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JEE Main 2002 Annual Paper 1 Question Paper with Solutions | JEE Arc

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JEE Main 2002Annual, Paper 1

Physics 65Chemistry 62Mathematics 70

Physics

Q5862The power factor of AC circuit having resistance (R) and inductance (L) connected in series and an angular velocity ω isElectromagnetic Induction and Alternating Currents
Q5935In a transformer, number of turns in the primary coil are 140 and that in the secondary coil are 280. If current in primary coil is 4A, then that in the…Electromagnetic Induction and Alternating Currents
Q5964If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n=2 isAtoms and Nuclei
Q6068If N₀ is the original mass of the substance of half-life period t 1/2 = 5 years, then the amount of substance left after 15 years isAtoms and Nuclei
Q6069At a specific instant emission of radioactive compound is deflected in a magnetic field. The compound can emit (i) electrons (ii) protons (iii) H e²⁺ (iv)…Atoms and Nuclei
Q6139Capacitance (in F) of a spherical conductor with radius 1 m isElectrostatics
Q6173If there are n capacitors in parallel connected to V volt source, then the energy stored is equal toElectrostatics
Q6257Two identical particles move towards each other with velocity 2v and v respectively. The velocity of center of mass isRotational Motion
Q6260The minimum velocity (in m s⁻¹) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding isKinematics
Q6390The mass of product liberated on anode in an electrochemical cell depends on (where t is the time period for which the current is passed).Current Electricity
Q6406If θ ₁, is the inversion temperature, θ n is the neutral temperature, θ c is the temperature of the cold junction, thenCurrent Electricity
Q6407A wire when connected to 220 V mains supply has power dissipation P₁. Now the wire is cut into two equal pieces which are connected in parallel to the same…Current Electricity
Q6446If an ammeter is to be used in place of a voltmeter, then we must connect with the ammeter aCurrent Electricity
Q6532Formation of covalent bonds in compounds exhibitsDual Nature of Matter and Radiation
Q6612Sodium and copper have work functions 2.3 eV and 4.5 eV respectively. Then the ratio of the wavelengths is nearest toDual Nature of Matter and Radiation
Q6728Electromagnetic waves are transverse in nature is evident byElectromagnetic Waves
Q6831Which of the following are not electromagnetic waves?Electromagnetic Waves
Q6849At absolute zero, Si acts asElectronic Devices
Q6850By increasing the temperature, the specific resistance of a conductor and a semiconductorElectronic Devices
Q6851The energy band gap is maximum inElectronic Devices
Q6890The part of a transistor which is most heavily doped to produce large number of majority carriers isElectronic Devices
Q6914If a charge q is placed at the center of the line joining two equal charges Q such that the system is in equilibrium then the value of q isElectrostatics
Q6990On moving a charge of 20 coulomb by 2 cm, 2 J of work is done, then the potential differences between the points isElectrostatics
Q7059Wavelength of light used in an optical instrument are λ ₁ = 4000 A° and λ ₂ = 5000 A°, then ratio of their respective resolving powers (corresponding to λ ₁…Optics
Q7060An astronomical telescope has a large aperture toOptics
Q7074If two mirrors are kept at 60° to each other, then the number of images formed by them isOptics
Q7090Which of the following is used in optical fibres?Optics
Q7174The escape velocity of a body depends upon mass asGravitation
Q7175The kinetic energy needed to project a body of mass m from the earth surface (radius R) to infinity isGravitation
Q7225Energy required to move a body of mass m from an orbit of radius 2R to 3R isGravitation
Q7244If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite willGravitation
Q7333Which of the following is more close to a black body?Properties of Solids and Liquids
Q7334If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water shouldProperties of Solids and Liquids
Q7335Two spheres of the same material have radii 1 m and 4 m and temperatures 4000 K and 2000 K respectively. The ratio of the energy radiated per second by the…Thermodynamics
Q7336Infrared radiation is detected byThermodynamics
Q7349At what temperature is the r.m.s velocity of a hydrogen molecule equal to that of an oxygen molecule at 47° C?Kinetic Theory of Gases
Q7350Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside willKinetic Theory of Gases
Q73511 mole of a gas with γ = 7/5 is mixed with 1 mole of a gas with γ = 5/3, then the value of γ for the resulting mixture isThermodynamics
Q7441Heat given to a body which raises its temperature by 1° C isThermodynamics
Q7539When forces F₁, F₂, F₃ are acting on a particle of mass m such that F₂ and F₃ are mutually perpendicular, then the particle remains stationary. If the force…Laws of Motion
Q7565A light string passing over a smooth light pulley connects two blocks of masses m₁ and m₂ (vertically). If the acceleration of the system is g/8, then the…Laws of Motion
Q7572A lift is moving down with acceleration a. A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and…Laws of Motion
Q7573Two forces are such that the sum of their magnitudes is 18 N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitudes of…Laws of Motion
Q7664If in a circular coil A of radius R, current I is flowing and in another coil B of radius 2R a current 2I is flowing, then the ratio of the magnetic fields B…Magnetic Effects of Current and Magnetism
Q7665If a current is passed through a spring then the spring willMagnetic Effects of Current and Magnetism
Q7731The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of itsMagnetic Effects of Current and Magnetism
Q7732If an electron and a proton having same momentum enter perpendicular to a magnetic field, thenMagnetic Effects of Current and Magnetism
Q7838Speeds of two identical cars are u and 4 u at the specific instant. The ratio of the respective distances in which the two cars are stopped from that instant…Kinematics
Q7854From a building two balls A and B are thrown such that A is thrown upwards and B downwards (both vertically with the same speed). If v A and v B are their…Kinematics
Q7890A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in m s⁻¹) through a small hole on the side wall of the cylinder…Properties of Solids and Liquids
Q8038Initial angular velocity of a circular disc of mass M is ω ₁. Then two small spheres of mass m are attached gently to diametrically opposite points on the…Rotational Motion
Q8063A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum…Rotational Motion
Q8077Moment of inertia of a circular wire of mass M and radius R about its diameter isRotational Motion
Q8124If a spring has time period T, and is cut into n equal parts, then the time period of each part will beOscillations and Waves
Q8125In a simple harmonic oscillator, at the mean positionOscillations and Waves
Q8178A child swinging on a swing in sitting position, stands up, then the time period of the swing willOscillations and Waves
Q8214Identify the pair whose dimensions are equalUnits and Measurements
Q8472Tube A has bolt ends open while tube B has one end closed, otherwise they are identical. The ratio of fundamental frequency of tube A and B isOscillations and Waves
Q8473length of a string tied to two rigid supports is 40 cm. Maximum length (wavelength in cm) of a stationary wave produced on it isOscillations and Waves
Q8474When temperature increases, the frequency of a tuning forkOscillations and Waves
Q8536A wave y=a sin (ω t - kx) on a string meets with another wave producing a node at x=0. Then the equation of the unknown wave isOscillations and Waves
Q8537A tuning fork arrangement (pair) produces 4 beats/sec with one fork of frequency 288 cps. A little wax is placed on the unknown fork and it then produces 2…Oscillations and Waves
Q8557A ball whose kinetic energy E, is projected at an angle of 45° to the horizontal. The kinetic energy of the ball at the highest point of its height will beWork, Energy and Power
Q8558If a body looses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest?Work, Energy and Power
Q8613A spring of force constant 800 N/m has an extension of 5 cm. The work done in extending it from 5 cm to 15 cm isWork, Energy and Power

Chemistry

Q79Arrangement of (CH₃)₃C-, (CH₃)₂CH-, CH₃-CH₂- when attached to benzyl or an unsaturated group in increasing order of inductive effect isSome Basic Principles of Organic Chemistry
Q91A similarity between optical and geometrical isomerism is thatSome Basic Principles of Organic Chemistry
Q92Racemic mixture is formed by mixing twoSome Basic Principles of Organic Chemistry
Q93Which of the following does not show geometrical isomerism?Some Basic Principles of Organic Chemistry
Q188The functional group, which is found in amino acid isBiomolecules
Q223RNA is different from DNA because RNA containsBiomolecules
Q259Which of the following statements is true?Chemical Bonding and Molecular Structure
Q274Hybridisation of underline atom changes inChemical Bonding and Molecular Structure
Q275A square planar complex is formed by hybridisation of which atomic orbitals ?Chemical Bonding and Molecular Structure
Q276In which of the following species the interatomic bond angle is 109^(o)28' ?Chemical Bonding and Molecular Structure
Q346Which of the following are arranged in an increasing order of their bond strengths?Chemical Bonding and Molecular Structure
Q390For the reaction CO (g) + (1/2) O₂ (g) CO₂ (g), K p /K c is:Equilibrium
Q430Change in volume of the system does not alter which of the following equilibria?Equilibrium
Q457If half-life of a substance is 5 yrs, then the total amount of substance left after 15 years, when initial amount is 64 grams isChemical Kinetics
Q458The integrated rate equation is Rt = log C₀ - log C t. The straight line graph is obtained by plottingChemical Kinetics
Q459Units of rate constant of first and zero order reactions in terms of molarity M unit are respectivelyChemical Kinetics
Q479β - particle is emitted in radioactivity byNuclear Chemistry (historical)
Q490For the reaction A + 2B → C, rate is given by R = [A] [B]² then the order of the reaction isChemical Kinetics
Q503The differential rate law for the reaction H₂ + I₂ → 2HI isChemical Kinetics
Q556CH₃ - Mg - Br is an organometallic compound due to:Coordination Compounds
Q603The most stable ion is:Coordination Compounds
Q666The type isomerism present in nitropentammine chromium (I I I) chloride is:Coordination Compounds
Q753How do we differentiate between Fe³⁺ and Cr³⁺ in group III?d- and f-Block Elements
Q797Most common oxidation states of Ce (cerium) are:d- and f-Block Elements
Q841Which of the following ions has the maximum magnetic moment?d- and f-Block Elements
Q923Conductivity (Seimen’s S) is directly proportional to area of the vessel and the concentration of the solution in it and is inversely proportional to the…Redox Reactions and Electrochemistry
Q958For the following cell with hydrogen electrodes at two different pressure p₁ and p₂. What will be the emf for the given cell: Pt(H₂)|H⁺ (aq)|Pt(H₂) p₁ 1M p₂Redox Reactions and Electrochemistry
Q959EMF of a cell in terms of reduction potential of its left and right electrodes is:Redox Reactions and Electrochemistry
Q960Which of the following reaction is possible at anode?Redox Reactions and Electrochemistry
Q961When the sample of copper with zinc impurity is to be purified by electrolysis, the appropriate electrodes are:Redox Reactions and Electrochemistry
Q1108Value of gas constant R isGaseous State
Q1109For an ideal gas, number of moles per litre in terms of its pressure P, gas constant R and temperature T isGaseous State
Q1116Kinetic theory of gases provesGaseous State
Q1133The reaction: (CH)₃C - Br H₂O (CH)₃C - OHOrganic Compounds Containing Halogens
Q1185Which of these will not react with acetylene ?Hydrocarbons
Q1186Acetylene does not react with:Hydrocarbons
Q1276Species acting as both Bronsted acid and base is:Equilibrium
Q12891 M NaCL and 1 M HCL are present in an aqueous solution. The solution isEquilibrium
Q1324Let the solubility of an aqueous solution of Mg(OH)₂ be x then its K s p is:Equilibrium
Q1375Aluminium is extracted by the electrolysis ofIsolation of Elements
Q1376The metal extracted by leaching with a cyanide isIsolation of Elements
Q1525Oxidation number of Cl in CaOCl₂ (bleaching powder) is:p-Block Elements
Q1543The correct order of ionic radius isClassification of Elements and Periodicity in Properties
Q1544C e⁺³, L a⁺³, P m⁺³ and Y b⁺³ have ionic radial in the increasing order asClassification of Elements and Periodicity in Properties
Q1713Polymer formation from monomers starts byPolymers
Q1793Which of the following is a redox reaction ?Redox Reactions and Electrochemistry
Q1821KO₂ (potassium super oxide) is used in oxygen cylinders in space and submarines because it:S Block Elements
Q1842The metallic sodium disolves in liquid ammonia to form a deep blue coloured solution. The deep blue colour is due to formation of:S Block Elements
Q1868A metal M readily forms its sulphate MSO₄, which is water-soluble. It forms its oxide MO which becomes inert on heating. It forms an insoluble hydroxide…S Block Elements
Q1912Na and Mg crystallize in BCC and FCC type crystals respectively, then the number of atoms of Na and Mg present in the unit cell of their respective crystal is:Solid State
Q1974Freezing point of an aqueous solution is (-0.186)^(o)C. Elevation of boiling point of the same solution is K b = 0.512 ^(o)C, K f = 1.86 ^(o)C, find the…Solutions
Q1995In a mixture of A and B, components show negative deviation when:Solutions
Q2020With increase of temperature, which of these changes?Some Basic Concepts in Chemistry
Q2061Number of atoms in 558.5 gram Fe (at. wt. of Fe = 55.85 g mol⁻¹) isSome Basic Concepts in Chemistry
Q2086In a compound C, H and N atoms are present in 9: 1: 3.5 by weight. Molecular weight of the compound is 108 g mol⁻¹. Molecular formula of compound isSome Basic Concepts in Chemistry
Q2108In a hydrogen atom, if energy of an electron in ground state is -13.6 eV, then that in the 2ⁿd excited state isAtomic Structure
Q2151Uncertainty in position of a minute particle of mass 25 g in space is 10⁻⁵ m. What is the uncertainty in its velocity (in ms⁻¹) (h = 6.6 × 10⁻³⁴ Js)Atomic Structure
Q2227Alum helps in purifying water by:Surface Chemistry
Q2284If an endothermic reaction is non-spontaneous at freezing point of water and becomes feasible at its boiling point, then:Chemical Thermodynamics
Q2309A heat engine absorbs heat Q₁ at temperature T₁ and heat Q₂ at temperature T₂. Work done by the engine is J (Q₁ + Q₂). This data:Chemical Thermodynamics
Q2324The heat required to raise the temperature of body by 1 K is called:Chemical Thermodynamics
Q2331For the reactions 2C + O₂ → 2CO₂; Δ H = -393 J 2Zn + O₂ → 2ZnO; Δ H = -412 JChemical Thermodynamics

Mathematics

Q2386A plane which passes through the point (3,2,0) and the line (x - 4)/1 = (y - 7)/5 = (z - 4)/4 is:Three Dimensional Geometry
Q2543The d.r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle π /4 with plane x+y=3 are:Three Dimensional Geometry
Q2617The maximum distance from origin of a point on the curve x = a sin t - b sin (at/b) y = a cos t - b cos (at/b), both a,b > 0 isLimit, Continuity and Differentiability
Q2691If 2a+3b+6c=0, (a,b,c R) then the quadratic equation a x² + bx + c = 0 hasLimit, Continuity and Differentiability
Q2792The area bounded by the curves y = ln x,y = ln | x |,y = | ln 1mu x | and y = | ln | x | | is:Integral Calculus
Q2886The positive integer just greater than (1 + 0.0001)¹⁰⁰⁰⁰ isBinomial Theorem and Its Simple Applications
Q2903The coefficients of x^(p) and x^(q) in the expansion of (1 + x)^(p + q) areBinomial Theorem and Its Simple Applications
Q2964If the sum of the coefficients in the expansion of (a + b)ⁿ is 4096, then the greatest coefficient in the expansion isBinomial Theorem and Its Simple Applications
Q2965r and n are positive integers r > 1, n > 2 and coefficient of (r + 2)^(th) term and 3r^(th) term in the expansion of (1 + x)²ⁿ are equal, then n equalsBinomial Theorem and Its Simple Applications
Q3017The equation of a circle with origin as a center and passing through an equilateral triangle whose median is of length 3 a is:Coordinate Geometry
Q3036If the chord y = mx + 1 of the circle x² + y² = 1 subtends an angle of measure 45° at the major segment of the circle then value of m is:Coordinate Geometry
Q3060The centres of a set of circles, each of radius 3, lie on the circle x² + y² = 25. The locus of any point in the set is:Coordinate Geometry
Q3105The centre of the circle passing through (0, 0) and (1, 0) and touching the circle x² + y² = 9 is:Coordinate Geometry
Q3144If | z - 4 | < | z - 2 |, its solution is given by:Complex Numbers and Quadratic Equations
Q3172The locus of the centre of a circle which touches the circle | z - z₁ | = a and | z - z₂ | = b externally (z, z₁ z₂ are complex numbers) will be:Complex Numbers and Quadratic Equations
Q3205z and w are two nonzero complex numbers such that | z | = | w | and Arg z + Arg w = π then z equalsComplex Numbers and Quadratic Equations
Q3279lim n → ∞ (1^(p) + 2^(p) + 3^(p) +..... + n^(p))/(n^(p + 1)) isIntegral Calculus
Q3324I n = ∫₀^(π /4) tan ⁿx dx then lim n → ∞ n[ I n + I n + 2 ] equalsIntegral Calculus
Q3325∫₀^(10π) | sin x |dx isIntegral Calculus
Q3326∫₀² [ x² ]dx isIntegral Calculus
Q3327∫ - π ^π (2x(1 + sin x))/(1 + cos ²x) dx isIntegral Calculus
Q3328If y=f(x) makes + ve intercept of 2 and 0 unit on x and y axes and encloses an area of 3/4 square unit with the axes then ∫₀² xf'(x)dx isIntegral Calculus
Q3572The order and degree of the differential equation (1 + 3dy/dx)^(2/3) = 4 d³y d x³ areDifferential Equations
Q3576The solution of the equation d²y d x² = e⁻²ˣDifferential Equations
Q3662If y = (x + √(1 + x²))ⁿ, then (1 + x²) d²y d x² + xdy/dx isLimit, Continuity and Differentiability
Q3837The domain of sin ⁻¹[ log ₃(x/3) ] isSets, Relations and Functions
Q3885The period of sin ²θ isSets, Relations and Functions
Q3886Which one is not periodic?Sets, Relations and Functions
Q4083cot ⁻¹(√(cos α)) - tan ⁻¹(√(cos α)) = x, then sin x is equal to:Trigonometry
Q4124f is defined in [ - 5,5 ] as f(x) = x if x is rational = - x if x is irrational. ThenLimit, Continuity and Differentiability
Q4168f(x) and g(x) are two differentiable functions on [0, 2] such that f''(x) - g''(x) = 0, f'(1) = 2, g'(1) = 4, f(2) = 3, g(2) = 9 then f(x) - g(x) at x = 3/2 isLimit, Continuity and Differentiability
Q4169If f(x + y) = f(x).f(y) x, y and f(5) = 2, f'(0) = 3, then f'(5) isLimit, Continuity and Differentiability
Q4220If f(1) = 1,f'(1) = 2, then lim x → 1 (√(f(x)) - 1)/(x - 1) isLimit, Continuity and Differentiability
Q4221Let f(2) = 4 and f'(x) = 4. Then lim x → 2 (xf(2) - 2f(x))/(x - 2) is given byLimit, Continuity and Differentiability
Q4248lim x → ∞ ((x² + 5x + 3)/(x² + x + 2))ˣLimit, Continuity and Differentiability
Q4260lim x → 0 (log xⁿ - [ x ])/([ x ]), n N, ([x] denotes the greatest integer less than or equal to x)Limit, Continuity and Differentiability
Q4263lim x → 0 (√(1 - cos 2x))/(2 x) isLimit, Continuity and Differentiability
Q4305If a n = √(7 + 7 + √(7 +.......)) having n radical signs then by methods of mathematical induction which is trueMathematical Induction
Q4433If a>0 and discriminant of a x² + 2bx + c is -ve, then | a b ax + b b c bx + c ax + b bx + c 0 | is equal toMatrices and Determinants
Q4677Two common tangents to the circle x² + y² = 2a² and parabola y² = 8ax are:Coordinate Geometry
Q4784Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed). Their number is:Permutations and Combinations
Q4785Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are:Permutations and Combinations
Q4786Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers are:Permutations and Combinations
Q4803The sum of integers from 1 to 100 that are divisible by 2 or 5 is:Permutations and Combinations
Q4867A dice is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is:Statistics and Probability
Q5012A problem in mathematics is given to three students A,B,C and their respective probability of solving the problem is 1/2,1/3 and 1/4. Probability that the…Statistics and Probability
Q5013A and B are events such that P(A B) = 3/4, P(A B) = 1/4, P(A) = 2/3 then P(A B) is:Statistics and Probability
Q5033In a triangle with sides a, b, c, r₁ > r₂ > r₃ (which are the ex-radii) then:Properties of Triangle
Q5065If a, b, c are distinct + ve real numbers and a² + b² + c² = 1 then ab + bc + ca isComplex Numbers and Quadratic Equations
Q5077Product of real roots of equation t²x² + | x | + 9 = 0Complex Numbers and Quadratic Equations
Q5109Difference between the corresponding roots of x² + ax + b = 0 and x² + bx + a = 0 is same and a ≠ b, thenComplex Numbers and Quadratic Equations
Q5110If p and q are the roots of the equation x² + px + q = 0, thenComplex Numbers and Quadratic Equations
Q5111If α ≠ β but α ² = 5α - 3 and β ² = 5β - 3 then the equation having α /β and β /α as its roots isComplex Numbers and Quadratic Equations
Q5189If 1, log ₉ (3¹⁻ˣ + 2), log ₃ (4.3ˣ - 1) are in A.P. then x equalsSequence and Series
Q5240Fifth term of a GP is 2, then the product of its 9 terms isSequence and Series
Q5241l, m, n are the p^(th), q^(th) and r^(th) term of a G.P all positive, then | log l p 1 log m q 1 log n r 1 | equalsSequence and Series
Q5242Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP isSequence and Series
Q52811³ - 2³ + 3³ - 4³ +... + 9³ =Sequence and Series
Q5282The value of 2^(1/4). 4^(1/8). 8^(1/16)...∞ isSequence and Series
Q5409In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the…Statistics and Probability
Q5547A triangle with vertices (4,0),(- 1, - 1),(3,5) is:Coordinate Geometry
Q5561Locus of mid point of the portion between the axes of x cos α + y sin α = p where p is constant is:Coordinate Geometry
Q5574If the pair of lines a x² + 2hxy + b y² + 2gx + 2fy + c = 0 intersect on the y -axis then:Coordinate Geometry
Q5575The pair of lines represented by 3a x² + 5xy + (a² - 2)y² = 0 are perpendicular to each other for:Coordinate Geometry
Q5705If a, b, c are vectors such that [ a b c ] = 4 then [ a × b b × c c × a ] =Vector Algebra
Q5757If | a | = 5,| b | = 4,| c | = 3 thus what will be the value of | a. b + b. c + c. a |, given that a + b + c = 0:Vector Algebra
Q5790If the vectors a, b and c from the sides B C, C A and A B respectively of a triangle A B C, then:Vector Algebra
Q5791If | a | = 4,| b | = 2 and the angle between a and b is π /6 then (a × b)² is equal to:Vector Algebra
Q5792If the vectors c, a = x i + y j + z k and b = j are such that a, c and b form a right handed system then c is:Vector Algebra
Q5793a = 3 i - 5 j and b = 6 i + 3 j are two vectors and c is a vector such that c = a × b then | a |:| b |:| c | =Vector Algebra