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JEE Main 2004 Annual Paper 1 Question Paper with Solutions | JEE Arc

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JEE Main 2004Annual, Paper 1

Physics 74Chemistry 62Mathematics 67

Physics

Q5863In an LCR series a.c. circuit, the voltage across each of the components, L,C and R is 50V. The voltage across the L.C combination will be:Electromagnetic Induction and Alternating Currents
Q5864In a LCR circuit capacitance is changed from C to 2 C. For the resonant frequency to remain unchaged, the inductance should be changed from L toElectromagnetic Induction and Alternating Currents
Q5865Alternating current can not be measured by D.C. ammeter becauseElectromagnetic Induction and Alternating Currents
Q5956An α -particle of energy 5 MeV is scattered through 180° by a fixed uranium nucleus. The distance of closest approach is of the order ofAtoms and Nuclei
Q6035The binding energy per nucleon of deuteron (₁² H) and helium nucleus (₂⁴ He) is 1.1 MeV and 7 MeV respectively. If two deuteron nuclei react to form a single…Atoms and Nuclei
Q6075A nucleus disintegrated into two nuclear parts which have their velocities in the ratio of 2:1. The ratio of their nuclear sizes will beAtoms and Nuclei
Q6232A machine gun fires a bullet of mass 40 g with a velocity 1200m s⁻¹. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he…Rotational Motion
Q6261Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed?Kinematics
Q6380The resistance of the series combination of two resistances is S. When they are jointed in parallel the total resistance is P. If S = nP then the Minimum…Current Electricity
Q6409The electrochemical equivalent of a metal is 3.35109⁻⁷ kg per Coulomb. The mass of the metal liberated at the cathode when a 3A current is passed for 2…Current Electricity
Q6410The thermo emf of a thermocouple varies with temperature θ of the hot junction as E = aθ + b θ ² in volts where the ratio a/b is 700° C. If the cold junction…Current Electricity
Q6485An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii are in the ratio of…Current Electricity
Q6486The Kirchhoff's first law (Σ i = 0) and second law (Σ iR = Σ E), where the symbols have their usual meanings, are respectively based onCurrent Electricity
Q6490In a meter bridge experiment null point is obtained at 20 cm, from one end of the wire when resistance X is balanced against another resistance Y. If X < Y…Current Electricity
Q6507Thermistors are usually made ofCurrent Electricity
Q6508A material 'B' has twice the specific resistance of 'A'. A circular wire made of 'B' has twice the diameter of a wire made of 'A'. Then for the two wires to…Current Electricity
Q6614The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photo-electron emission from this substance is approximately.Dual Nature of Matter and Radiation
Q6615According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal Vs the frequency, of the incident…Dual Nature of Matter and Radiation
Q6692In a uniform magnetic field of induction B a wire in the form of a semicircle of radius r rotates about the diameter of the circle with an angular frequency…Electromagnetic Induction and Alternating Currents
Q6693A coil having n turns and resistance RΩ is connected with a galvanometer of resistance 4RΩ. This combination is moved in time t seconds from a magnetic field…Electromagnetic Induction and Alternating Currents
Q6718A metal conductor of length 1 m rotates vertically about one of its ends at angular velocity 5 radians per second. If the horizontal component of earth's…Electromagnetic Induction and Alternating Currents
Q6729An electromagnetic wave of frequency v=3.0 MHz passes from vacuum into a dielectric medium with permittivity = 4.0. ThenElectromagnetic Waves
Q6730A radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the surface isElectromagnetic Waves
Q6855A piece of copper and another of germanium are cooled from room temperature to 77K, the resistance ofElectronic Devices
Q6856The manifestation of band structure in solids is due toElectronic Devices
Q6857When p - n junction diode is forward biased thenElectronic Devices
Q6891When npn transistor is used as an ampliferElectronic Devices
Q6892For a transistor amplifier in common emitter configuration for load impedance of 1k Ω (h fe = 50. and. h oe = 25) the current gain isElectronic Devices
Q6952Four charges equal to - Q are placed at the four corners of a square and a charge q is at its center. If the system is in equilibrium the value of q isElectrostatics
Q6953A charged oil drop is suspended in a uniform field of 3 × 10⁴ v/m so that it neither falls nor rises. The charge on the drop will be (Take the mass of the…Electrostatics
Q6992Two spherical conductors B and C having equal radii and carrying equal charges on them repel each other with a force F when kept apart at some distance. A…Electrostatics
Q6993A charge particle 'q' is shot towards another charged particle 'Q' which is fixed, with a speed 'v'. It approaches 'Q' upto a closest distance r and then…Electrostatics
Q7024A plano convex lens of refractive index 1.5 and radius of curvature 30 cm. Is silvered at the curved surface. Now this lens has been used to form the image of…Optics
Q7177Suppose the gravitational force varies inversely as the n^(t)h power of distance. Then the time period of a planet in circular orbit of radius R around the…Gravitation
Q7226If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of the earth…Gravitation
Q7247The time period of an earth satellite in circular orbit is independent ofGravitation
Q7248A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the…Gravitation
Q7338If the temperature of the sun were to increase from T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on earth to what it was…Thermodynamics
Q7352One mole of ideal monatomic gas (γ = 5/3) is mixed with one mole of diatomic gas (γ = 7/5). What is γ for the mixture? γ Denotes the ratio of specific heat at…Thermodynamics
Q7442Time taken by a 836 W heater to heat one litre of water from 10° C to 40° C isThermodynamics
Q7527Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T₁,T₂), volume (V₁,V₂) and pressure (P₁,P₂) respectively. If the value joining…Thermodynamics
Q7528Which of the following statements is correct for any thermodynamic system ?Thermodynamics
Q7547A block rests on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of static friction between the block and the plane is 0.8…Laws of Motion
Q7609The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is 2s. The magnet is cut…Magnetic Effects of Current and Magnetism
Q7631Curie temperature is the temperature above whichMagnetic Effects of Current and Magnetism
Q7632The materials suitable for making electromagnets should haveMagnetic Effects of Current and Magnetism
Q7656A current i ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube isMagnetic Effects of Current and Magnetism
Q7666The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is 54 μ T. What will be…Magnetic Effects of Current and Magnetism
Q7667A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is B. It is then bent into a…Magnetic Effects of Current and Magnetism
Q7696Two long conductors, separated by a distance d carry current I₁ and I₂ in the same direction. They exert a force F on each other. Now the current in one of…Magnetic Effects of Current and Magnetism
Q7773A projectile can have the same range 'R' for two angles of projection. If T₁ and T₂ be the time of flights in the two cases, then the product of the two time…Kinematics
Q7774A ball is thrown from a point with a speed ν₀ at an angle of projection θ. From the same point and at the same instant person starts running with a constant…Kinematics
Q7840An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, i.e 120 km/h, the stopping…Kinematics
Q7855A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the position of the ball in T/3 seconds?Kinematics
Q7891Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball isProperties of Solids and Liquids
Q7924A wire fixed at the upper end stretches by length l by applying a force F. The work done in stretching isProperties of Solids and Liquids
Q8005If two soap bubbles of different radii are connected by a tubeProperties of Solids and Liquids
Q8040A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which on of the following will not be affected ?Rotational Motion
Q8079One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively I A and I…Rotational Motion
Q8114In forced oscillation of a particle the amplitude is maximum for a frequency ω ₁ of the force while the energy is maximum for a frequency ω ₂ of the force; thenOscillations and Waves
Q8128The total energy of particle, executing simple harmonic motion isOscillations and Waves
Q8182The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is t₀ in air. Neglecting…Oscillations and Waves
Q8183A particle at the end of a spring executes S.H.M with a period t₁. While the corresponding period for another spring is t₂. If the period of oscillation with…Oscillations and Waves
Q8184A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency ω ₀. An external force F(t) proportional to cos ω t(ω…Oscillations and Waves
Q8217Which one of the following represents the correct dimensions of the coefficient of viscosity?Units and Measurements
Q8370If A × B = B × A, then the angle beetween A and B isKinematics
Q8409The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double-slit experiment, is:Optics
Q8455The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refractive index n) is:Optics
Q8476The displacement y of a particle in a medium can be expressed as, y = 10⁻⁶ sin (100t + 20x + (π)/4) m where t is in second and x in meter. The speed of the…Oscillations and Waves
Q8560A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional toWork, Energy and Power
Q8561A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg…Work, Energy and Power
Q8562A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particles takes…Work, Energy and Power
Q8600A body of mass ' m ', acceleration uniformly from rest to 'v₁' in time T. The instantaneous power delivered to the body as a function of time is given byWork, Energy and Power
Q8615A force F = (5 i + 3 j + 2 k)N is applied over a particle which displaces it from its origin to the point r = (2 i - j)m. The work done on the particle in…Work, Energy and Power

Chemistry

Q42Which one of the following reduced with zinc and hydrochloric acid to give the corresponding hydrocarbon?Organic Compounds Containing Oxygen
Q66Consider the acidity of the carboxylic acids: (a) PhCOOH (b) o – NO₂C₆H₄COOH (c) p – NO₂C₆H₄COOH (d) m – NO₂C₆H₄COOH Which of the following order is correct?Some Basic Principles of Organic Chemistry
Q95Which of the following compound is not chiral?Some Basic Principles of Organic Chemistry
Q96Which of the following will have meso-isomer also?Some Basic Principles of Organic Chemistry
Q189Identify the correct statements regarding enzymesBiomolecules
Q190Insulin production and its action in human body are responsible for the level of diabetes. This compound belongs to which of the following categories?Biomolecules
Q225Which base is present in RNA but not in DNA?Biomolecules
Q250The correct order of bond angles (smallest first) in H₂S, NH₃, BF₃ and SiH₄ isChemical Bonding and Molecular Structure
Q278The states of hybridization of boron and oxygen atoms in boric acid (H₃BO₃) are respectivelyChemical Bonding and Molecular Structure
Q279Which one of the following has the regular tetrahedral structure? (Atomic nos: B = 5, S = 16, Ni = 28, Xe = 54)Chemical Bonding and Molecular Structure
Q280The maximum number of 90° angles between bond pair of electrons is observed inChemical Bonding and Molecular Structure
Q347The bond order in NO is 2.5 while that in NO⁺ is 3. Which of the following statements is true for these two species?Chemical Bonding and Molecular Structure
Q392For the reaction, CO(g) + Cl₂(g) COCl₂(g) the K p /K c is equal to:Equilibrium
Q393What is the equilibrium expression for the reaction P₄ (s) + 5O₂ P₄O₁₀ (s)?Equilibrium
Q394The equilibrium constant for the reaction N₂(g) + O₂(g) 2NO(g) at temperature T is 4 × 10⁻⁴. The value of K c for the reaction NO(g) 1 2 N₂ (g) + 1 2 O₂ (g)…Equilibrium
Q461In a first order reaction, the concentration of the reactant decreases from 0.8 M to 0.4 M in 15 minutes. The time taken for the concentration to change from…Chemical Kinetics
Q482Consider the following nuclear reactions ₉₂²³⁸M → Y ^(X)N + 2₂⁴He Y ^(X)N → B ^(A)L + 2β ⁺ The number of neutrons in the element L isNuclear Chemistry (historical)
Q483The half – life of a radioisotope is four hours. If the initial mass of the isotope was 200 g, the mass remaining after 24 hours undecayed isNuclear Chemistry (historical)
Q492The rate equation for the reaction 2A + B → C is found to be: rate k[A][B]. The correct statement in relation to this reaction is that theChemical Kinetics
Q557Coordination compound have great importance in biological systems. In this context which of the following statements is incorrect?Coordination Compounds
Q581The coordination number of central metal atom in a complex is determined by:Coordination Compounds
Q667Which one the following has largest number of isomers? (R = alkyl group, en = ethylenediamine)Coordination Compounds
Q704The correct order of magnetic moments (spin only values in B.M.) among is: (Atomic numbers: Mn = 25; Fe = 26, Co =27)Coordination Compounds
Q705Which one of the following complexes in an outer orbital complex?Coordination Compounds
Q706Among the properties (a) reducing (b) oxidising (c) complexing, the set of properties shown by CN^– ion towards metal species is:Coordination Compounds
Q756Excess of KI reacts with CuSO₄ solution and then Na₂S₂O₃ solution is added to it. Which of the statements is incorrect for this reaction?d- and f-Block Elements
Q799Cerium (Z = 58) is an important member of the lanthanoids. Which of the following statements about cerium is incorrect?d- and f-Block Elements
Q847Of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one of them?d- and f-Block Elements
Q912In a hydrogen – oxygen fuel cell, combustion of hydrogen occurs to:Redox Reactions and Electrochemistry
Q925The limiting molar conductivities Λ° for NaCl, KBr and KCl are 126, 152 and 150 S cm² mol⁻¹ respectively. The Λ° for NaBr isRedox Reactions and Electrochemistry
Q965Consider the following E^(o) values E_ F e³⁺ /F e²⁺ ^(o) = 0.77 V; E_ S n²⁺ /S n ^(o) = -0.14 V Under standard conditions the potential for the reaction Sn(s)…Redox Reactions and Electrochemistry
Q966The standard e.m.f of a cell, involving one electron change is found to be 0.591 V at 25^(o)C. The equilibrium constant of the reaction is (F = 96,500 C…Redox Reactions and Electrochemistry
Q967In a cell that utilises the reaction Zn(s) + 2H⁺ (aq) → Zn2+(aq) + H2(g) addition of H₂SO₄ to cathode compartment, willRedox Reactions and Electrochemistry
Q968The E M³⁺/M²⁺ ^(o) values for Cr, Mn, Fe and Co are – 0.41, +1.57, + 0.77 and +1.97 V respectively. For which one of these metals the change in oxidation…Redox Reactions and Electrochemistry
Q1013The smog is essentially caused by the presence of:Environmental Chemistry
Q1118As the temperature is raised from 20°C to 40°C, the average kinetic energy of neon atoms changes by a factor of which of the following?Gaseous State
Q1122In Van der Waals equation of state of the gas law, the constant ‘b’ is a measure ofGaseous State
Q1160The compound formed on heating chlorobenzene with chloral in the presence concentrated sulphuric acid isOrganic Compounds Containing Halogens
Q1167Which one of the following has the minimum boiling point?Hydrocarbons
Q1277The conjugate base of H₂PO₄⁻ is:Equilibrium
Q1326The molar solubility (in ol L⁻¹) of a sparingly soluble salt MX₄ is "s". The corresponding solubility product is K s p. 's' is given in term of K s p by the…Equilibrium
Q1349Which one of the following ores is best concentrated by froth – floatation method?Isolation of Elements
Q1448Beryllium and aluminium exhibit many properties which are similar. But the two elements differ in:p-Block Elements
Q1538Which one the following statement regarding helium is incorrect?p-Block Elements
Q1546Which one of the following ions has the highest value of ionic radius?Classification of Elements and Periodicity in Properties
Q1586The formation of the oxide ion O²⁻(g) requires first an exothermic and then an endothermic step as shown below O_(g) + e⁻ = O (g) ⁻ Δ H^(o) = -142 kJmol⁻¹ O…Classification of Elements and Periodicity in Properties
Q1628Among Al₂O₃, SiO₂, P₂O₃ and SO₂ the correct order of acid strength isClassification of Elements and Periodicity in Properties
Q1722The compound formed in the positive test for nitrogen with the Lassaigne solution of an organic compound isPrinciples Related to Practical Chemistry
Q1870One mole of magnesium nitride on the reaction with an excess of water gives:S Block Elements
Q1951Which one of the following statements is false?Solutions
Q1952Which one of the following aqueous solutions will exhibit highest boiling point?Solutions
Q1996Which of the following liquid pairs shows a positive deviation from Raoult’s law?Solutions
Q1997For which of the following parameters the structural isomers C₂H₅OH and CH₃OCH₃ would be expected to have the same values? (Assume ideal behaviour)Solutions
Q2022To neutralise completely 20 mL of 0.1 M aqueous solution of phosphorous acid (H₃PO₃), the volume of 0.1 M aqueous KOH solution required isSome Basic Concepts in Chemistry
Q20236.02 × 10²⁰ molecules of urea are present in 100 ml of its solution. The concentration of urea solution is (Avogadro constant, N A = 6.02 × 10²³ mol⁻¹)Some Basic Concepts in Chemistry
Q2056The ammonia evolved from the treatment of 0.30 g of an organic compound for the estimation of nitrogen was passed in 100 mL of 0.1 M sulphuric acid. The…Some Basic Concepts in Chemistry
Q2133Which one of the following sets of ions represents the collection of isoelectronic species? (Atomic nos.: F = 9, Cl = 17, Na = 11, Mg = 12, Al = 13, K = 19…Atomic Structure
Q2154The wavelength of the radiation emitted when in a hydrogen atom electron falls from infinity to stationary state 1, would be (Rydberg constant = 1.097 × 10⁷…Atomic Structure
Q2189Which of the following sets of quantum numbers is correct for an electron in 4f orbital?Atomic Structure
Q2190Consider the ground state of Cr atom (Z = 24). The number of electrons with the azimuthal quantum numbers, l = 1 and 2 are respectivelyAtomic Structure
Q2311An ideal gas expands in volume from 1 × 10⁻³ m³ to 1 × 10⁻² m³ at 300 K against a constant pressure of 1 × 10⁵ Nm⁻². The work done is:Chemical Thermodynamics
Q2334The enthalpies of combustion of carbon and carbon monoxide are -393.5 and -283 kJ mol-1 respectively. The enthalpy of formation of carbon monoxide per mole is:Chemical Thermodynamics

Mathematics

Q2369A line makes the same angle θ, with each of the x and z axis. If the angle β, which it makes with y-axis, is such that sin ²β = 3 sin ²θ, then cos ²θ equals:Three Dimensional Geometry
Q2477A line with direction cosines proportional to 2,1,2 meets each of the lines x=y+a=z and x+a=2y=2z. The co-ordinates of each of the points of intersection are…Three Dimensional Geometry
Q2478If the straight lines x=1+s,y=-3 - λ s, z = 1 + λ s and x = t/2,y = 1 + t,z = 2 - t, with parameters s and t respectively, are co-planar, then λ equals:Three Dimensional Geometry
Q2547The intersection of the spheres x² + y² + z² + 7x - 2y - z = 13 and x² + y² + z² - 3x + 3y + 4z = 8 is the same as the intersection of one of the sphere and…Three Dimensional Geometry
Q2548Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is:Three Dimensional Geometry
Q2692If 2a+3b+6c=0, then at least one root of the equation a x² + bx + c = 0 lies in the intervalLimit, Continuity and Differentiability
Q2738A point on the parabola y² = 18x at which the ordinate increases at twice the rate of the abscissa isLimit, Continuity and Differentiability
Q2751A function y=f(x) has a second order derivative f''(x) = 6(x - 1). If its graph passes through the point (2, 1) and at that point the tangent to the graph is…Limit, Continuity and Differentiability
Q2752The normal to the curve x = a(1 + cos θ), y = a sin θ at 'θ ' always passes through the fixed pointLimit, Continuity and Differentiability
Q2794The area of the region bounded by the curves y = | x - 2 |,x = 1,x = 3 and the x -axis is:Integral Calculus
Q2905The coefficient of xⁿ in expansion of (1 + x)(1 - x)ⁿ isBinomial Theorem and Its Simple Applications
Q2954The coefficient of the middle term in the binomial expansion in powers of x of (1 + α x)⁴ and (1 - α x)⁶ is the same if α equalsBinomial Theorem and Its Simple Applications
Q2966If S n = Σ r = 0 ⁿ 1 ⁿ C r and t n = Σ r = 0 ⁿ r ⁿ C r, then (t n)/S n is equal toBinomial Theorem and Its Simple Applications
Q3038If the lines 2x + 3y + 1 + 0 and 3x - y - 4 = 0 lie along diameter of a circle of circumference 10 π, then the equation of the circle is:Coordinate Geometry
Q3039Intercept on the line y = x by the circle x² + y² - 2x = 0 is AB. Equation of the circle on AB as a diameter is:Coordinate Geometry
Q3061A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is:Coordinate Geometry
Q3103If a circle passes through the point (a, b) and cuts the circle x² + y² = 4 orthogonally, then the locus of its centre is:Coordinate Geometry
Q3207Let z and w be complex numbers such that z + i w = 0 and arg zw = π. Then arg z equals:Complex Numbers and Quadratic Equations
Q3230If z = x - iy and z^(1/3) = p + iq, then ((x/p + y/q))/((p² + q²)) is equal to:Complex Numbers and Quadratic Equations
Q3247If | z² - 1 | = | z |² + 1, then z lies on:Complex Numbers and Quadratic Equations
Q3281Lim n → ∞ Σ r = 1 ⁿ 1/n e^(r/n) isIntegral Calculus
Q3333The value of I = ∫₀^(π /2) ((sin x + cos x)²)/(√(1 + sin 2x))dx isIntegral Calculus
Q3334The value of ∫₋₂³ | 1 - x² |dx isIntegral Calculus
Q3335If ∫₀^π xf(sin x)dx = A∫₀^(π /2) f(sin x)dx, then A isIntegral Calculus
Q3336If f(x) = (eˣ)/(1 + eˣ),I₁ = ∫ f(- a) ^(f(a)) xg x(1 - x) and I₂ = ∫ f(- a) ^(f(a)) g x(1 - x), then the value of I₂/I₁ isIntegral Calculus
Q3489The differential equation for the family of circle x² + y² - 2ay = 0, where a is an arbitrary constant is:Differential Equations
Q3577Solution of the differential equation ydx + (x + x²y)dy = 0 isDifferential Equations
Q3685If x = e^(y + e^(y) + e^(y +.....∞)), x > 0, then dy/dx isLimit, Continuity and Differentiability
Q3740The eccentricity of an ellipse, with its centre at the origin, is 1/2. If one of the directrices is x=4, then the equation of the ellipse is:Coordinate Geometry
Q3790If f:R → S, defined by f(x) = sin x - 3 cos x + 1, is onto, then the interval of S isSets, Relations and Functions
Q3839The domain of the function f(x) = (sin ⁻¹(x - 3))/(√(9 - x²))Sets, Relations and Functions
Q3853The graph of the function y = f(x) is symmetrical about the line x = 2, thenSets, Relations and Functions
Q3887The range of the function f(x) = ⁷⁻ˣP x - 3 isSets, Relations and Functions
Q3899A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he…Height and Distance
Q4041∫ dx/(cos x - sin x) is equal toIntegral Calculus
Q4042If ∫ (sin x)/(sin (x - α))dx = Ax + B log sin (x - α), + C, then value of (A, B) isIntegral Calculus
Q4125Let f(x) = (1 - tan x)/(4x - π), x ≠ (π)/4, x [ 0,(π)/2 ]. If f(x) is continuous in [ 0,(π)/2 ], then f((π)/4) isLimit, Continuity and Differentiability
Q4249If lim x → ∞ (1 + a/x + b/(x²))²ˣ = e², then the value of a and b, areLimit, Continuity and Differentiability
Q4306Let S(K) = 1 + 3 + 5... + (2K - 1) = 3 + K². Then which of the following is trueMathematical Induction
Q4435If a₁,a₂,a₃,.........,a n,...... are in G.P., then the value of the determinant | log a n log a n + 1 log a n + 2 log a n + 3 log a n + 4 log a n + 5 log a n…Matrices and Determinants
Q4474Let A = (1 - 1 1 2 1 - 3 1 1 1). and 10 B = (4 2 2 - 5 0 α 1 - 2 3). if B is the inverse of matrix A, then α isMatrices and Determinants
Q4475Let A = (0 0 - 1 0 - 1 0 - 1 0 0). The only correct statement about the matrix A isMatrices and Determinants
Q4668If a ≠ 0 and the line 2bx+3cy+4d=0 passes through the points of intersection of the parabolas y² = 4ax and x² = 4ay, then:Coordinate Geometry
Q4787How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical orderPermutations and Combinations
Q4810The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty isPermutations and Combinations
Q4869The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is:Statistics and Probability
Q4900The probability that A speaks truth is 4/5, while the probability for B is 3/4. The probability that they contradict each other when asked to speak on a fact…Statistics and Probability
Q5051If one root of the equation x² + px + 12 = 0 is 4, while the equation x² + px + q = 0 has equal roots, then the value of 'q' isComplex Numbers and Quadratic Equations
Q5114Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equationComplex Numbers and Quadratic Equations
Q5115If (1 - p) is a root of quadratic equation x² + px + (1 - p) = 0 then its root areComplex Numbers and Quadratic Equations
Q5190Let T r be the rth term of an A.P. whose first term is a and common difference is d. If for some positive integers m, n, m ≠ n, T m = 1/n and T n = 1/m, then…Sequence and Series
Q5284The sum of the first n terms of the series 1² + 2.2² + 3² + 2.4² + 5² + 2.6² +.... is n (n + 1)² 2 when n is even. When n is odd the sum isSequence and Series
Q5285The sum of series 1/(2 !) + 1/(4 !) + 1/(6 !) +........ isSequence and Series
Q5367Let R=\(1,3),(4,2),(2,4),(2,3),(3,1) be a relation on the set A=\1,2,3,4. The relation R is:Sets, Relations and Functions
Q5420Consider the following statements: (a) Mode can be computed from histogram (b) Median is not independent of change of scale (c) Variance is independent of…Statistics and Probability
Q5421In a series of 2n observations, half of them equal a and remaining half equal –a. If the standard deviation of the observations is 2, then |a| equalsStatistics and Probability
Q5564Let A(2, - 3) and B(-2, 1) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is…Coordinate Geometry
Q5577If the sum of the slopes of the lines given by x² - 2cxy - 7y² = 0 is four times their product c has the value:Coordinate Geometry
Q5578If one of the lines given by 6x² - xy + 4c y² = 0 is 3x + 4y = 0, then c equals:Coordinate Geometry
Q5594The equation of the straight line passing through the point (4, 3) and making intercepts on the co-ordinate axes whose sum is -1 is:Coordinate Geometry
Q5633Let α, β be such that π < α - β < 3π. If sin 1mu α + sin β = - 21/65 and cos α + cos β = - 27/65 then the value of cos (α - β)/2:Trigonometry
Q5657If u = √(a² cos ²θ + b² sin ²θ) + √(a² sin ²θ + b² cos ²θ) then the difference between the maximum and minimum values of u² is given by:Trigonometry
Q5681Let a, b and c be three non-zero vectors such that no two of these are collinear. If the vector a + 2 b is collinear with c and b + 3 c is collinear with a (λ…Vector Algebra
Q5707If a, b, c are non-coplanar vectors and λ is a real number, then the vectors a + 2 b + 3 c, λ b + 4 c and (2λ - 1) c are non coplanar for:Vector Algebra
Q5759A particle acted on by constant forces 4 i + j - 3 k and 3 i + j - k is displaced from the point i + 2 j + 3 k to the point 5 i + 4 j + k. The total work done…Vector Algebra
Q5760Let u, v, w be such that | u | = 1, | v |2, | w |3. If the projection v along u is equal to that of w along u and v, w are perpendicular to each other then |…Vector Algebra
Q5797Let a, b and c be non-zero vectors such that (a × b) × c = 1/3| b || c | a. If θ is the acute angle between the vectors b and c, then sinθ equals:Vector Algebra