21
Dr. H. P. Sharma,Yash Srivastava
&Dr. N.K. Singh
By
Upkar Prakashan, AGRA-2
© Publishers
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CONTENTS
● Previous Year's Solved Paper
PHYSICSUnit 1 : Physics and Measurement (Units and Dimensions)………………………….……….…… 3–7
Unit 2 : Kinematics (Rectilinear and Circular Motion) ……………………………….…………… 8–13
Unit 3 : Vector Analysis and Projectile Motion ……………………………………...…………… 14–21
Unit 4 : Laws of Motion (Newton’s Law and Friction) ……………………………..………..…… 22–28
Unit 5 : Work, Power and Energy (Collision of Particles) ………………..…………..…………… 29–38
Unit 6 : Rotational Motion and Moment of Inertia …………………………………..….………… 39–49
Unit 7 : Gravitation and Satellites …………………………………………………...…………….. 50–59
Unit 8 : Elasticity ……………………………………………………………………..…………… 60–64
Unit 9 : Surface Tension, Viscosity and Flow of Fluids ………………………….…..…………… 65–72
Unit 10 : Heat, Thermodynamics and Kinetics Theory of Gases …………………..………..……… 73–93
Unit 11 : Transference of Heat ……………………………….………………………...…………… 94–104
Unit 12 : Oscillations..………………………..……………………………………………………… 105–114
Unit 13 : Wave Motion ………………………………………………….……………..…………… 115–131
Unit 14 : Electrostatics ………………………………………………………………....…………… 132–155
Unit 15 : Current Electricity …………………………….……………………………..…………… 156–173
Unit 16 : Magnetic Effects of Current ………………………………………….……....…………… 174–194
Unit 17 : Magnetostatics ……………………………………………………………….....………… 195–206
Unit 18 : Thermal and Chemical Effects of Current ..…………………………...……..…………… 207–215
Unit 19 : Electromagnetic Induction and Alternating Currents………………………....…...……… 216–241
Unit 20 : Electromagnetic Waves ……………………………………………………...…….……… 242–248
Unit 21 : Ray Optics……………………………………………..…………………….……..……… 249–276
Unit 22 : Wave Optics…………………………………………………………………..…………… 277–286
Unit 23 : Electrons and Photons …………………………………………………………………… 287–296
Unit 24 : Dual Nature of Matter and Radiation …………………………………………….…..…… 297–299
Unit 25 : Atoms, Molecules and Nuclei …………………………………...…………..…………… 300–316
Unit 26 : Solids and Semiconductors Devices : Crystal Structure ……………………..…………… 317–341
Unit 27 : Communication Systems ………………………………………………..…..….………… 342–345
Experimental Skills ……………………………………..………………………………….....…..………… 346–352
CHEMISTRYUnit 1 : Basic Concepts in Chemistry……………………………………………………………… 3–9
Unit 2 : Gaseous State………………………………………………...…………….……………… 10–20
Unit 3 : Atomic Structure ………………………………………………………..………………… 21–38
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Unit 4 : Solution ……………………………………………………………………………..…… 39–52
Unit 5 : Chemical Energetics and Thermodynamics……………………………………..………… 53–65
Unit 6 : Chemical Equilibrium …………………………………………………………………… 66–91
Unit 7 : Redox Reactions and Electrochemistry…………………………………………………… 92–109
Unit 8 : Rates of Chemical Reactions and Chemical Kinetics …………………………………… 110–122
Unit 9 : Surface Chemistry : Colloidal State …………………………………….………....……… 123–137
Unit 10 : Chemical Families : Periodic Properties ………………………………………….……… 138–151
Unit 11 : Chemical Bonding and Molecular Structure………………………………….…………… 152–169
Unit 12 : Principles and Processes of Extraction of Elements …………………………..………… 170–179
Unit 13 : s-and p-Block Elements ……………………………………………………….………… 180–231
Unit 14 : d-and f-Block (The Transition and Inner Transition Elements)…………………………… 232–249
Unit 15 : Co-ordination Chemistry and Organometallics …………………………….………..…… 250–265
Unit 16 : Nuclear Chemistry…………………………………………………….……………...…… 266–278
Unit 17 : Analysis, Classification and Nomenclature of Organic Compounds ………………..…… 279–301
Unit 18 : General Organic Chemistry …………………………………………………...………… 302–335
Unit 19 : Aliphatic Hydrocarbons ……………………………………………………….…..……… 336–361
Unit 20 : Aromatic Compounds……………………………………………………………...……… 362–373
Unit 21 : Halogen Derivatives …………………………………………………..…………...……… 374–385
Unit 22 : Alcohols, Phenols and Ethers ………………………………………..…………………… 386–405
Unit 23 : Aldehydes and Ketones ………………………………………………..……….………… 406–417
Unit 24 : Acids and Acid Derivatives…………………………………………………………..…… 418–427
Unit 25 : Nitrogen Containing Organic Compounds…………………………………...…………… 428–437
Unit 26 : Polymers, Biomolecules and Chemistry in Action ………………………….…………… 438–444
Unit 27 : Solid State …………………………………………………………………....…………… 445–450
Unit 28 (I) : Aliphatic Conversions (Organic Chemistry) ………………………………...…………… 451–453
Unit 28 (II) : Aromatic Conversions (Organic Chemistry)…………………………….………...……… 454–456
Unit 29 (I) : Important Name Reactions………………………………………………………………… 457–460
Unit 29 (II) : Important Name Reactions………………………………………………………………… 461–464
MATHEMATICS1. Sets—Cartesian Product of Sets, Relations and Functions ……………………………….………… 3–10
2. Complex Numbers ………………………………………………………………………..………… 11–23
3. Quadratic Equations ………………………………………………………………………………… 24–36
4. Inequalities …………………………………………………………………………………….…… 37–45
5. Binomial Theorem ………………………………………………………………………………….. 46–57
6. Sequence and Series ………………………………………………………………………………… 58–70
7. Logarithm ……………………………………………………………………………….…………… 71–72
8. Matrix ………………………………………………………………………………………………. 73–86
9. Determinant ………………………………………………………………………………………… 87–101
10. Mathematical Induction …………………………………………………………………………….. 102–104
11. Permutations and Combinations ………………………………………………………………….… 105–117
12. Probability………………………………………………………..………………………………...… 118–129
13. Trigonometric Ratios and Identities ………………………………………………………...……… 130–147
14. Trigonometric Equations …………………………………………………………………………… 148–157
15. Inverse Trigonometric Functions ………………………………..………………………………… 158–169
16. Properties of Triangles …………………………………..…………………………………………… 170–185
17. Heights and Distances…………………………...…………………………………………………… 186–200
( v )
18. Rectangular Cartesian Co-ordinates……………………………………………………………...…… 201–213
19. Straight Lines and Pair of Straight Lines ………………………………..…………………………… 214–234
20. Circle………………………………………..…………………………………………...…………… 235–241
21. Parabola…………………………………………………………………………………..…………… 242–248
22. Ellipse…………………………………………………………………………………….…………… 249–253
23. Hyperbola………………………..…………………………………………………………………… 254–257
24. Function ……………………………..………………………………………………..……………… 258–268
25. Limits, Continuity and Differentiability ……………………..…………….………………………… 269–280
26. Differentiation……………………………………..……………………….………………………… 281–292
27. Applications of Derivatives …………………………………..……………………………………… 293–306
28. Indefinite Integration ………………………………………………..…..…………………………… 307–319
29. Definite Integration ………………………….…………………….………………………………… 320–332
30. Differential Equation ……………………………………..…………………..……………………… 333–334
31. Vector Algebra……………………………………..………………………………………………… 335–354
32. Three Dimensional Geometry…………………………………..…………….……………………… 355–364
33. Statistics ……………………………………………………………………..………..……………… 365–376
34. Mathematical Reasoning ………………………………………………………..…………………… 377–386
SYLLABUS
Physics The syllabus contains two Sections-A and B. Section-A pertains to the TheoryPart having 80% weightage, while Section-B contains Practical Component(Experimental Skills) having 20% weightage.
SECTION : A
UNIT-1
PHYSICS AND MEASUREMENT
Physics, technology and society, SI units,Fundamental and derived units. Least count, accuracy andprecision of measuring instruments, Errors inmeasurement, Dimensions of physical quantities,dimensional analysis and its applications.
UNIT-2
KINEMATICSFrame of reference. Motion in a straight line :
Position-time graph, speed and velocity. Uniform andnon-uniform motion, average speed and instantaneousvelocity uniformly accelerated motion, velocity-time,position-time graphs, relations for uniformly acceleratedmotion. Scalars and Vectors, Vector addition andSubtraction, Zero Vector, Scalar and Vector products,Unit Vector, Resolution of a Vector. Relative Velocity,Motion in a plane, Projectile Motion, Uniform CircularMotion.
UNIT-3
LAWS OF MOTION
Force and inertia, Newton’s first law of motion;Momentum, Newton’s second law of motion; Impulse;Newton’s third law of motion. Law of conservation oflinear momentum and its applications, Equilibrium ofconcurrent forces.
Static and Kinetic friction, laws of friction, rollingfriction.
Dynamics of uniform circular motion : Centripetalforce and its applications.
UNIT-4
WORK, ENERGY AND POWER
Work done by a constant force and a variable force;kinetic and potential energies, work energy theorem,power. Potential energy of a spring, conservation ofmechanical energy, conservative and non-conservative
forces; Elastic and inelastic collisions in one and twodimensions.
UNIT-5
ROTATIONAL MOTIONCentre of mass of a two-particle system, Centre of
mass of a rigid body; Basic concepts of rotational motion;moment of a force, torque, angular momentum,conservation of angular momentum and its applications;moment of inertia, radius of gyration. Values of momentsof inertia for simple geometrical objects, parallel andperpendicular axes theorems and their applications. Rigidbody rotation, equations of rotational motion.
UNIT-6
GRAVITATIONThe universal law of gravitation. Acceleration due to
gravity and its variation with altitude and depth. Kepler’slaws of planetary motion. Gravitational potential energy;gravitational potential. Escape velocity. Orbital velocityof a satellite. Geo-stationary satellites.
UNIT-7
PROPERTIES OF SOLIDS AND LIQUIDSElastic behaviour, Stress-strain relationship, Hooke’s
law, Young’s modulus, bulk modulus, modulus ofrigidity. Pressure due to a fluid column; Pascal’s law andits applications. Viscosity, Stokes’ law, terminal velocity,streamline and turbulent flow, Reynolds number.Bernoulli’s principle and its applications. Surface energyand surface tension, angle of contact, application ofsurface tension—drops, bubbles and capillary rise. Heat,temperature, thermal expansion; specific heat capacity,calorimetry; change of state, latent heat. Heat transfer—conduction, convection and radiation, Newton’s law ofcooling.
UNIT-8
THERMODYNAMICSThermal equilibrium, zeroth law of thermodynamics,
concept of temperature. Heat, work and internal energy.First law of thermodynamics. Second law ofthermodynamics: reversible and irreversible processes.Carnot engine and its efficiency.
( vii )
UNIT-9
KINETIC THEORY OF GASES
Equation of state of a perfect gas, work done oncompressing a gas. Kinetic theory of gases—assumptions, concept of pressure. Kinetic energy andtemperature : rms speed of gas molecules; Degrees offreedom, Law of equipartition of energy, applications tospecific heat capacities of gases; Mean free path,Avogadro’s number.
UNIT-10
OSCILLATIONS AND WAVESPeriodic motion—Period, frequency, displacement as
a function of time. Periodic functions. Simple harmonicmotion (S.H.M.) and its equation; phase; oscillations of aspring—restoring force and force constant; energy inS.H.M.—kinetic and potential energies; Simplependulum - derivation of expression for its time-period;Free, forced and damped oscillations, resonance.
Wave motion—Longitudinal and transverse waves,speed of a wave. Displacement relation for a progressivewave. Principle of superposition of waves, reflection ofwaves, Standing waves in strings and organ pipes,fundamental mode and harmonics, Beats, Doppler effectin sound.
UNIT-11
ELECTROSTATICSElectric charges : Conservation of charge, Coulomb’s
law—forces between two point charges, forces betweenmultiple charges; superposition principle and continuouscharge distribution.
Electric field : Electric field due to a point charge,Electric field lines, Electric dipole, Electric field due to adipole, Torque on a dipole in a uniform electric field.
Electric flux, Gauss’s law and its applications to findfield due to infinitely long uniformly charged straightwire, uniformly charged infinite plane sheet anduniformly charged thin spherical shell. Electric potentialand its calculation for a point charge, electric dipole andsystem of charges; Equipotential surfaces, Electricalpotential energy of a system of two point charges in anelectrostatic field.
Conductors and insulators, Dielectrics and electricpolarization, capacitor, combination of capacitors inseries and in parallel, capacitance of a parallel platecapacitor with and without dielectric medium between theplates, Energy stored in a capacitor.
UNIT-12
CURRENT ELECTRICITY
Electric current, Drift velocity, Ohm’s law, Electricalresistance, Resistances of different materials, V-Icharacteristics of ohmic and non-ohmic conductors,Electrical energy and power, Electrical resistivity, Colourcode for resistors; Series and parallel combinations ofresistors; Temperature dependence of resistance.
Electric cell and its internal resistance, potentialdifference and emf of a cell, combination of cells in series
and in parallel. Kirchhoff’s laws and their applications.Wheatstone bridge, Meter bridge. Potentiometer—principle and its applications.
UNIT-13
MAGNETIC EFFECTS OF CURRENT ANDMAGNETISM
Biot-Savart law and its application to currentcarrying circular loop. Ampere’s law and its applicationsto infinitely long current carrying straight wire andsolenoid. Force on a moving charge in uniform magneticand electric fields. Cyclotron.
Force on a current-carrying conductor in a uniformmagnetic field. Force between two parallel current-carrying conductors—definition of ampere. Torqueexperienced by a current loop in uniform magnetic field;Moving coil galvanometer, its current sensitivity andconversion to ammeter and voltmeter.
Current loop as a magnetic dipole and its magneticdipole moment. Bar magnet as an equivalent solenoid,magnetic field lines; Earth’s magnetic field and magneticelements. Para-, dia- and ferro-magnetic substances.
Magnetic susceptibility and permeability, Hysteresis,Electromagnets and permanent magnets.
UNIT-14
ELECTROMAGNETIC INDUCTION ANDALTERNATING CURRENTS
Electromagnetic induction; Faraday’s law, inducedemf and current; Lenz’s law, Eddy currents. Self andmutual inductance. Alternating currents, peak and rmsvalue of alternating current/voltage; reactance andimpedance; LCR series circuit, resonance; Quality factor,power in AC circuits, wattless current. AC generator andtransformer.
UNIT-15
ELECTROMAGNETIC WAVES
Electromagnetic waves and their characteristics.Transverse nature of electromagnetic waves.Electromagnetic spectrum (radiowaves, microwaves,infrared, visible, ultraviolet, X-rays, gamma rays).Applications of e.m. waves.
UNIT-16
OPTICS
Reflection and refraction of light at plane andspherical surfaces, mirror formula, Total internalreflection and its applications, Deviation and Dispersionof light by a prism, Lens formula, Magnification, Powerof a Lens, Combination of thin lenses in contact,Microscope and Astronomical Telescope (reflecting andrefracting) and their magnifying powers.
Wave optics : Wavefront and Huygens’ principle,Laws of reflection and refraction using Huygens’principle. Interference, Young’s double slit experimentand expression for fringe width. Diffraction due to asingle slit, width of central maximum. Resolving powerof microscopes and astronomical telescopes, Polarisation,
( viii )
plane polarized light; Brewster’s law, uses of planepolarized light and Polaroids.
UNIT-17
DUAL NATURE OF MATTER AND RADIATION
Dual nature of radiation. Photoelectric effect, Hertzand Lenard’s observations; Einstein’s photoelectricequation; particle nature of light. Matter waves—wavenature of particle, de Broglie relation. Davisson-Germerexperiment.
UNIT-18
ATOMS AND NUCLEI
Alpha-particle scattering experiment; Rutherford’smodel of atom; Bohr model, energy levels, hydrogenspectrum. Composition and size of nucleus, atomicmasses, isotopes, isobars; isotones. Radioactivity—alpha,beta and gamma particles/rays and their properties;radioactive decay law. Mass-energy relation, mass defect;binding energy per nucleon and its variation with massnumber, nuclear fission and fusion.
UNIT-19
ELECTRONIC DEVICES
Semiconductors; semiconductor diode : I-Vcharacteristics in forward and reverse bias; diode as arectifier; I-V characteristics of LED, photodiode, solarcell and Zener diode; Zener diode as a voltage regulator.Junction transistor, transistor action, characteristics of atransistor; transistor as an amplifier (common emitterconfiguration) and oscillator. Logic gates (OR, AND,NOT, NAND and NOR). Transistor as a switch.
UNIT-20
COMMUNICATION SYSTEMSPropagation of electromagnetic waves in the
atmosphere; Sky and space wave propagation, Need formodulation, Amplitude and frequency modulation,Bandwidth of signals, Bandwidth of transmissionmedium, Basic elements of a communication system(Block diagram only).
SECTION : B
UNIT-21
EXPERIMENTAL SKILLS
Familiarity with the basic approach and observationsof the experiments and activities :
1. Vernier callipers—its use to measure internal andexternal diameter and depth of a vessel.
2. Screw gauge—its use to determine thickness/diameter of thin sheet/wire.
3. Simple pendulum-dissipation of energy by plotting agraph between square of amplitude and time.
4. Meter Scale-mass of a given object by principle ofmoments.
5. Young’s modulus of elasticity of the material of ametallic wire.
6. Surface tension of water by capillary rise and effectof detergents.
7. Coefficient of viscosity of a given viscous liquid bymeasuring terminal velocity of a given sphericalbody.
8. Plotting a cooling curve for the relationship betweenthe temperature of a hot body and time.
9. Speed of sound in air at room temperature using aresonance tube.
10. Specific heat capacity of a given (i) solid and(ii) liquid by method of mixtures.
11. Resistivity of the material of a given wire usingmeter bridge.
12. Resistance of a given wire using Ohm’s law.
13. Potentiometer –
(i) Comparison of emf of two primary cells.
(ii) Determination of internal resistance of a cell.
14. Resistance and figure of merit of a galvanometer byhalf deflection method.
15. Focal length of :
(i) Convex mirror
(ii) Concave mirror, and
(iii) Convex lens
using parallax method.
16. Plot of angle of deviation Vs angle of incidence for atriangular prism.
17. Refractive index of a glass slab using a travellingmicroscope.
18. Characteristic curves of a p-n junction diode inforward and reverse bias.
19. Characteristic curves of a Zener diode and findingreverse break down voltage.
20. Characteristic curves of a transistor and findingcurrent gain and voltage gain.
21. Identification of Diode, LED, Transistor, IC,Resistor, Capacitor from mixed collection of suchitems.
22. Using multimeter to :
(i) Identify base of a transistor.
(ii) Distinguish between n-p-n and p - n - p typetransistor.
(iii) See the unidirectional flow of current in case ofa diode and an LED.
(iv) Check the correctness or otherwise of a givenelectronic component (diode, transistor or IC).
( ix )
Chemistry
SECTION : A
PHYSICAL CHEMISTRY
UNIT-1
SOME BASIC CONCEPTS IN CHEMISTRYMatter and its nature, Dalton’s atomic theory;
Concept of atom, molecule, element and compound;Physical quantities and their measurements in Chemistry,precision and accuracy, significant figures, S.I. Units,dimensional analysis; Laws of chemical combination;Atomic and molecular masses, mole concept, molar mass,percentage composition, empirical and molecularformulae; Chemical equations and stoichiometry.
UNIT-2STATES OF MATTER
Classification of matter into solid, liquid and gaseousstates.
Gaseous State :Measurable properties of gases; Gas laws—Boyle’s
law, Charle’s law, Graham’s law of diffusion, Avogadro’slaw, Dalton’s law of partial pressure; Concept of Absolutescale of temperature; Ideal gas equation, Kinetic theory ofgases (only postulates); Concept of average, root meansquare and most probable velocities; Real gases,deviation from Ideal behaviour, compressibility factor,van der Waals equation.
Liquid State :Properties of liquids—vapour pressure, viscosity and
surface tension and effect of temperature on them(qualitative treatment only).
Solid State :Classification of solids : molecular, ionic, covalent
and metallic solids, amorphous and crystalline solids(elementary idea); Bragg’s Law and its applications, Unitcell and lattices, packing in solids (fcc, bcc and hcplattices), voids, calculations involving unit cellparameters, imperfection in solids; electrical, magneticand dielectric properties.
UNIT-3ATOMIC STRUCTURE
Thomson and Rutherford atomic models and theirlimitations; Nature of electromagnetic radiation,photoelectric effect; spectrum of hydrogen atom, Bohrmodel of hydrogen atom—its postulates, derivation of therelations for energy of the electron and radii of thedifferent orbits, limitations of Bohr’s model; dual natureof matter, de-Broglie’s relationship, Heisenberguncertainty principle. Elementary ideas of quantummechanics, quantum mechanical model of atom, itsimportant features, ψ and ψ2, concept of atomic orbitalsas one electron wave functions; Variation of ψ and ψ2
with r for 1s and 2s orbitals; various quantum numbers(principal, angular momentum and magnetic quantumnumbers) and their significance; shapes of s, p and d-orbitals, electron spin and spin quantum number; rules forfilling electrons in orbitals - aufbau principle, Pauli’sexclusion principle and Hund’s rule, electronicconfiguration of elements, extra stability of half-filledand completely filled orbitals.
UNIT-4
CHEMICAL BONDING AND MOLECULARSTRUCTURE
Kossel - Lewis approach to chemical bondformation, concept of ionic and covalent bonds.
Ionic Bonding : Formation of ionic bonds, factorsaffecting the formation of ionic bonds; calculation oflattice enthalpy.
Covalent Bonding : Concept of electronegativity,Fajan’s rule, dipole moment; Valence Shell Electron PairRepulsion (VSEPR) theory and shapes of simplemolecules.
Quantum mechanical approach to covalentbonding : Valence bond theory—Its important features,concept of hybridization involving s, p and d orbitals;Resonance.
Molecular Orbital Theory : Its important features,LCAOs, types of molecular orbitals (bonding,antibonding), sigma and pi-bonds, molecular orbitalelectronic configurations of homonuclear diatomicmolecules, concept of bond order, bond length and bondenergy.
Elementary idea of metallic bonding. Hydrogenbonding and its applications.
UNIT-5
CHEMICAL THERMODYNAMICS
Fundamentals of thermodynamics : System andsurroundings, extensive and intensive properties, statefunctions, types of processes.
First law of thermodynamics : Concept of work,heat internal energy and enthalpy, heat capacity, molarheat capacity, Hess’s law of constant heat summation;Enthalpies of bond dissociation, combustion, formation,atomization, sublimation, phase transition, hydration,ionization and solution.
Second law of thermodynamics : Spontaneity ofprocesses; DS of the universe and DG of the system ascriteria for spontaneity, DG° (Standard Gibbs energychange) and equilibrium constant.
UNIT-6
SOLUTIONSDifferent methods for expressing concentration of
solution - molality, molarity, mole fraction, percentage
( x )
(by volume and mass both), vapour pressure of solutionsand Raoult’s Law—Ideal and non-ideal solutions, vapourpressure —composition plots for ideal and non-idealsolutions; Colligative properties of dilute solutions—relative lowering of vapour pressure, depression offreezing point, elevation of boiling point and osmoticpressure; Determination of molecular mass usingcolligative properties; Abnormal value of molar mass,van’t Hoff factor and its significance.
UNIT-7
EQUILIBRIUM
Meaning of equilibrium, concept of dynamicequilibrium.
Equilibria involving physical processes : Solid-liquid, liquid - gas and solid - gas equilibria, Henry’s law,general characteristics of equilibrium involving physicalprocesses.
Equilibria involving chemical processes : Law ofchemical equilibrium, equilibrium constants (Kp and Kc)and their significance, significance of DG and DG° inchemical equilibria, factors affecting equilibriumconcentration, pressure, temperature, effect of catalyst;Le Chatelier's principle.
Ionic equilibrium : Weak and strong electrolytes,ionization of electrolytes, various concepts of acids andbases (Arrhenius, Bronsted - Lowry and Lewis) and theirionization, acid - base equilibria (including multistageionization) and ionization constants, ionization of water,pH scale, common ion effect, hydrolysis of salts and pHof their solutions, solubility of sparingly soluble salts andsolubility products, buffer solutions.
UNIT-8
REDOX REACTIONS ANDELECTROCHEMISTRY
Electronic concepts of oxidation and reduction,redox reactions, oxidation number, rules for assigningoxidation number, balancing of redox reactions.
Eectrolytic and metallic conduction, conductance inelectrolytic solutions, specific and molar conductivitiesand their variation with concentration : Kohlrausch’s lawand its applications.
Electrochemical cells : Electrolytic and Galvaniccells, different types of electrodes, electrode potentialsincluding standard electrode potential, half - cell and cellreactions, emf of a Galvanic cell and its measurement;Nernst equation and its applications; Relationshipbetween cell potential and Gibbs’ energy change; Drycell and lead accumulator; Fuel cells.
UNIT-9
CHEMICAL KINETICS
Rate of a chemical reaction, factors affecting the rateof reactions; concentration, temperature, pressure andcatalyst; elementary and complex reactions, order andmolecularity of reactions, rate law, rate constant and itsunits, differential and integral forms of zero and firstorder reactions, their characteristics and half - lives,effect of temperature on rate of reactions—Arrhenius
theory, activation energy and its calculation, collisiontheory of bimolecular gaseous reactions (no derivation).
UNIT-10
SURFACE CHEMISTRY
Adsorption : Physisorption and chemisorption andtheir characteristics, factors affecting adsorption of gaseson solids—Freundlich and Langmuir adsorptionisotherms, adsorption from solutions.
Colloidal state : distinction among true solutions,colloids and suspensions, classification of colloids—lyophilic, lyophobic; multi molecular, macromolecularand associated colloids (micelles), preparation andproperties of colloids—Tyndall effect, Brownianmovement, electrophoresis, dialysis, coagulation andflocculation; Emulsions and their characteristics.
SECTION : BINORGANIC CHEMISTRY
UNIT-11
CLASSIFICATION OF ELEMENTS ANDPERIODICITY IN PROPERTIES
Modern periodic law and present form of theperiodic table, s, p, d and f block elements, periodictrends in properties of elements atomic and ionic radii,ionization enthalpy, electron gain enthalpy, valence,oxidation states and chemical reactivity.
UNIT-12
GENERAL PRINCIPLES AND PROCESSES OFISOLATION OF METALS
Modes of occurrence of elements in nature, minerals,ores; steps involved in the extraction of metals—concentration, reduction (chemical and electrolyticmethods) and refining with special reference to theextraction of Al, Cu, Zn and Fe; Thermodynamic andelectrochemical principles involved in the extraction ofmetals.
UNIT-13
HYDROGEN
Position of hydrogen in periodic table, isotopes,preparation, properties and uses of hydrogen; physicaland chemical properties of water and heavy water;Structure, preparation, reactions and uses of hydrogenperoxide; Hydrogen as a fuel.
UNIT-14
S-BLOCK ELEMENTS (ALKALI ANDALKALINE EARTH METALS)
Group-1 and 2 Elements
General introduction, electronic configuration andgeneral trends in physical and chemical properties ofelements, anomalous properties of the first element ofeach group, diagonal relationships.
( xi )
Preparation and properties of some importantcompounds —sodium carbonate and sodium hydroxide;Industrial uses of lime, limestone, Plaster of Paris andcement; Biological significance of Na, K, Mg and Ca.
UNIT-15
P - BLOCK ELEMENTS
Group - 13 to Group-18 Elements
General Introduction : Electronic configuration andgeneral trends in physical and chemical properties ofelements across the periods and down the groups; uniquebehaviour of the first element in each group.
Groupwise study of the p - block elements Group - 13
Preparation, properties and uses of boron andaluminium; properties of boric acid, diborane, borontrifluoride, aluminium chloride and alums.
Group - 14
Allotropes of carbon, tendency of catenation;Structure & Properties of silicates and zeolites.
Group - 15Properties and uses of nitrogen and phosphorus;
Allotrophic forms of phosphorus; Preparation, properties,structure and uses of ammonia, nitric acid, phosphine andphosphorus halides, (PCl3, PCl5); Structures of oxidesand oxoacids of nitrogen and phosphorus.
Group - 16Preparation, properties, structures and uses of ozone;
Allotropic forms of sulphur; Preparation, properties,structures and uses of sulphuric acid (including itsindustrial preparation); Structures of oxoacids of sulphur.
Group - 17Preparation, properties and uses of hydrochloric acid;
Trends in the acidic nature of hydrogen halides;Structures of Interhalogen compounds and oxides andoxoacids of halogens.
Group -18
Occurrence and uses of noble gases; Structures offluorides and oxides of xenon.
UNIT-16
d - and f - BLOCK ELEMENTS
Transition Elements
General introduction, electronic configuration,occurrence and characteristics, general trends inproperties of the first row transition elements—physicalproperties, ionization enthalpy, oxidation states, atomicradii, colour, catalytic behaviour, magnetic properties,complex formation, interstitial compounds, alloyformation; Preparation, properties and uses of K2 Cr2 O7
and KMnO4.
Inner Transition Elements
Lanthanoids : Electronic configuration, oxidationstates and lanthanoid contraction.
Actinoids : Electronic configuration and oxidationstates.
UNIT-17
CO-ORDINATION COMPOUNDS
Introduction to co-ordination compounds, Werner’stheory; ligands, co-ordination number, denticity,chelation; IUPAC nomenclature of mononuclear co-ordination compounds, isomerism; Bonding Valencebond approach and basic ideas of Crystal field theory,colour and magnetic properties; Importance of co-ordination compounds (in qualitative analysis, extractionof metals and in biological systems).
UNIT-18
ENVIRONMENTAL CHEMISTRY
Environmental pollution : Atmospheric, water andsoil.
Atmospheric pollution : Tropospheric andstratospheric.
Tropospheric pollutants : Gaseous pollutants :Oxides of carbon, nitrogen and sulphur, hydrocarbons;their sources, harmful effects and prevention; Greenhouse effect and Global warming; Acid rain.
Particulate pollutants : Smoke, dust, smog, fumes,mist; their sources, harmful effects and prevention.
Stratospheric pollution : Formation and breakdownof ozone, depletion of ozone layer—its mechanism andeffects.
Water pollution : Major pollutants such as,pathogens, organic wastes and chemical pollutants; theirharmful effects and prevention.
Soil pollution : Major pollutants such as : Pesticides(insecticides, herbicides and fungicides), their harmfuleffects and prevention.
Strategies to control environmental pollution.
SECTION : CORGANIC CHEMISTRY
UNIT-19
PURIFICATION AND CHARACTERISATION OFORGANIC COMPOUNDS
Purification : Crystallization, sublimation, distilla-tion, differential extraction and chromatography—principles and their applications.
Qualitative analysis : Detection of nitrogen,sulphur, phosphorus and halogens.
Quantitative analysis (basic principles only) :Estimation of carbon, hydrogen, nitrogen, halogens,sulphur, phosphorus.
( xii )
Calculations of empirical formulae and molecularformulae; Numerical problems in organic quantitativeanalysis.
UNIT-20
SOME BASIC PRINCIPLES OF ORGANICCHEMISTRY
Tetravalency of carbon; Shapes of simple mole-cules— hybridization (s and p); Classification of organiccompounds based on functional groups : — C = C — ,— C ≡ C — and those containing halogens, oxygen,nitrogen and sulphur, Homologous series; Isomerism—structural and stereoisomerism.
Nomenclature (Trivial and IUPAC)
Covalent bond fission : Homolytic and heterolytic :free radicals, carbocations and carbanions; stability ofcarbocations and free radicals, electrophiles andnucleophiles.
Electronic displacement in a covalent bond :Inductive effect, electromeric effect, resonance andhyperconjugation.
UNIT-21
HYDROCARBONS
Classification, isomerism, IUPAC nomenclature,general methods of preparation, properties and reactions.
Alkanes : Conformations : Sawhorse and Newmanprojections (of ethane); Mechanism of halogenation ofalkanes.
Alkenes : Geometrical isomerism; Mechanism ofelectrophilic addition : addition of hydrogen, halogens,water, hydrogen halides (Markownikoff’s and peroxideeffect); Ozonolysis and polymerization.
Alkynes : Acidic character; addition of hydrogen,halogens, water and hydrogen halides; polymerization.
Aromatic hydrocarbons : Nomenclature, benzene -structure and aromaticity; Mechanism of electrophilicsubstitution : halogenation, nitration, Friedel - Craft’salkylation and acylation, directive influence of functionalgroup in mono-substituted benzene.
UNIT-22
ORGANIC COMPOUNDS CONTAININGHALOGENS
General methods of preparation, properties andreactions; Nature of C—X bond; Mechanisms ofsubstitution reactions.
Uses; environmental effects of chloroform andiodoform.
UNIT-23
ORGANIC COMPOUNDS CONTAINING OXYGEN
General methods of preparation, properties, reactionsand uses.
ALCOHOLS, PHENOLS AND ETHERS
Alcohols : Identification of primary, secondary andtertiary alcohols; mechanism of dehydration.
Phenols : Acidic nature, electrophilic substitutionreactions: halogenation, nitration and sulphonation,Reimer - Tiemann reaction.
Ethers : Structure.
Aldehyde and Ketones : Nature of carbonyl group;Nucleophilic addition to >C=O group, relative reactivitiesof aldehydes and ketones; Important reactions such as—Nucleophilic addition reactions (addition of HCN, NH3
and its derivatives), Grignard reagent; oxidation;reduction (Wolff Kishner and Clemmensen); acidity of a-hydrogen, aldol condensation, Cannizzaro reaction,Haloform reaction; Chemical tests to distinguish betweenAldehydes and Ketones.
CARBOXYLIC ACIDS
Acidic strength and factors affecting it.
UNIT-24
ORGANIC COMPOUNDS CONTAININGNITROGEN
General methods of preparation, properties, reactionsand uses.
Amines : Nomenclature, classification, structure,basic character and identification of primary, secondaryand tertiary amines and their basic character.
Diazonium Salts : Importance in synthetic organicchemistry.
UNIT-25
POLYMERS
General introduction and classification of polymers,general methods of polymerization—addition andcondensation, copolymerization; Natural and syntheticrubber and vulcanization; some important polymers withemphasis on their monomers and uses—polythene, nylon,polyester and bakelite.
UNIT-26
BIOMOLECULES
General introduction and importance of biomolecules.
Carbohydrates : Classification : aldoses andketoses; monosaccharides (glucose and fructose),constituent monosaccharides of oligosaccharides(sucrose, lactose and maltose).
Proteins : Elementary Idea of a-amino acids, peptidebond, polypeptides; Proteins : primary, secondary,tertiary and quaternary structure (qualitative idea only),denaturation of proteins, enzymes.
Vitamins : Classification and functions.
( xiii )
Nucleic acids : Chemical constitution of DNA andRNA.
Biological functions of Nucleic acids.
UNIT-27
CHEMISTRY IN EVERYDAY LIFE
● Chemicals in medicines : Analgesics, tranquilizers,antiseptics, disinfectants, antimicrobials, antifertilitydrugs, antibiotics, antacids, antihistamins—theirmeaning and common examples.
● Chemicals in food : Preservatives, artificial sweet-ening agents—common examples.
● Cleansing agents : Soaps and detergents, cleansingaction.
UNIT-28
PRINCIPLES RELATED TO PRACTICALCHEMISTRY
* Detection of extra elements (N,S, halogens) inorganic compounds; Detection of the followingfunctional groups : hydroxyl (alcoholic andphenolic), carbonyl (aldehyde and ketone), carboxyland amino groups in organic compounds.
* Chemistry involved in the preparation of thefollowing :
Inorganic compounds : Mohr’s salt, potash alum.
Organic compounds : Acetanilide, p-nitroacetanilide,aniline yellow, iodoform.
* Chemistry involved in the titrimetric excercises—Acids bases and the use of indicators, oxalic-acid VsKMnO4, Mohr’s salt Vs KMnO4.
* Chemical principles involved in the qualitative saltanalysis :
Cations—Pb2+ , Cu2+, Al 3+, Fe3+, Zn2+, Ni2+, Ca2+,
Ba2+ , Mg2+ , NH 4+.
Anions—CO32–, S2–, SO4
2–, NO2– , NO3– , Cl– , Br, I.
(Insoluble salts excluded).
* Chemical principles involved in the followingexperiments :
1. Enthalpy of solution of CuSO4.
2. Enthalpy of neutralization of strong acid andstrong base.
3. Preparation of lyophilic and lyophobic sols.
4. Kinetic study of reaction of iodide ion withhydrogen peroxide at room temperature.
MathematicsUNIT-1
SETS, RELATIONS AND FUNCTIONS
Sets and their representation; Union, intersection andcomplement of sets and their algebraic properties; Powerset; Relation, Types of relations, equivalence relations,functions; one-one, into and onto functions, compositionof functions.
UNIT-2
COMPLEX NUMBERS AND QUADRATICEQUATIONS
Complex numbers as ordered pairs of reals,Representation of complex numbers in the form a+ib andtheir representation in a plane, Argand diagram, algebraof complex numbers, modulus and argument (oramplitude) of a complex number, square root of acomplex number, triangle inequality, Quadratic equationsin real and complex number system and their solutions.Relation between roots and co-efficients, nature of roots,formation of quadratic equations with given roots.
UNIT-3MATRICES AND DETERMINANTS
Matrices, algebra of matrices, types of matrices,determinants and matrices of order two and three.
Properties of determinants, evaluation of determinants,area of triangles using determinants. Adjoint andevaluation of inverse of a square matrix usingdeterminants and elementary transformations, Test ofconsistency and solution of simultaneous linear equationsin two or three variables using determinants and matrices.
UNIT-4PERMUTATIONS AND COMBINATIONS
Fundamental principle of counting, permutation asan arrangement and combination as selection, Meaning ofP (n,r) and C (n,r), simple applications.
UNIT-5MATHEMATICAL INDUCTION
Principle of Mathematical Induction and its simpleapplications.
UNIT-6BINOMIAL THEOREM AND ITS SIMPLE
APPLICATIONS
Binomial theorem for a positive integral index,general term and middle term, properties of Binomial co-efficients and simple applications.
( xiv )
UNIT-7
SEQUENCES AND SERIES
Arithmetic and Geometric progressions, insertion ofarithmetic, geometric means between two given numbers.Relation between A.M. and G.M. Sum upto n terms ofspecial series : Sn, Sn 2, Sn 3. Arithmetic-Geometricprogression.
UNIT-8
LIMIT, CONTINUITY ANDDIFFERENTIABILITY
Real-valued functions, algebra of functions,polynomials, rational, trigonometric, logarithmic andexponential functions, inverse functions. Graphs ofsimple functions. Limits, continuity and differentiability.Differentiation of the sum, difference, product andquotient of two functions. Differentiation oftrigonometric, inverse trigonometric, logarithmic,exponential, composite and implicit functions; derivativesof order upto two. Rolle's and Lagrange's Mean ValueTheorems. Applications of derivatives : Rate of change ofquantities, monotonic-increasing and decreasingfunctions, Maxima and minima of functions of onevariable, tangents and normals.
UNIT-9
INTEGRAL CALCULUS
Integral as an anti-derivative. Fundamental integralsinvolving algebraic, trigonometric, exponential andlogarithmic functions. Integration by substitution, byparts and by partial fractions. Integration usingtrigonometric identities.
Evaluation of simple integrals of the type
∫
dxx2 ± a2
, ⌡⎮⎮⌠
dx
√⎯⎯⎯⎯x2 ± a2
,
∫
dxa2 – x2
, ⌡⎮⎮⌠
dx
√⎯⎯⎯⎯a2 – x2
,
∫
dxax2 + bx + c
⌡⎮⎮⌠
dx
√⎯⎯⎯⎯⎯⎯⎯⎯ax2 + bx + c ,
∫ (px + q)dx
ax2 + bx + c ,
⌡⎮⎮⌠
(px + q)dx
√⎯⎯⎯⎯⎯⎯⎯⎯⎯ax2 + bx + c
∫
√⎯⎯⎯⎯⎯a2 ± x2 dx ∫
√⎯⎯⎯⎯x2 – a2 dx
Integral as limit of a sum. Fundamental Theorem ofCalculus. Properties of definite integrals. Evaluation ofdefinite integrals, determining areas of the regionsbounded by simple curves in standard form.
UNIT-10DIFFERENTIAL EQUATIONS
Ordinary differential equations, their order anddegree. Formation of differential equations. Solution ofdifferential equations by the method of separation ofvariables, solution of homogeneous and linear differentialequations of the type :
dydx
+ p (x) y = q (x)
UNIT-11 CO-ORDINATE GEOMETRY
Cartesian system of rectangular co-ordinates in aplane, distance formula, section formula, locus and itsequation, translation of axes, slope of a line, parallel andperpendicular lines, intercepts of a line on the co-ordinateaxes.
Straight lines
Various forms of equations of a line, intersection oflines, angles between two lines, conditions forconcurrence of three lines, distance of a point from a line,equations of internal and external bisectors of anglesbetween two lines, co-ordinates of centroid, orthocentreand circumcentre of a triangle, equation of family of linespassing through the point of intersection of two lines.
Circles, conic sections
Standard form of equation of a circle, general formof the equation of a circle, its radius and centre, equationof a circle when the end points of a diameter are given,points of intersection of a line and a circle with the centreat the origin and condition for a line to be tangent to acircle, equation of the tangent. Sections of cones,equations of conic sections (parabola, ellipse andhyperbola) in standard forms, condition for y = mx + c tobe a tangent and point(s) of tangency.
UNIT-12THREE DIMENSIONAL GEOMETRY
Co-ordinates of a point in space, distance betweentwo points, section formula, direction ratios and directioncosines, angle between two intersecting lines. Skew lines,the shortest distance between them and its equation.Equations of a line and a plane in different forms,intersection of a line and a plane, coplanar lines.
UNIT-13VECTOR ALGEBRA
Vectors and scalars, addition of vectors, componentsof a vector in two dimensions and three dimensionalspace, scalar and vector products, scalar and vector tripleproduct.
( xv )
UNIT-14
STATISTICS AND PROBABILITY
Measures of Dispersion : Calculation of mean,median, mode of grouped and ungrouped data.Calculation of standard deviation, variance and meandeviation for grouped and ungrouped data.
Probability : Probability of an event, addition andmultiplication theorems of probability, Baye's theorem,probability distribution of a random variate, Bernoullitrials and Binomial distribution.
UNIT-15TRIGONOMETRY
Trigonometrical identities and equations.Trigonometrical functions. Inverse trigonometricalfunctions and their properties. Heights and Distances.
UNIT-16MATHEMATICAL REASONING
Statements, logical operations and, or, implies,implied by, if and only if. Understanding of tautology,contradiction, converse and contrapositive.
All India Engineering Entrance Exam., 2011 Solved Paper
Part-A : Mathematics1. Consider 5 independent Bernoulli’s trials each with
probability of success p. If the probability of at least
one failure is greater than or equal to 3132
, then p lies
in the interval—
(A) [ ]1112
‚ 1 (B) [ ]12 ‚
34
(C) [ ]34 ‚
1112
(D) [ ]0‚ 12
2. The coefficient of x7 in the expansion of (1 – x – x2 +x3)6 is—
(A) 132 (B) 144(C) – 132 (D) – 144
3. limx→2
⎝⎜⎛
⎠⎟⎞√⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯1 – cos{2(x – 2)}
x – 2
(A) Equals 1
√⎯ 2(B) Does not exist
(C) Equals √⎯ 2 (D) Equals – √⎯ 2
4. Let R be the set of real numbers.
Statement 1 : A = {(x, y) ∈ R × R : y – x is aninteger} is an equivalence relation on R.
Statement 2 : B = {(x, y) ∈ R × R : x = ∝y for somerational number α} is an equivalence relation on R.
(A) Statement 1 is false, Statement 2 is true.
(B) Statement 1 is true, Statement 2 is true;Statement 2 is a correct explanation forStatement 1.
(C) Statement 1 is true, Statement 2 is true;Statement 2 is not a correct explanation forStatement 1
(D) Statement 1 is true, Statement 2 is false.
5. Let α , β be real and z be a complex number. Ifz2 + αz + β = 0 has two distinct roots on the line Rez = 1, then it is necessary that—
(A) β ∈ (1, ∞) (B) β ∈ (0, 1)
(C) β ∈ (– 1, 0) (D) | β | = 1
6.d2xdy2 equals—
(A) – ( )d2ydx2 ( )dy
dx
– 3(B) ( )d2y
dx2
– 1
(C) – ( )d2ydx2
– 1 ( )dy
dx
– 3(D) ( )d2y
dx2 ( )dydx
– 2
7. The number of values of k for which the linearequations
4x + ky + 2z = 0kx + 4y + z = 02x + 2y + z = 0
possess a non-zero solution is—(A) Zero (B) 3(C) 2 (D) 1
8. Statement 1 : The point A(1, 0, 7) is the mirrorimage of the point B(1, 6, 3) in the line—
x1 =
y – 12
= z – 2
3
Statement 2 : The line : x1 =
y – 12
= z – 2
3 bisects the
line segment joining A(1, 0, 7) and B(1, 6, 3).(A) Statement 1 is false, Statement 2 is true.(B) Statement 1 is true, Statement 2 is true;
Statement 2 is a correct explanation forStatement 1.
(C) Statement 1 is true, Statement 2 is true;Statement 2 is not a correct explanation forStatement 1.
(D) Statement 1 is true, Statement 2 is false.
9. Consider the following statementsP : Suman is brilliantQ : Suman is richR : Suman is honestThe negation of the statement “Suman is brilliant anddishonest if and only if Suman is rich” can beexpressed as—(A) ~ (P ^ ~ R) ↔ Q (B) ~ P ^ (Q ↔ ~ R)
(C) ~ [Q ↔ (P ^ ~ R)] (D) ~ Q ↔ ~ P ^ R
10. The lines L1 : y – x = 0 and L2 : 2x + y = 0 intersectthe line L3 : y + 2 = 0 at P and Q respectively. Thebisector of the acute angle between L1 and L2
intersects L3 at R.
Statement 1 : The ratio PR : RQ equals 2√⎯ 2 : √⎯ 5.Statement 2 : In any triangle, bisector of an angledivides the triangle into two similar triangles.(A) Statement-1 is false, Statement-2 is true.(B) Statement-1 is true, Statement-2 is true;
Statement-2 is a correct explanation forStatement-1.
(C) Statement-1 is true, Statement-2 is true;Statement-2 is not a correct explanation forStatement-1.
(D) Statement-1 is true, Statement-2 is false.
2 | AIEEE 2011
11. A man saves 200 in each of the first three monthsof his service. In each of the subsequent months hissaving increases by 40 more than the saving ofimmediately previous month. His total saving fromthe start of service will be 11040 after—
(A) 21 months (B) 18 months
(C) 19 months (D) 20 months
12. Equation of the ellipse whose axes are the axes ofcoordinates and which passes through the point (– 3,
1) and has eccentricity 25 is—
(A) 5x2 + 3y2 – 32 = 0 (B) 3x2 + 5y2 – 32 = 0
(C) 5x2 + 3y2 – 48 = 0 (D) 3x2 + 5y2 – 15 = 0
13. If A = sin2 x + cos4 x, then for all real x—
(A)34 ≤ A ≤
1316
(B)34 ≤ A ≤ 1
(C)1316
≤ A ≤ 1 (D) 1 ≤ A ≤ 2
14. The value of
1
∫0
8 log (1 + x)
1 + x2 dx is—
(A) log 2 (B) π log 2
(C)π8
log 2 (D)π2 log 2
15. If the angle between the line x = y – 1
2 =
z – 3λ
and
the plane x + 2y + 3z = 4 is cos– 1 ⎝⎜⎛
⎠⎟⎞5
14 , then λ
equals—
(A)53
(B)23
(C)32
(D)25
16. For x ∈ ( )0‚ 5π2
, define f(x) =
x
∫0
√⎯ t sin t dt Then f
has—
(A) Local maximum at π and local minimum at 2π(B) Local maximum at π and 2π(C) Local minimum at π and 2π(D) Local minimum at π and local maximum at 2π
17. The domain of the function f (x) = 1
√⎯⎯⎯⎯⎯| x | – x is—
(A) (– ∞, ∞) – {0} (B) (– ∞, ∞)
(C) (0, ∞) (D) (– ∞, 0)
18. If the mean deviation about the median of thenumbers a, 2a, ………, 50a is 50, then | a | equals—
(A) 5 (B) 2
(C) 3 (D) 4
19. If →a =
1
√⎯⎯10 (3 i + k) and
→b =
17 (2 i + 3 j – 6 k), then
the value of ( )2→a –
→b .[ ]( )→
a × →b × ( )→
a + 2→b
is—(A) 3 (B) – 5(C) – 3 (D) 5
20. The values of p and q for which the function
f (x) =
⎩⎪⎨⎪⎧
sin (p + 1)x + sin xx
‚ x < 0
q ‚ x = 0
√⎯⎯⎯⎯x + x2 – √⎯ xx3/2 ‚ x > 0
is continuous for all x in R, are—
(A) P = 12 , q =
32
(B) p = 12 , q = –
32
(C) p = 52 , q =
12
(D) p = – 32 , q =
12
21. The two circles x2 + y2 = ax and x2 + y2 = c2(c > 0)touch each other if—(A) | a | = 2c (B) 2 | a | = c(C) | a | = c (D) a = 2c
22. Let I be the purchase value of an equipment and V(t)be the value after it has been used for t years. Thevalue V(t) depreciates at a rate given by differential
equation dV (t)
dt = – k (T – t), where k > 0 is a constant
and T is the total life in years of the equipment. Thenthe scrap value V (T) of the equipment is—
(A) e– kT (B) T2 – Ik
(C) I – kT2
2(D) I –
k (T – t)2
2
23. If C and D are two events such that C ⊂ D and P(D)≠ 0, then the correct statement among the followingis—
(A) P (C⏐D) = P (D)P (C)
(B) P(C⏐D) = P(C)
(C) P(C⏐D) ≥ P(C) (D) P(C⏐D) < P(C)
24. Let A and B be two symmetric matrices of order 3.Statement-1 : A (BA) and (AB) A are symmetricmatrices.Statement-2 : AB is symmetric matrix if matrixmultiplication of A with B is commutative.(A) Statement-1 is false, Statement-2 is true.(B) Statement-1 is true, Statement-2 is true; State-
ment-2 is a correct explanation for Statement-1.(C) Statement-1 is true, Statement-2 is true;
Statement-2 is not a correct explanation forStatement-1.
(D) Statement-1 is true, Statement-2 is false.
25. If ω (≠ 1) is a cube root of unity, and (1 + ω)7 = A +Bω. Then (A, B) equals—(A) (– 1, 1) (B) (0, 1)(C) (1, 1) (D) (1, 0)
AIEEE 2011 | 3
26. Statement-1 : The number of ways of distributing 10identical balls in 4 distinct boxes such that no box isempty is 9C3.
Statement-2 : The number of ways of choosing any3 places from 9 different places is 9C3.
(A) Statement-1 is false, Statement-2 is true.(B) Statement-1 is true, Statement-2 is true; State-
ment-2 is a correct explanation for Statement-1.(C) Statement-1 is true, Statement-2 is true; State-
ment-2 is not a correct explanation for State-ment-1.
(D) Statement-1 is true, Statement-2 is false.
27. The shortest distance between line y – x = 1 andcurve x = y2 is—
(A)4
√⎯ 3(B)
√⎯ 34
(C)3√⎯ 2
8(D)
8
3√⎯ 2
28. The area of the region enclosed by the curves y = x, x= e, y = 1/x and the positive x-axis is—
(A)52 square units (B)
12 square units
(C) 1 square units (D)32 square units
29. If dydx
= y + 3 > 0 and y (0) = 2, then y (ln 2) is equal
to—(A) – 2 (B) 7(C) 5 (D) 13
30. The vectors →a and
→b are not perpendicular and
→c
and →d are two vectors satisfying :
→b ×
→c =
→b ×
→d
and →a .
→d = 0. Then the vector
→d is equal to—
(A)→c –
⎝⎜⎜⎛
⎠⎟⎟⎞→
a .→c
→a .
→b
→b (B)
→b –
⎝⎜⎜⎛
⎠⎟⎟⎞→
b .→c
→a .
→b
→c
(C)→c +
⎝⎜⎜⎛
⎠⎟⎟⎞→
a .→c
→a .
→b
→b (D)
→b +
⎝⎜⎜⎛
⎠⎟⎟⎞→
b .→c
→a .
→b
→c
Part-B : Chemistry31. Among the following the maximum covalent
character is shown by the compound—(A) SnCl2 (B) AlCl3(C) MgCl2 (D) FeCl2
32. The presence or absence of hydroxy group on whichcarbon atom of sugar differentiates RNA and DNA ?(A) 2nd (B) 3rd(C) 4th (D) 1st
33. Trichloroacetaldehyde was subjected to Cannizzaro’sreaction by using NaOH. The mixture of the productscontains sodium trichloroacetate and anothercompound. The other compound is—
(A) Trichloromethanol(B) 2, 2, 2-Trichloropropanol(C) Chloroform(D) 2, 2, 2-Trichloroethanol
34. Sodium ethoxide has reacted with ethanoyl chloride.The compound that is produced in the above reactionis—
(A) 2-Butanone (B) Ethyl chloride
(C) Ethyl ethanoate (D) Diethyl ether
35. The reduction potential of hydrogen half-cell will benegative if—(A) p(H2) = 1 atm and [H+] = 1·0 M
(B) p(H2) = 2 atm and [H+] = 1·0 M
(C) p(H2) = 2 atm and [H+] = 2·0 M
(D) p(H2) = 1 atm and [H+] = 2·0) M
36. The strongest acid amongst the following compoundsis—
(A) HCOOH
(B) CH3CH2CH(Cl)CO2H
(C) ClCH2CH2CH2COOH
(D) CH3COOH
37. The degree of dissociation (α) of a weak electrolyte,AxBy is related to van’t Hoff factor (i) by theexpression—
(A) α = i – 1
x + y + 1(B) α =
x + y – 1i – 1
(C) α = x + y + 1
i – 1(D) α =
i – 1(x + y – 1)
38. ‘a’ and ‘b’ are van der Waals’ constants for gases.Chlorine is more easily liquefied than ethanebecause—
(A) a and b for Cl2 < a and b for C2H6
(B) a for Cl2 < a for C2H6 but b for Cl2 > b for C2H6
(C) a for Cl2 > a for C2H6 but b for Cl2 < b for C2H6
(D) a and b for Cl2 > a and b for C2H6
39. A vessel at 1000 K contains CO2 with a pressure of0·5 atm. Some of the CO2 is converted into CO onthe addition of graphite. If the total pressure atequilibrium is 0·8 atm, the value of K is—(A) 3 atm (B) 0·3 atm(C) 0·18 atm (D) 1·8 atm
40. Boron cannot form which one of the followinganions ?(A) BH4
– (B) B(OH)4–
(C) BO2– (D) BF6
3–
41. Which of the following facts about the complex[Cr(NH3)6]Cl3 is wrong ?
(A) The complex is paramagnetic.(B) The complex is an outer orbital complex.
4 | AIEEE 2011
(C) The complex gives white precipitate with silvernitrate solution.
(D) The complex involves d2sp3 hybridisation and isoctahedral in shape.
42. Ethylene glycol is used as an antifreeze in a coldclimate. Mass of ethylene glycol which should beadded to 4 kg of water to prevent it from freezing at– 6°C will be— (Kf for water = 1·86 K kg mol– 1, andmolar mass of ethylene glycol = 62 g mol– 1)—(A) 204·30 g (B) 400·00 g(C) 304·60 g (D) 804·32 g
43. Which one of the following orders presents thecorrect sequence of the increasing basic nature of thegiven oxides ?(A) MgO < K2O < Al2O3 < Na2O
(B) Na2O < K2O < MgO < Al2O3
(C) K2O < Na2O < Al2O3 < MgO
(D) Al2O3 < MgO < Na2O < K2O
44. The rate of a chemical reaction doubles for every10°C rise of temperature. If the temperature is raisedby 50°C, the rate of the reaction increases by about—(A) 24 times (B) 32 times(C) 64 times (D) 10 times
45. The magnetic moment (spin only) of [NiCl4]2– is—
(A) 5·46 BM (B) 2·82 BM(C) 1·41 BM (D) 1·82 BM
46. The hybridisation of orbitals of N atom in NO3–,
NO2+ and NH4
+ are respectively—
(A) sp2, sp, sp3 (B) sp, sp3, sp2
(C) sp2, sp3, sp (D) sp, sp2, sp3
47. In context of the lanthanoids, which of the followingstatements is not correct ?(A) All the members exhibit + 3 oxidation state.(B) Because of similar properties the separation of
lanthanoids is not easy.(C) Availability of 4f electrons results in the
formation of compounds in + 4 state for all themembers of the series.
(D) There is a gradual decrease in the radii of themembers with increasing atomic number in theseries.
48. A 5·2 molal aqueous solution of methyl alcohol,CH3OH, is supplied. What is the mole fraction ofmethyl alcohol in the solution ?(A) 0·190 (B) 0·086(C) 0·050 (D) 0·100
49. Which of the following statement is wrong ?(A) Nitrogen cannot form dπ – pπ bond(B) Single N–N bond is weaker than the single P–P
bond(C) N2O4 has two resonance structures.
(D) The stability of hydrides increases form NH3 toBiH3 in group 15 of the periodic table.
50. The outer electronic configuration of Gd (AtomicNo : 64) is—(A) 4f 8 5d° 6s2 (B) 4f 4 5d4 6s2
(C) 4f 7 5d1 6s2 (D) 4f 3 5d5 6s2
51. Which of the following statements regarding sulphuris incorrect ?(A) The vapour at 200°C consists mostly of S8 rings.
(B) At 600°C the gas mainly consists of S2
molecules.(C) The oxidation state of sulphur is never less than
+ 4 in its compounds.(D) S2 molecule is paramagnetic.
52. The structure of IF7 is—
(A) Trigonal bipyramid(B) Octahedral(C) Pentagonal bipyramid(D) Square pyramid
53. Ozonolysis of an organic compound givesformaldehyde as one of the products. This confirmsthe presence of—(A) A vinyl group(B) An isopropyl group(C) An acetylenic triple bond(D) Two ethylenic double bonds
54. A gas absorbs a photon of 355 nm and emits at twowavelengths. If one of the emissions is at 680 nm,the other is at—(A) 325 nm (B) 743 nm(C) 518 nm (D) 1035 nm
55. Silver Mirror test is given by which one of thefollowing compounds ?
(A) Acetone (B) Formaldehyde
(C) Benzophenone (D) Acetaldehyde
56. Which of the following reagents may be used todistinguish between phenol and benzoic acid ?
(A) Tollen’s reagent (B) Molisch reagent
(C) Neutral FeCl3 (D) Aqueous NaOH
57. Phenol is heated with a solution of mixture of KBrand KBrO3. The major product obtained in the abovereaction is—
(A) 3-Bromophenol
(B) 4-Bromophenol
(C) 2, 4, 6–Tribromophenol
(D) 2-Bromophenol
58. In a face centred cubic lattice, atom A occupies thecorner positions and atom B occupies the face centrepositions. If one atom of B is missing from one of theface centred points, the formula of the compoundis—(A) AB2 (B) A2B3
(C) A2B5 (D) A2B
CBSE All India Engineering EntranceExam. B.E./B.Tech.
Publisher : Upkar Prakashan ISBN : 9789350132272Author : Dr. H. P. Sharma,Yash Srivastava and Dr.N.K. Singh
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