This book has been designed for the students preparing for IIT JEE, AIEEE and various other National and Regional Engineering Entrance Examinations such as BITSAT, VITEE, SMU, BVP etc. This book contains questions and solutions of Mathematics asked in various engineering entrance examinations up to 2013. The book has been divided into 2 parts containing 30 Chapters in total. The book has been divided in sync with Class XI and XII NCERT Mathematics Textbooks. The previous years objective questions have been given Chapterwise and Topicwise. Answers to the questions along with their explanations have been given at the end of each chapter. Questions asked in 2011, 2012 and 2013 engineering entrances have been given separately at the end of the book to make students aware about the current trend of the examinations.
Table of Contents :-
Sets, Relations and FunctionsTypes of Sets, Operation and Cartesian ProductRelation, Equivalence RelationTypes of MappingDomain-Range, Odd-Even and Periodic FunctionInverse, Composition and Different Types of FunctionsComplex NumbersAlgebraic Operations and Equality of Complex NumbersConjugate, Modulus and ArgumentDe-Moivre's Theorem, Square Root and Roots of UnityApplications in GeometryEquations and InequalitiesSurds and IndicesLogarithm and Its PropertiesRelation between Roots and CoefficientsSolution of Equations, Nature of RootsCondition for Common Roots, Quadratic Expressions and Position of RootsTypes of Partial FractionsSolution of InequalitiesSequences and SeriesArithmetic Progression and Its MeanGeometric Progression and Its MeanHarmonic Progression and Its MeanRelation between AP, GP and HPArithmetic - Geometric ProgressionSpecial Series, Sum to Terms and Infinite Number of TermsLogarithmic SeriesExponential SeriesPermutations and CombinationsNumber of Permutations, Conditional PermutationsCircular PermutationsNumber of Combinations, Division into Groups and DearrangementsUsed in Geometrical ProblemBinomial Theorem and Mathematical InductionExpansion of Binomial Theorem and General TermIndependent Term, Middle Termand Greatest TermProperties of Binomial CoefficientsMultinomial TheoremMathematical InductionMatrices and DeterminantsAlgebra of Matrices, Types of MatricesProperties and Solution of DeterminantsTranspose, Adjoint and Inverse of MatricesSystem of Linear Equations, Rank of MatricesTrigonometric Identities and EquationsTrigonometrical Ratios of Allied Angles and Basic FundamentalTrigonometrical Ratios of Sum and Difference of Two and Three AnglesTrigonometrical Ratios of Multiple and Submultiple AnglesMaximum-Minimum Values and Conditional Trigonometrical IdentitiesHyperbolic FunctionsSolution of Trigonometrical EquationsInverse Trigonometric FunctionsSolutions of Inverse Trigonometrical FunctionsProperties of TriangleRelation between Sides and AnglesCircle Connected with Triangle
Heights and Distances
Rectangular Cartesian CoordinatesSystem of Coordinates and Distance between PointsOrthocentre, Circumcentre and IncentreArea of Some Geometrical FigureTransformation of Axes and LocusStraight Line and Pair of Straight LinesEquation of Line and Pair of LinesDistance between Lines and Foot of PerpendicularAngle between Intersection Lines, Condition for Parallel andPerpendicular LinesPosition of a Point, Bisectors of the LinesCircle and System of CirclesCircle and Its EquationsTangent and Normal to a CircleChord of Contact of Tangent, Pole and PolarSystem of CirclesConic SectionBasic Terms of ConicsEquation of Conics and Intersection of Two CurvesTangent and Normal of ConicChord of Contact, Pole and Polar, Director CircleDiameter, Auxiliary Circle and AsymptotesLimits, Continuity and DifferentiabilityLimits of Algebraic, Exponential and Logarithmic FunctionsLimits of Trigonometric Functions and SeriesContinuityDifferentiationDifferentiabilityDifferentiation of Algebraic and Transcendental FunctionsDifferentiation by Substitution, Higher Order DerivativesPartial DerivativeApplications of DerivativesRate of Measure and Application in MechanicsTangent and Normal, Maxima and MinimaIncreasing and Decreasing Functions, Rolle's and Mean Value TheoremsIndefinite IntegralsFundamental of Indefinite IntegralsIntegration by Substitution, Parts, Partial FractionsDefinite IntegralsFundamental of Definite IntegrationDefinite Integration by Substitution, Parts, Partial FractionsProperties and Summation of Series of Definite IntegrationDefinite Integration by Gamma Function Leibnitz Rule,Walli's FormulaApplications of IntegralsArea of Bounded RegionVolume and Surface Area of SolidsDifferential EquationsOrder and Degree, Formation of Differential EquationVariable Separable MethodHomogeneous Differential EquationLinear Differential EquationApplication of Differential Equations, Some Standard Results of SolutionsVector AlgebraAlgebra and Modulus of VectorsScalar or Dot Product of Two Vectors and Its ApplicationsVector or Cross Product of Two Vectors and Its ApplicationsScalar Triple Product and Its ApplicationsVector Triple Product and Its ApplicationsApplications of Vector in GeometryThree Dimensional GeometrySystem of Coordinates, Direction Cosines, Direction Ratios and ProjectionLinePlaneLine and PlaneSphereStatisticsMean, Median and ModeMeasure of DispersionCorrelation and Rank CorrelationRegressionProbabilitySimple Problems on ProbabilityOdds in Favour and Against, Use of Permutations and CombinationsAddition Theorem, Conditional Probability and Baye's TheoremBinomial Poisson and Probability DistributionsMathematical Logic and Boolean AlgebraMathematical LogicBoolean AlgebraLinear Programming
Statics and DynamicsVelocity and Acceleration, Relative VelocitiesRectilinear motion with Acceleration, Motion Under Gravity and Laws of MotionProjectiles, Momentum, Energy and Direct Impact of Smooth BodiesBasic Laws of Mechanics, Composition and Equilibrium of ForcesComposition of Coplanar, Concurrent and Parallel Forces, Lami's TheoremMoment, Couple and FrictionMiscellaneousNumber TheoryBinary NumberNumerical MethodGroup TheoryPrevious Year Questions 2011Questions Asked in 2012Questions Asked in 2013