Complete Companion for IIT JEE Main Part 2 Volume II

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Cover Half Title Title Copy Right Contents Preface Mathematics Trend Analysis (2011 To 2019) JEE MAINS 2019 PAPER Chapter 1 Functions FUNCTION OR MAPPING FEATURES OF A MAPPING F : X → Y VALUE OF A FUNCTION DOMAIN AND RANGE OF A FUNCTION INTERVALS IN R METHOD TO FIND THE DOMAIN OF A FUNCTION METHOD TO FIND THE RANGE OF A FUNCTION TYPES OF FUNCTIONS METHOD TO CHECK WHETHER THEFUNCTION F : X → Y IS ONE–ONE ORMANY-ONE ONTO OR SURJECTIVE FUNCTION METHOD TO CHECK WHETHER THEFUNCTION f : X → Y IS ONTO OR INTO BIJECTIVE FUNCTION SOME IMPORTANT FUNCTIONS IDENTITY FUNCTION MODULUS FUNCTION OR ABSOLUTE VALUEFUNCTION GREATEST INTEGER FUNCTION/STEPFUNCTION/FLOOR FUNCTION LEAST INTEGER FUNCTION/CEILINGFUNCTION FRACTIONAL-PART FUNCTION SIGNUM FUNCTION RECIPROCAL FUNCTION EXPONENTIAL FUNCTION LOGARITHMIC FUNCTION POLYNOMIAL FUNCTION RATIONAL FUNCTION TRIGONOMETRIC FUNCTIONS INVERSE TRIGONOMETRIC FUNCTIONS TWO WAYS OF DEFINING A FUNCTION EXPLICIT AND IMPLICIT FUNCTIONS OPERATIONS ON FUNCTIONS COMPOSITION OF FUNCTIONS PROPERTIES OF COMPOSITE FUNCTIONS INVERSE FUNCTIONS METHOD TO FIND THE INVERSE OF AFUNCTION PROPERTIES OF INVERSE FUNCTIONS ODD AND EVEN FUNCTIONS PROPERTIES OF ODD AND EVEN FUNCTIONS PERIODIC FUNCTION SHORT-CUT METHOD TO CHECK THEPERIODICITY OF A FUNCTION NCERT EXEMPLARS PRACTICE EXERCISES Chapter 2 Matrices MATRIX TYPES OF MATRICES ALGEBRA OF MATRICES SYMMETRIC MATRIX ORTHOGONAL MATRIX IDEMPOTENT MATRIX INVOLUTORY MATRIX NILPOTENT MATRIX SINGULAR MATRIX NCERT EXEMPLARS PRACTICE EXERCISES Chapter 3 Determinants DETERMINANTS MINORS AND COFACTORS EXPANSION OF A DETERMINANT OF ORDERTHREE PROPERTIES OF DETERMINANTS EVALUATION OF DETERMINANTS USINGELEMENTARY OPERATIONS PRODUCT OF DETERMINANTS OF SAMEORDER SOLUTION OF LINEAR EQUATIONS BYDETERMINANTS NCERT EXEMPLARS PRACTICE EXERCISES Chapter 4 Continuity and Differentiability CONTINUITY DISCONTINUITY OF A FUNCTION GEOMETRICAL MEANING OF CONTINUITY NCERT EXEMPLARS PRACTICE EXERCISES Chapter 5 Differentiation DERIVATIVE OF A FUNCTION DERIVATIVE AT A POINT STANDARD DERIVATIVES RULES FOR DIFFERENTIATION DERIVATIVE OF PARAMETRIC FUNCTIONS DERIVATIVE OF IMPLICIT FUNCTIONS DIFFERENTIATION OF A FUNCTION WITHRESPECT TO ANOTHER FUNCTION LOGARITHMIC DIFFERENTIATION SUCCESSIVE DIFFERENTIATION NCERT EXEMPLARS PRACTICE EXERCISES Chapter 6 Applications of Derivatives TANGENTS AND NORMALS SLOPE OF TANGENT EQUATION OF TANGENT SLOPE OF NORMAL EQUATION OF NORMAL ANGLE OF INTERSECTION OF TWO CURVES LENGTH OF TANGENT, LENGTH OF NORMAL,SUB-TANGENT AND SUBNORMAL LENGTH OF INTERCEPT MADE ON AXESBY THE TANGENT LENGTH OF PERPENDICULAR FROM ORIGINTO THE TANGENT INCREASING AND DECREASING FUNCTIONS(MONOTONICITY) TEST FOR MONOTONICITY OF FUNCTIONS MAXIMA AND MINIMA OF FUNCTIONS METHOD TO DETERMINE THE POINTSOF LOCAL MAXIMA AND LOCALMINIMA GREATEST AND LEAST VALUES OFA FUNCTION IN A CLOSED INTERVAL(ABSOLUTE MAXIMUM ANDABSOLUTE MINIMUM) CONCAVITY AND CONVEXITYOF A FUNCTION POINT OF INFLEXION ROLLE’S AND LAGRANGE’S MEAN VALUETHEOREM LAGRANGE’S MEAN VALUE THEOREM APPLICATION OF dy/dxAS A RATE MEASURE NCERT EXEMPLARS PRACTICE EXERCISES Chater 7 Indefinite Integration INDEFINITE INTEGRAL PROPERTIES OF INDEFINITE INTEGRATION STANDARD FORMULAE OF INTEGRATION METHODS OF INTEGRATION SOME USEFUL TRIGONOMETRIC IDENTITIES METHOD OF SUBSTITUTION METHOD OF INTEGRATION BY PARTS METHOD OF PARTIAL FRACTIONS FORRATIONAL FUNCTIONS SOME SPECIAL INTEGRALS REDUCTION FORMULA SOME USEFUL REDUCTION FORMULAE NCERT EXEMPLARS PRACTICE EXERCISES Chapter 8 Definite Integral and Area DEFINITE INTEGRAL FUNDAMENTAL THEOREM OF INTEGRALCALCULUS DIFFERENTIATION UNDER INTEGRAL SIGN INTEGRATION OF MOD FUNCTIONS AREA OF PLANE REGIONS CURVE TRACING NCERT EXEMPLARS PRACTICE EXERCISES Chapter 9 Three Dimensional Geometry ORIGIN COORDINATE AXES DISTANCE FORMULA DISTANCE OF A POINT FROM COODINATEAXES VECTOR FORM DIRECTION COSINES ANGLE BETWEEN TWO LINES PROJECTION VECTOR FORM STRAIGHT LINE ANGLE BETWEEN TWO LINES INTERSECTION OF TWO LINES PERPENDICULAR FROM A POINT TO A LINE SKEW LINES VECTOR FORM POINT OF INTERSECTION OF A LINE AND APLANE IMAGE OF A POINT IN A PLANE IMAGE OF A LINE ABOUT A PLANE SPHERE EQUATION OF A SPHERE SECTION OF A SPHERE BY A PLANE NCERT EXEMPLARS PRACTICE EXERCISES 10 PROBABILITY EXPERIMENT REMARKS TYPES OF EVENTS PROBABILITY OF OCCURRENCE OF AN EVENT SOME IMPORTANT RESULTS ON PROBABILITY CONDITIONAL PROBABILITY MULTIPLICATION THEOREM OF PROBABILITY LAW OF TOTAL PROBABILITY BAYE’S THEOREM PROBABILITY DISTRIBUTION BINOMIAL DISTRIBUTION MATHEMATICAL EXPECTATION POISSON DISTRIBUTION NCERT EXEMPLARS PRACTICE EXERCISES Chapter 11 Inverse Trigonometric Functions INVERSE FUNCTIONS INVERSE TRIGONOMETRIC FUNCTIONS DOMAIN AND RANGE OF INVERSETRIGONOMETRIC FUNCTIONS GRAPHS OF INVERSE TRIGONOMETRICFUNCTIONS PRINCIPAL VALUES FOR INVERSETRIGONOMETRIC FUNCTIONS PROPERTIES OF INVERSE TRIGONOMETRICFUNCTIONS SOLUTIONS OF BASIC INVERSETRIGONOMETRIC INEQUALITIES SOME USEFUL SUBSTITUTIONS NCERT EXEMPLARS PRACTICE EXERCISES MOCK TEST-I MOCK TEST-II MOCK TEST-III MOCK TEST-IV MOCK TEST-V