Loading…

Questions and solutions are free, always.

Practise

Practice
Revision queue
Revision planner
Take a test
Build a test

Browse

All topics
Blog
Notes & printables
Physics
Chemistry
Mathematics

Account

Your numbers
Study plan
Saved
Plus
Privacy
Terms
Delete account

Skip to content

JEE Main 2003 Annual Paper 1 Question Paper with Solutions | JEE Arc

Past papers

Ctrl K

Practice
Revise
Tests
Topics
More
Dashboard Settings My progress Notes & printables Revision planner Study plan Saved questions Explore Plus

81days to JEE Main

Study

PracticePractice

Study planPlanPlus

Library

Past papersPapers

ProgressProgress

SettingsSettings

JEE Arc Plus₹49 a month. Mocks, plans, notes.→?GuestSign in to save progress

JEE Main 2003Annual, Paper 1

Physics 69Chemistry 61Mathematics 67

Physics

Q5936The core of any transformer is laminated so as toElectromagnetic Induction and Alternating Currents
Q5945In an oscillating LC circuit the maximum charge on the capacitor is Q. The charge on the capacitor when the energy is stored equally between the electric and…Electromagnetic Induction and Alternating Currents
Q5965The wavelengths involved in the spectrum of deuterium (₁² D) are slightly different from that of hydrogen spectrum, becauseAtoms and Nuclei
Q5966Which of the following atoms has the lowest ionization potential ?Atoms and Nuclei
Q5967If the binding energy of the electron in a hydrogen atom is 13.6eV, the energy required to remove the electron from the first excited state of L i⁺⁺ isAtoms and Nuclei
Q6034In the nuclear fusion reaction ₁²H + ₁³H → ₂⁴He + n given that the repulsive potential energy between the two nuclei is 7.7 × 10⁻¹⁴J, the temperature at which…Atoms and Nuclei
Q6070When a U²³⁸ nucleus originally at rest, decays by emitting an alpha particle having a speed 'u', the recoil speed of the residual nucleus isAtoms and Nuclei
Q6071A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 minutes, the rate is 1250 disintegrations per minute…Atoms and Nuclei
Q6072A nucleus with Z=92 emits the following in a sequence: α,β ^ -,β ^ -,α,α,α,α,α,β ^ -,β ^ -,α,β ⁺,β ⁺,α Then Z of the resulting nucleus isAtoms and Nuclei
Q6073Which of the following cannot be emitted by radioactive substances during their decay ?Atoms and Nuclei
Q6074Which of the following radiations has the least wavelength ?Atoms and Nuclei
Q6146A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitorElectrostatics
Q6174The work done in placing a charge of 8 × 10⁻¹⁸ coulomb on a condenser of capacity 100 micro-farad isElectrostatics
Q6231Consider the following two statements: A. Linear momentum of a system of particles is zero B. Kinetic energy of a system of particles is zero. thenRotational Motion
Q6300Consider telecommunication through optical fibres. Which of the following statements is not true?Communication Systems
Q6391The nagative Zn pole of a Daniell cell, sending a constant current through a circuit, decreases in mass by 0.13g in 30 minutes. If the electrochemical…Current Electricity
Q6408A 220 volt, 1000 watt bulb is connected across a 110 volt mains supply. The power consumed will beCurrent Electricity
Q6447The thermo e.m.f. of a thermo -couple is 25 μ V/° C at room temperature. A galvanometer of 40 ohm resistance, capable of detecting current as low as 10⁻⁵ A…Current Electricity
Q6448An ammeter reads upto 1 ampere. Its internal resistance is 0.81 ohm. To increase the range to 10 A the value of the required shunt isCurrent Electricity
Q6499The length of a wire of a potentiometer is 100 cm, and the e. m. f. of its standard cell is E volt. It is employed to measure the e.m.f. of a battery whose…Current Electricity
Q6506The length of a given cylindrical wire is increased by 100%. Due to the consequent decrease in diameter the change in the resistance of the wire will beCurrent Electricity
Q6613Two identical photo-cathodes receive light of frequencies f₁ and f₂. If the velocities of the photo electrons (of mass m) coming out are respectively v₁ and…Dual Nature of Matter and Radiation
Q6673When the current changes from + 2A to -2A in 0.05 second, an e.m.f. of 8 V is inducted in a coil. The coefficient of self- induction of the coil isElectromagnetic Induction and Alternating Currents
Q6674Two coils are placed close to each other. The mutual inductance of the pair of coils depends uponElectromagnetic Induction and Alternating Currents
Q6852A strip of copper and another of germanium are cooled from room temperature to 80K. The resistance ofElectronic Devices
Q6853The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in theElectronic Devices
Q6854In the middle of the depletion layer of a reverse- biased p - n junction, theElectronic Devices
Q6980If the electric flux entering and leaving an enclosed surface respectively is φ ₁ and φ ₂, the electric charge inside the surface will beElectrostatics
Q6991A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the center of the shell. The electrostatic potential at a point P…Electrostatics
Q7061The image formed by an objective of a compound microscope isOptics
Q7075To get three images of a single object, one should have two plane mirrors at an angle ofOptics
Q7176The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of 45° with the…Gravitation
Q7245The time period of satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, the new…Gravitation
Q7246Two spherical bodies of mass M and 5M radii R 2R respectively are released in free space with initial separation between their centers equal to 12R. If they…Gravitation
Q7329''Heat cannot by itself flow from a body at lower temperature to a body at higher temperature'' is a statement or consequence of:Thermodynamics
Q7337The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given byThermodynamics
Q7469During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio C p /C V for the gas isThermodynamics
Q7526Which of the following parameters does not characterize the thermodynamic state of mattter?Thermodynamics
Q7546A marble block of mass 2 kg lying on ice when given a velocity of 6 m/s is stopped by friction in 10 s. Then the coefficient of friction isLaws of Motion
Q7566A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force P is applied at the free end of the rope, the force…Laws of Motion
Q7574A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift…Laws of Motion
Q7575A rocket with a lift-off mass 3.5 × 10⁴ kg is blasted upwards with an initial acceleration of 10m/s². Then the initial thrust of the blast isLaws of Motion
Q7576A light spring balance hangs from the hook of the other light spring balance and a block of mass M kg hangs from the former one. Then the true statement about…Laws of Motion
Q7607A magnetic needle lying parallel to a magnetic field requires W units of work to turn it through 60°. The torque needed to maintain the needle in this…Magnetic Effects of Current and Magnetism
Q7608The magnetic lines of force inside a bar magnetMagnetic Effects of Current and Magnetism
Q7618A thin rectangular magnet suspended freely has a period of oscillation equal to T. Now it is broken into two equal halves (each having half of the original…Magnetic Effects of Current and Magnetism
Q7733A particle of mass M and charge Q moving with velocity v describe a circular path of radius R when subjected to a uniform transverse magnetic field of…Magnetic Effects of Current and Magnetism
Q7734A particle of charge - 16 × 10⁻¹⁸ coulomb moving with velocity 10m s⁻¹ along the x -axis enters a region where a magnetic field of induction B is along the y…Magnetic Effects of Current and Magnetism
Q7772A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an angle of 30° with the horizontal. How far from the throwing point…Kinematics
Q7832The co-ordinates of a moving particle at any time 't' are given by x = α t³ and y = βt³. The speed to the particle at time 't' is given byKinematics
Q7839A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6 m. If the same car is moving at a speed of 100 km/hr, the minimum stopping…Kinematics
Q7970According to Newton's law of cooling, the rate of cooling of a body is proportional to (Δ θ)ⁿ, where Δ θ is the difference of the temperature of the body and…Properties of Solids and Liquids
Q8039A particle performing uniform circular motion has angular frequency is doubled its kinetic energy halved, then the new angular momentum isRotational Motion
Q8078A circular disc X of radius R is made from an iron plate of thickness t, and another disc Y of radius 4 R is made from an iron plate of thickness t/4. Then…Rotational Motion
Q8105Let F be the force acting on a particle having position vector r, and τ be the torque of this force about the origin. ThenRotational Motion
Q8126The displacement of particle varies according to the relation x=4 (cos π t + sin π t). The amplitude of the particle isOscillations and Waves
Q8127A body executes simple harmonic motion. The potential energy (P.E), the kinetic energy (K.E) and total energy (T.E) are measured as a function of displacement…Oscillations and Waves
Q8179A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T. If the…Oscillations and Waves
Q8180Two particles A and B of equal masses are suspended from two massless springs of spring of spring constant k₁ and k₂, respectively. If the maximum velocities…Oscillations and Waves
Q8181The length of a simple pendulum executing simple harmonic motion is increased by 21%. The percentage increase in the time period of the pendulum of increased…Oscillations and Waves
Q8215Dimensions of 1/(μ ₀ε ₀), where symbols have their usual meaning, areUnits and Measurements
Q8216The physical quantities not having same dimensions areUnits and Measurements
Q8408To demonstrate the phenomenon of interference, we require two sources which emit radiationOptics
Q8475The displacement y of a wave travelling in the x -direction is given by y = 10⁻⁴ sin (600t - 2x + (π)/3) metres where x is expressed in metres and t in…Oscillations and Waves
Q8538A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when…Oscillations and Waves
Q8539A metal wire of linear mass density of 9.8 g/m is stretched with a tension of 10 kg - wt between two rigid supports 1 metre apart. The wire passes at its…Oscillations and Waves
Q8559A wire suspended vertically from one of its ends is stretched by attaching a weight of 200N to the lower end. The weight stretches the wire by 1 mm. Then the…Work, Energy and Power
Q8599A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time 't' is proportional toWork, Energy and Power
Q8614A spring of spring constant 5 × 10³ N/m is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another…Work, Energy and Power

Chemistry

Q1During dehydration of alcohols to alkenes by heating with conc. H₂SO₄ the initiation step isOrganic Compounds Containing Oxygen
Q18An ethar is more volatile than an alcohol having the same molecular formula. This is due toOrganic Compounds Containing Oxygen
Q80In the anion HCOO^(- t)he two carbon-oxygen bonds are found to be of equal length. What is the reason for it?Some Basic Principles of Organic Chemistry
Q94The general formula C n H₂nO₂ could be for open chainSome Basic Principles of Organic Chemistry
Q146Complete hydrolysis of cellulose givesBiomolecules
Q224The reason for double helical structure of DNA is operation ofBiomolecules
Q266Which one of the following pairs of molecules will have permanent dipole moments for both membersChemical Bonding and Molecular Structure
Q277Which one of the following compounds has the smallest bond angle in its molecule?Chemical Bonding and Molecular Structure
Q391For the reaction equilibrium N₂O₄ (g) 2NO₂ (g) the concentrations of N₂O₄ and NO₂ at equilibrium are 4.8 × 10⁻² and 1.2 × 10⁻² mol L⁻¹ respectively. The value…Equilibrium
Q431Consider the reaction equilibrium 2 SO₂ (g) + O₂ (g) 2 SO₃ (g); Δ H^(o) = -198 kJ One the basis of Le Chatelier's principle, the condition favourable for the…Equilibrium
Q439In respect of the equation k = Ae^(-E) a /RT in chemical kinetics, which one of the following statements is correct?Chemical Kinetics
Q460For the reaction system: 2NO(g) + O₂(g) → 2NO₂(g) volume is suddenly reduce to half its value by increasing the pressure on it. If the reaction is of first…Chemical Kinetics
Q480The radionucleide ₉₀²³⁴Th undergoes two successive β -decays followed by one α -decay. The atomic number and the mass number respectively of the resulting…Nuclear Chemistry (historical)
Q481The half-life of a radioactive isotope is three hours. If the initial mass of the isotope were 256 g, the mass of it remaining undecayed after 18 hours would beNuclear Chemistry (historical)
Q491The rate law for a reaction between the substances A and B is given by Rate = k[A]ⁿ [B]^(m) On doubling the concentration of A and halving the concentration…Chemical Kinetics
Q579One mole of the complex compound Co(NH₃)₅Cl₃, gives 3 moles of ions on dissolution in water. One mole of the same complex reacts with two moles of AgNO₃…Coordination Compounds
Q580In the coordination compound, K₄[Ni(CN)₄], the oxidation state of nickel is:Coordination Compounds
Q754What would happen when a solution of potassium chromate is treated with an excess of dilute nitric acid?d- and f-Block Elements
Q755Which one of the following nitrates will leave behind a metal on strong heating?d- and f-Block Elements
Q798The radius of La³⁺ (Atomic number of La = 57) is 1.06 Å. Which one of the following given values will be closest to the radius of Lu³⁺ (Atomic number of Lu =…d- and f-Block Elements
Q842For making good quality mirrors, plates of float glass are used. These are obtained by floating molten glass over a liquid metal which does not solidify…d- and f-Block Elements
Q843The number of d-electrons retained in Fe²⁺ (At no of Fe = 26) ion is:d- and f-Block Elements
Q844A red solid is insolvable in water. However it becomes soluble if some K I is added to water. Heating the red solid in a test tube results in liberation of…d- and f-Block Elements
Q845Which one of the following statements is correct?d- and f-Block Elements
Q846The atomic numbers of vanadium (V), Chromium (Cr), manganese (Mn) and iron (Fe) are respectively 23, 24, 25 and 26. Which one of these may be expected to have…d- and f-Block Elements
Q911Several blocks of magnesium are fixed to the bottom of a ship to:Redox Reactions and Electrochemistry
Q924When during electrolysis of a solution of AgNO₃, 9650 coulombs of charge pass through the electroplating bath, the mass of silver deposited on the cathode…Redox Reactions and Electrochemistry
Q962For a cell reaction involving a two-electron change, the standard e.m.f. of the cell is found to be 0.295 V at 25^(o)C. The equilibrium constant of the…Redox Reactions and Electrochemistry
Q963For the redox reaction Zn(s) + Cu²⁺(0.1 M) → Zn²⁺(1M) + Cu(s) taking place in a cell, E cell ^(o) is 1.10 volt. E c ell for the cell will be (2.303RT/F =…Redox Reactions and Electrochemistry
Q964Standard reduction electrode potentials of three metals A,B C are respectively +0.5 V, -3.0 V -1.2 V. The reducing, powers of these metals areRedox Reactions and Electrochemistry
Q1117According to the kinetic theory of gases, in an ideal gas, between two successive collisions of a gas molecule travelsGaseous State
Q1156Bottles containing C₆H₅l and C₆H₅CH₂I lost their original labels. They were labelled A and B for testing A and B were separately taken in test tubes and…Organic Compounds Containing Halogens
Q1175On mixing a certain alkane with chlorine and irradiating it with ultravioletlight, it forms only one monochloroalkane. This alkane could beHydrocarbons
Q1183Butene-1 may be converted to butane by reaction withHydrocarbons
Q1192Which one of the following process will produce hard water?Hydrogen
Q1237Which of the following could act as a propellant for rockets?Hydrogen
Q1290When rain is accompanied by a thunderstorm, the collected rain water will have a pH value:Equilibrium
Q1325The solubility in water of a sparingly soluble salt AB₂ is 1.0 × 10⁻⁵ mol L⁻¹. Its solubility product number will be:Equilibrium
Q1466Glass is a:p-Block Elements
Q1502Which one of the following substances has the highest proton affinity?p-Block Elements
Q1545The reduction in atomic size with increase in atomic number is a characteristic of elements ofClassification of Elements and Periodicity in Properties
Q1593The atomic numbers of Vanadium (V), Chromium (cr), Manganese (Mn) and Iron (Fe), respectively, 23,24,25 and 26. Which one of these may be expected to have the…Classification of Elements and Periodicity in Properties
Q1627Which one of the following is an amphoteric oxide?Classification of Elements and Periodicity in Properties
Q1643According to the Periodic Law of elements, the variation in properties of elements is related to theirClassification of Elements and Periodicity in Properties
Q1714Nylon threads are made ofPolymers
Q1869The solubilities of carbonates decrease down the magnesium group due to a decrease in:S Block Elements
Q1939How many unit cells are present in a cubeshaped ideal crystal of NaCl of mass 1.00 g? [Atomic masses: Na = 23, Cl = 35.5]Solid State
Q1949In a 0.2 molal aqueous solution of a weak acid HX the degree of ionization is 0.3. Taking k f for water as 1.85, the freezing point of the solution will be…Solutions
Q1950If liquids A and B form an ideal solutionSolutions
Q1985A pressure cooker reduces cooking time for food becauseSolutions
Q202125 ml of a solution of barium hydroxide on titration with a 0.1 molar solution of hydrochloric acid gave a litre value of 35 ml. The molarity of barium…Some Basic Concepts in Chemistry
Q2055What volume of hydrogen gas at 273 K and 1 atm pressure will be consumed in obtaining 21.6 g of elemental boron (atomic mass = 10.8) from the reduction of…Some Basic Concepts in Chemistry
Q2109In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the following inter-orbit jumps of the electron for…Atomic Structure
Q2128The de Broglie wavelength of a tennis ball of mass 60 g moving with a velocity of 10 meters per second is approximatelyAtomic Structure
Q2132Which one of the following groupings represents a collection of isoelectronic species? (At. nos.: Cs: 55, Br: 35)Atomic Structure
Q2188The orbital angular momentum for an electron revolving in an orbit is given by √(l(l + 1)) h/(2π). This momentum for an s-electron will be given byAtomic Structure
Q2285In an irreversible process taking place at constant T and P and in which only pressure-volume work is being done, the change in Gibbs free energy (dG) and…Chemical Thermodynamics
Q2286The correct relationship between free energy change in a reaction and the corresponding equilibrium constant K c is:Chemical Thermodynamics
Q2310The internal energy change when a system goes from state A to B is 40 kJ/mole. If the system goes from A to B by a reversible path and returns to state A by…Chemical Thermodynamics
Q2332If at 298 K the bond energies of C - H, C - C, C = C and H - H bonds are respectively 414, 347, 615 and 435 kJ/mol, the value of enthalpy change for the…Chemical Thermodynamics
Q2333The enthalpy change for a reaction does not depend upon:Chemical Thermodynamics

Mathematics

Q2368The two lines x=ay+b,z=cy+d and x = a'y + b',z = c'y + d' will be perpendicular, if and only if:Three Dimensional Geometry
Q2476The lines (x - 2)/1 = (y - 3)/1 = (z - 4)/(- k) and (x - 1)/k = (y - 4)/2 = (z - 5)/1 are coplanar if:Three Dimensional Geometry
Q2544The shortest distance from the plane 12x+4y+3z=327 to the sphere x² + y² + z² + 4x - 2y - 6z = 155 isThree Dimensional Geometry
Q2545Two systems of rectangular axes have the same origin. If a plane cuts then at distances a,b,c and a', b', c' from the origin thenThree Dimensional Geometry
Q2546The radius of the circle in which the sphere x² + y² + z² + 2x - 2y - 4z - 19 = 0 is cut by the plane x+2y+2z+7=0 isThree Dimensional Geometry
Q2618The real number x when added to its inverse gives the minimum sum at x equal:Limit, Continuity and Differentiability
Q2619If the function f(x) = 2x³ - 9a x² + 12a²x + 1, where a>0, attains its maximum and minimum at p and q respectively such that p² = q, then a equalsLimit, Continuity and Differentiability
Q2793The area of the region bounded by the curves y = | x - 1 | and y = 3 - | x | is:Integral Calculus
Q2904The number of integral terms in the expansion of (3 + 8 5)²⁵⁶ isBinomial Theorem and Its Simple Applications
Q2960If x is positive, the first negative term in the expansion of (1 + x)^(27/5) isBinomial Theorem and Its Simple Applications
Q3037The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then the equation of the circle is:Coordinate Geometry
Q3088If the two circles (x - 1)² + (y - 3)² = r² and x² + y² - 8x + 2y + 8 = 0 intersect in two distinct point, then:Coordinate Geometry
Q3173Let Z₁ and Z₂ be two roots of the equation Z² + aZ + b = 0, Z being complex. Further, assume that the origin, Z₁ and Z₂ form an equilateral triangle. Then:Complex Numbers and Quadratic Equations
Q3206If z and ω are two non-zero complex numbers such that | zω | = 1 and Arg(z) - Arg(ω) = (π)/2, then z ω is equal toComplex Numbers and Quadratic Equations
Q3235If ((1 + i)/(1 - i))ˣ = 1 then:Complex Numbers and Quadratic Equations
Q3280lim n → ∞ (1 + 2⁴ + 3⁴ +.... + n⁴)/(n⁵) - lim n → ∞ (1 + 2³ + 3³ +.... + n³)/(n⁵)Integral Calculus
Q3299The value of lim x → 0 (∫₀^(x²) sec ²tdt)/xsinx isIntegral Calculus
Q3329If f(y) = e^(y), g(y) = y;y > 0 and F(t) = ∫₀^(t) f(t - y)g(y)dy, then:Integral Calculus
Q3330The value of the integral I = ∫₀¹ x (1 - x)ⁿ dx isIntegral Calculus
Q3331Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be a function that satisfies f(x) + g(x) = x². Then the value of the integral ∫₀¹…Integral Calculus
Q3332If f(a + b - x) = f(x) then ∫ a ^(b) xf(x)dx is equal toIntegral Calculus
Q3505The solution of the differential equation (1 + y²) + (x - e^(tan ⁻¹y))dy/dx = 0, is:Differential Equations
Q3573The degree and order of the differential equation of the family of all parabolas whose axis is x -axis, are respectively.Differential Equations
Q3663Let f(x) be a polynomial function of second degree. If f(1) = f(- 1) and a,b,c are in A.P, then f'(a),f'(b),f'(c) are inLimit, Continuity and Differentiability
Q3704If f(x) = xⁿ, then the value of f(1) - (f'(1))/(1!) + (f''(1))/(2!) - (f'''(1))/(3!) +.......... (- 1)ⁿ fⁿ (1) n! isLimit, Continuity and Differentiability
Q3789A function f from the set of natural numbers to integers defined by f(n) = \ (n - 1)/2, when n is odd - n/2, when n is even. isSets, Relations and Functions
Q3838Domain of definition of the function f(x) = 3/(4 - x²) + log ₁₀(x³ - x), isSets, Relations and Functions
Q3852The function f(x) = log (x + √(x² + 1)), isSets, Relations and Functions
Q3856If f:R → R satisfies f (x + y) = f (x) + f (y), for all x, y R and f (1) = 7, then Σ r = 1 ⁿ f(r) isSets, Relations and Functions
Q3957The foci of the ellipse (x²)/16 + (y²)/(b²) = 1 and the hyperbola (x²)/144 - (y²)/81 = 1/25 coincide. Then the value of b² is:Coordinate Geometry
Q4058The trigonometric equation sin ⁻¹x = 2 sin ⁻¹a has a solution for:Trigonometry
Q4170Let f(a) = g(a) = k and their n^(t)h derivatives fⁿ(a), gⁿ(a) exist and are not equal for some n. Further if lim x → a (f(a)g(x) - f(a) - g(a)f(x) +…Limit, Continuity and Differentiability
Q4171If f(x) = \ x e^(- (1/(| x |) + 1/x)),x ≠ 0 0,x = 0. then f(x) isLimit, Continuity and Differentiability
Q4261If lim x → 0 (log (3 + x) - log (3 - x))/x = k, the value of k isLimit, Continuity and Differentiability
Q4264lim x → (π)/2 ([ 1 - tan (x/2) ][ 1 - sin x ])/([ 1 + tan (x/2) ][ π - 2x ]³) isLimit, Continuity and Differentiability
Q4434If 1, ω,ω ² are the cube roots of unity, then Δ = | 1 ω ⁿ ω ²ⁿ ω ⁿ ω ²ⁿ 1 ω ²ⁿ 1 ω ⁿ | is equal toMatrices and Determinants
Q4488If A = [ a b b a ] and A² = [ α β β α ], thenMatrices and Determinants
Q4549If the system of linear equations x + 2ay + az = 0; x + 3by + bz = 0; x + 4cy + cz = 0; has a non - zero solution, then a, b, c.Matrices and Determinants
Q4702The normal at the point (bt₁²,2b t₁) on a parabola meets the parabola again in the point (bt₂²,2b t₂), then:Coordinate Geometry
Q4765The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given byPermutations and Combinations
Q4769A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices…Permutations and Combinations
Q4809If ⁿ C r denotes the number of combination of n things taken r at a time, then the expression ⁿ C r + 1 + ⁿ C r - 1 + 2 × ⁿ C r equalsPermutations and Combinations
Q4868The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then P(X=1) is:Statistics and Probability
Q4899Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is:Statistics and Probability
Q5014Events A, B, C are mutually exclusive events such that P(A) = (3x + 1)/3, P(B) = (1 - x)/4 and P(C) = (1 - 2x)/2 The set of possible values of x are in the…Statistics and Probability
Q5034The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is:Properties of Triangle
Q5035If in a Δ ABC a cos ²(C/2) + c cos ²(A/2) = 3b/2, then the sides a, b and c:Properties of Triangle
Q5037In a triangle ABC, medians AD and BE are drawn. If AD=4, DAB = (π)/6 and ABE = (π)/3, then the area of the Δ ABC is:Properties of Triangle
Q5078The number of real solutions of the equation x² - 3| x | + 2 = 0 isComplex Numbers and Quadratic Equations
Q5112If the sum of the roots of the quadratic equation a x² + bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/c, b/a and c/b are inComplex Numbers and Quadratic Equations
Q5113The value of ' a ' for which one root of the quadratic equation (a² - 5a + 3)x² + (3a - 1)x + 2 = 0 is twice as large as the other isComplex Numbers and Quadratic Equations
Q5283The sum of the serier 1/1.2 - 1/2.3 + 1/3.4.............. up to ∞ is equal toSequence and Series
Q5410The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set:Statistics and Probability
Q5419In an experiment with 15 observations on x, then following results were available: Σ x² = 2830, Σ x = 170 One observation that was 20 was found to be wrong…Statistics and Probability
Q5562Locus of centroid of the triangle whose vertices are (a cos t,a sin t),(b sin t, - b cos t) and (1,0), where t is a parameter, is:Coordinate Geometry
Q5563If the equation of the locus of a point equidistant from the point (a 1, b₁) and (a 2, b₂) is (a₁ - a₂)x + (b₁ - b₂)y + c = 0, then the value of 'c' is:Coordinate Geometry
Q5576If the pair of straight lines x² - 2pxy - y² = 0 and x² - 2qxy - y² = 0 be such that each pair bisects the angle between the other pair, then:Coordinate Geometry
Q5592If x₁,x₂,x₃ and y₁,y₂,y₃ are both in G.P. with the same common ratio, then the points (x₁,y₁),(x₂,y₂) and (x₃,y₃):Coordinate Geometry
Q5593A square of side a lies above the x -axis and has one vertex at the origin. The side passing through the origin makes an angle α (0 < α < (π)/4) with the…Coordinate Geometry
Q5678If | a a² 1 + a³ b b² 1 + b³ c c² 1 + c³ | = 0 and vectors (1,a,a²), (1,b,b²) and (1,c,c²) are non-coplanar, then the product abc equals:Vector Algebra
Q5679Consider points A, B, C and D with position vectors 7 i - 4 j + 7 k, i - 6 j + 10 k, - i - 3 j + 4 k and 5 i - j + 5 k respectively. Then ABCD is a:Vector Algebra
Q5680The vectors AB = 3 i + 4 k AC = 5 i - 2 j + 4 k are the sides of triangle ABC. The length of the median through A is:Vector Algebra
Q5706If u, v and w are three non-coplanar vectors, then (u + v - w).(u - v) × (v - w) equals:Vector Algebra
Q5758a, b, c are 3 vectors, such that a + b + c = 0, | a | = 1 | b | = 2, | c | = 3,, then a. b + b. c + c. a is equal to:Vector Algebra
Q5794If a × b = b × c = c × a then a + b + c =Vector Algebra
Q5795A tetrahedron has vertices at O(0,0,0), A(1,2,1) B(2,1,3) and C(-1,1,2). Then the angle between the faces OAB and ABC will be:Vector Algebra
Q5796Let u = i + j, v = i - j and w = i + 2 j + 3 k. If n is a unit vector such that u. n = 0 and v. n = 0, then | w. n | is equal to:Vector Algebra