spontaneous process:Chemical Thermodynamics

Mathematics

Q2370If a line makes an angle of π /4 with the positive directions of each of x -axis and y -axis, then the angle that the line makes with the positive direction…Three Dimensional Geometry
Q2371Let L be the line of intersection of the planes 2x+3y+z=1 and x+3y+2z=2. If L makes an angle α with the positive x -axis, then cos α equalsThree Dimensional Geometry
Q2623If p and q are positive real numbers such that p² + q² = 1, then the maximum value of (p+q) isLimit, Continuity and Differentiability
Q2695A value of c for which conclusion of Mean Value Theorem holds for the function f(x) = log e x on the interval [ 1,3 ] isLimit, Continuity and Differentiability
Q2704The function f(x) = tan ⁻¹(sin x + cos x) is an incresing function inLimit, Continuity and Differentiability
Q2796The area enclosed between the curves y² = x and y = | x | is:Integral Calculus
Q2908In the binomial expansion of (a - b)ⁿ, n ≥ 5, the sum of 5^(th) and 6^(th) terms is zero, then a/b equalsBinomial Theorem and Its Simple Applications
Q2969The sum of the series ²⁰C₀ - ²⁰C₁ + ²⁰C₂ - ²⁰C₃ +..... -..... + ²⁰C₁₀ isBinomial Theorem and Its Simple Applications
Q3063Consider a family of circles which are passing through the point (-1, 1) and are tangent to x -axis. If (h, k) are the coordinate of the centre of the…Coordinate Geometry
Q3174If | z + 4 | ≤ 3, then the maximum value of | z + 1 | is:Complex Numbers and Quadratic Equations
Q3343The solution for x of the equation ∫ 2 ˣ dt/(t√(t² - 1)) = (π)/2 isIntegral Calculus
Q3344Let I = ∫₀¹ (sin x)/(x)dx and J = ∫₀¹ (cos x)/(x)dx. Then which one of the following is true?Integral Calculus
Q3345Let F(x) = f(x) + f(1/x), where f(x) = ∫ l ˣ (log t)/(1 + t)dt, Then F(e) equalsIntegral Calculus
Q3490The differential equation of all circles passing through the origin and having their centres on the x -axis is:Differential Equations
Q3840The largest interval lying in (- (π)/2,(π)/2) for which the function f(x) = 4^(- x²) + cos ⁻¹(x/2 - 1) + log (cos x), is defined, isSets, Relations and Functions
Q3900A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB(=a) subtends an angle of 60° at the foot of…Height and Distance
Q3948The normal to a curve at P(x,y) meets the x -axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a:Coordinate Geometry
Q3958For the Hyperbola (x²)/(cos ²α) - (y²)/(sin ²α) = 1, which of the following remains constant when α varies = ?Coordinate Geometry
Q4043∫ dx/(cos x + 3 sin x) equalsIntegral Calculus
Q4085If sin⁻¹ (x/5) + cosec⁻¹ (5/4) = (π)/2, then the value of x is:Trigonometry
Q4126The function f:R/ 0 → R given by f(x) = 1/x - 2/(e²ˣ - 1) can be made continuous at x = 0 by defining f (0) asLimit, Continuity and Differentiability
Q4175Let f:R → R be a function defined by f(x) = min x + 1,| x | + 1, then which of the following is true?Limit, Continuity and Differentiability
Q4438If D = | 1 1 1 1 1 + x 1 1 1 1 + y | for x ≠ 0,y ≠ 0, then D is:Matrices and Determinants
Q4514Let A = | 5 5α α 0 α 5α 0 0 5 |. If | A² | = 25, then | α | equalsMatrices and Determinants
Q4734The equation of a tangent to the parabola y² = 8x is y=x+2. The point on this line from which the other tangent to the parabola is perpendicular to the given…Coordinate Geometry
Q4812The set S = 1, 2, 3,........., 12 is to be partitioned into three sets A, B, C of equal size. Thus A B C = S, A B = B C = A C = φ. The number of ways to…Permutations and Combinations
Q4870A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is:Statistics and Probability
Q4936Two aeroplanes I and I I bomb a target in succession. The probabilities of I and I I scoring a hit correctly are 0.3 and 0.2, respectively. The second plane…Statistics and Probability
Q5120If the difference between the roots of the equation x² + ax + 1 = 0 is less than 5, then the set of possible values of a isComplex Numbers and Quadratic Equations
Q5243In a geometric progression consisting of positive terms, each term equals the sum of the next two terns. Then the common ratio of its progression is equalsSequence and Series
Q5287The sum of series 1/(2!) - 1/(3!) + 1/(4!) -....... upto infinity isSequence and Series
Q5412The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class isStatistics and Probability
Q5508Let P = (- 1,0), Q = (0,0) and R = (3,3 3) be three point. The equation of the bisector of the angle PQR is:Coordinate Geometry
Q5513Let A (h,k), B (1,1) and C (2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1 square unit, then the…Coordinate Geometry
Q5579If one of the lines of m y² + (1 - m²)xy - m x² = 0 is a bisector of angle between the lines xy = 0, then m is:Coordinate Geometry
Q5711Let a = i + j + k, b = i - j + 2 k and c = x i + (x - 2) j - k. If the vectors c lies in the plane of a and b, then x equals:Vector Algebra
Q5799If u and v are unit vectors and θ is the acute angle between them, then 2 u × 3 v is a unit vector for:Vector Algebra