Complete Companion For Jee Main 2020 Mathematics Vol 1

Cover
Half Title
Title
Copyright
Contents
Preface
Mathematics Trend Analysis (2011 To 2019)
Chapter 1 Set Theory
	SET
	REPRESENTATION OF A SET
	TYPES OF SETS
	OPERATIONS ON SETS
	ALGEBRA OF SETS
	CARTESIAN PRODUCT OF TWO SETS
	RELATIONS
	TYPES OF RELATIONS ON A SET
	EQUIVALENCE RELATION
	CONGRUENCE MODULO M
	NCERT EXEMPLARS
	PRACTICE EXERCISES
Chapter 2 Complex Numbers
	IMAGINARY NUMBERS
	INTEGRAL POWERS OF i
	COMPLEX NUMBERS
	CONJUGATE OF A COMPLEX NUMBER
	MODULUS OF A COMPLEX NUMBER
	SQUARE ROOTS OF A COMPLEX NUMBER
	ARGAND PLANE AND GEOMETRICAL REPRESENTATION OF COMPLEX NUMBERS
	POLAR FORM OF A COMPLEX NUMBER
	PARTICULAR CASES OF POLAR FORM
	EULERIAN REPRESENTATION OF A COMPLEX NUMBER
	LOGARITHM OF A COMPLEX NUMBER
	VECTORIAL REPRESENTATION OF A COMPLEX NUMBER
	ROOTS OF A COMPLEX NUMBER
	GEOMETRY OF COMPLEX NUMBERS
	PRACTICE EXERCISES
Chapter 3 Quadratic Equations and Expressions
	QUADRATIC EQUATION
	COMMON ROOTS
	SYMMETRIC FUNCTION OF THE ROOTS
	GRAPH OF A QUADRATIC EXPRESSION
	GREATEST AND LEAST VALUES OF AQUADRATIC EXPRESSION
	NATURE OF ROOTS OF A QUADRATICE QUATION WITH RESPECT TO ONE OR TWO REAL NUMBERS
	RELATION BETWEEN ROOTS AND COEFFICIENTS OF A POLYNOMIAL EQUATION
	FORMATION OF A POLYNOMIAL EQUATION FROM GIVEN ROOTS
	SIGN OF A POLYNOMIAL EXPRESSION
	RATIONAL ALGEBRAIC EXPRESSION
	NCERT EXEMPLARS
	PRACTICE EXERCISES
Chapter 4 Permutations and Combinations
	FACTORIAL NOTATION
	FUNDAMENTAL PRINCIPLES OF COUNTING
	PERMUTATION
	COMBINATION
	KEY RESULTS ON COMBINATION
	DERANGEMENT
	EXPONENT OF PRIME p IN n!
	NUMBER OF DIVISORS
	NCERT EXEMPLARS
	PRACTICE EXERCISES
Chapter 5 Mathematical Induction
	MATHEMATICAL INDUCTION
	NCERT EXEMPLARS
	PRACTICE EXERCISES
Chapter 6 Binomial Theorem
	BINOMIAL EXPRESSION
	BINOMIAL THEOREM
	SPECIAL CASES
	PASCAL’S TRIANGLE
	MIDDLE TERM IN THE BINOMIAL EXPANSION
	NCERT EXEMPLARS
	PRACTICE EXERCISES
Chapter 7 Sequence and Series
	SEQUENCE
	SERIES
	PROGRESSIONS
	ARITHMETIC PROGRESSION (A.P.)
	SUM OF n TERMS OF AN A.P.
	PROPERTIES OF A.P.
	ARITHMETIC MEAN (A.M.)
	GEOMETRIC PROGRESSION (G.P.)
	GEOMETRIC MEAN (G.M.)
	SOME SPECIAL SEQUENCES
	ARITHMETICO-GEOMETRIC PROGRESSION (A.G.P.)
	METHOD FOR FINDING SUM OF A.G. SERIES
	NCERT EXEMPLARS
	PRACTICE EXERCISES
Chapter 8 Limits
	LIMIT OF A FUNCTION
	INDETERMINATE FORMS
	ALGEBRA OF LIMITS
	EVALUATION OF LIMITS
	ALGEBRAIC LIMITS
	LIMIT OF AN ALGEBRAIC FUNCTIONWHEN X → ∞
	TRIGONOMETRIC LIMITS
	EXPONENTIAL AND LOGARITHMIC LIMITS
	EVALUATION OF LIMITS USING L’HOSPITAL’S RULE
	PRACTICE EXERCISES
Chapter 9 Differential Equations
	DIFFERENTIAL EQUATION
	LINEAR AND NON-LINEAR DIFFERENTIAL EQUATIONS
	INITIAL VALUE PROBLEMS
	HOMOGENEOUS DIFFERENTIAL EQUATIONS
	SOLUTION BY INSPECTION
	NCERT EXEMPLARS
	PRACTICE EXERCISES
Chapter 10 Coordinates and Straight Lines
	DISTANCE FORMULA
	SECTION FORMULAE
	AREA OF A TRIANGLE
	CONDITION FOR COLLINEARITY OF THREE POINTS
	STAIR METHOD FOR FINDING THE AREA
	AREA OF A QUADRILATERAL
	AREA OF A POLYGON
	STAIR METHOD
	LOCUS
	TRANSLATION OF AXES
	ROTATION OF AXES
	REFLECTION (IMAGE) OF A POINT
	GENERAL EQUATION OF A STRAIGHT LINE
	SLOPE OF A LINE
	INTERCEPT OF A LINE ON THE AXES
	EQUATION OF A STRAIGHT LINE IN VARIOUS FORMS
	REDUCTION OF THE GENERAL EQUATION TO DIFFERENT STANDARD FORMS
	ANGLE BETWEEN TWO INTERSECTING LINES
	CONDITION FOR TWO LINES TO BE COINCIDENT, PARALLEL, PERPENDICULAR OR INTERSECTING
	EQUATION OF A LINE PARALLEL TO A GIVEN LINE
	EQUATION OF A LINE PERPENDICULAR TO A GIVEN LINE
	POINT OF INTERSECTION OF TWO GIVEN LINES
	CONCURRENT LINES
	POSITION OF TWO POINTS RELATIVE TO ALINE
	LENGTH OF PERPENDICULAR FROM A POINTON A LINE
	DISTANCE BETWEEN TWO PARALLEL LINES
	EQUATIONS OF STRAIGHT LINES PASSING THROUGH A GIVEN POINT AND MAKING A GIVEN ANGLE WITH A GIVEN LINE
	REFLECTION ON THE SURFACE
	IMAGE OF A POINT WITH RESPECT TO A LINE
	EQUATIONS OF THE BISECTORS OF THE ANGLES BETWEEN TWO LINES
	EQUATIONS OF LINES PASSING THROUGH THE POINT OF INTERSECTION OF TWO GIVEN LINES
	STANDARD POINTS OF A TRIANGLE
	ORTHOCENTRE
	COORDINATES OF NINE POINT CIRCLE
	NCERT EXEMPLARS
	PRACTICE EXERCISES
Chapter 11 Circles
	CIRCLE
	STANDARD EQUATION OF A CIRCLE
	GENERAL EQUATION OF A CIRCLE
	CONDITIONS FOR AN EQUATION TO REPRESENT A CIRCLE
	EQUATION OF A CIRCLE IN SOME SPECIALCASES
	EQUATION OF A CIRCLE IN DIAMETER FORM
	INTERCEPTS MADE BY A CIRCLEON THE AXES
	PARAMETRIC EQUATIONS OF A CIRCLE
	POSITION OF A POINT WITH RESPECTTO A CIRCLE
	CIRCLE THROUGH THREE POINTS
	INTERSECTION OF A LINE AND A CIRCLE
	LENGTH OF INTERCEPT MADE BY A CIRCLEON A LINE
	THE LEAST AND GREATEST DISTANCE OF APOINT FROM A CIRCLE
	CONTACT OF TWO CIRCLES
	TANGENT TO A CIRCLE AT A GIVEN POINT
	EQUATION OF THE TANGENT IN SLOPE FORM
	CONDITION OF TANGENCY
	TANGENTS FROM A POINT OUT SIDE THE CIRCLE
	LENGTH OF THE TANGENT FROM A POINT TOA CIRCLE
	NORMAL TO THE CIRCLE AT A GIVEN PO
	PAIR OF TANGENTS
	COMMON TANGENTS TO TWO CIRCLES
	POWER OF A POINT WITH RESPECT TO A CIRCLE
	DIRECTOR CIRCLE
	EQUATION OF CHORD OF CONTACT
	EQUATION OF CHORD IF ITS MID POINTIS KNOWN
	COMMON CHORD OF TWO CIRCLES
	DIAMETER OF A CIRCLE
	ANGLE OF INTERSECTION OF TWO CIRCLES
	ORTHOGONAL INTERSECTION OF TWO CIRCLES
	FAMILY OF CIRCLES
	IMAGE OF THE CIRCLE BY THE LINE MIRROR
	PRACTICE EXERCISES
Chapter 12 Conic Sections (Parabola, Ellipse and Hyperbola)
	CONIC SECTION
	IMPORTANT TERMS
	SECTION OF A RIGHT CIRCULAR CONE BYDIFFERENT PLANES
	EQUATION OF CONIC
	GENERAL EQUATION
	CENTRE OF CONIC
	PARABOLA
	SOME TERMS RELATED TO PARABOLA
	INTERSECTION OF A LINE AND A PARABOLA
	EQUATION OF A CHORD
	POINT OF INTERSECTION OF TANGENTS
	POSITION OF A POINT WITH RESPECT TO APARABOLA
	NUMBER OF TANGENTS DRAWN FROM APOINT TO A PARABOLA
	EQUATION OF THE PAIR OF TANGENTS
	EQUATIONS OF NORMAL IN DIFFERENT FORMS
	POINT OF INTERSECTION OF NORMALS
	CO-NORMAL POINTS
	CHORD OF CONTACT
	CHORD WITH A GIVEN MID POINT
	ELLIPSE
	POSITION OF A POINT WITH RESPECT TO ANELLIPSE
	EQUATION OF NORMAL IN DIFFERENT FORMS
	EQUATION OF THE PAIR OF TANGENTS
	CHORD WITH A GIVEN MID POINT
	OPTICAL PROPERTY OF PARABOLA
	EQUATION OF A HYPERBOLA IN STANDARD FORM
	SOME TERMS AND PROPERTIES RELATED TO A HYPERBOLA
	CONJUGATE HYPERBOLA
	POSITION OF A POINT WITH RESPECT TO A HYPERBOLA
	EQUATION OF THE PAIR OF TANGENTS
	CHORD WITH A GIVEN MID POINT
	CHORD OF CONTACT
	NCERT EXEMPLARS
	PRACTICE EXERCISES
Chapter 13 Vector Algebra
	SCALARS AND VECTORS
	REPRESENTATION OF VECTORS
	TYPES OF VECTORS
	EQUAL VECTORS
	FIXED VECTORS
	FREE VECTORS
	ANGLE BETWEEN TWO VECTORS
	ADDITION (SUM OR RESULTANT) OF TWO VECTORS
	POSITION VECTOR
	COMPONENT OF A VECTOR
	LINEAR COMBINATION
	LINEARLY DEPENDENT AND INDEPENDENT SYSTEM OF VECTORS
	COLLINEARITY OF THREE POINTS
	COPLANARITY OF FOUR POINTS
	SOME RESULTS ON LINEARLY DEPENDENTAND INDEPENDENT VECTORS
	PRODUCT OF TWO VECTORS
	SCALAR PRODUCT OF TWO VECTORS
	SOME USEFUL IDENTITIES
	WORK DONE BY A FORCE
	VECTOR PRODUCT OF TWO VECTORS
	MOMENT OF A FORCE ABOUT A POINT
	SCALAR TRIPLE PRODUCT
	NCERT EXEMPLARS
	PRACTICE EXERCISES
Chapter 14 Measures of Central Tendency and Dispersion
	MEASURES OF CENTRAL TENDENCY
	ARITHMETIC MEAN
	GEOMETRIC MEAN
	HARMONIC MEAN
	MEDIAN
	QUARTILES, DECILES AND PERCENTILES
	MODE
	SYMMETRIC DISTRIBUTION
	PRACTICE EXERCISES
Chapter 15 Trigonometric Ratios and ldentities
	ANGLE
	MEASUREMENT OF ANGLES
	RELATION BETWEEN DIFFERENT SYSTEMS OFMEASUREMENT OF ANGLES
	RELATION BETWEEN SIDES AND INTERIORANGLES OF A REGULAR POLYGON
	FUNDAMENTAL TRIGONOMETRICIDENTITIES
	SIGNS OF TRIGONOMETRIC RATIOS INDIFFERENT QUADRANTS
	INCREASE AND DECREASE OF TRIGONOMETRIC FUNCTIONS
	DOMAIN AND RANGE OF TRIGONOMETRICRATIOS
	TRIGONOMETRIC RATIOS OF STANDARDANGLES
	TRIGONOMETRIC RATIOS FOR SOME SPECIAL ANGLES
	TRIGONOMETRIC RATIOS OF ALLIED ANGLES
	TABLE FOR TRIGONOMETRIC RATIOS OF ALLIED ANGLES
	TRIGONOMETRIC RATIOS IN TERMS OF EACH OTHER
	ADDITION AND SUBTRACTION FORMULAE
	TRANSFORMATION FORMULAE
	PRODUCT INTO SUM OR DIFFEREN
	SUM AND DIFFERENCE INTO PRODUCT
	TRIGONOMETRIC RATIOS OF MULTIPLE ANGLES
	TRIGONOMETRIC RATIOS OFSUBMULTIPLE ANGLES
	GREATEST AND LEAST VALUES OF THE EXPRESSION
	CONDITIONAL IDENTITIES
	GRAPHS OF TRIGONOMETRIC FUNCTIONS
	PRACTICE EXERCISES
Chapter 16 Trigonometric Equations
	TRIGONOMETRIC EQUATION
	SOLUTION OR ROOT OF A TRIGONOMETRIC EQUATION
	METHOD FOR FINDING PRINCIPAL VALUE (SOLUTION)
	SOLUTION OF AN EQUATION OF THE FORM
	SOLUTIONS OF BASIC TRIGONOMETRIC INEQUALITIES
	NCERT EXEMPLARS
	PRACTICE EXERCISES
Chapter 17 Heights and Distances
	SOME TERMINOLOGY RELATED TO HEIGHT AND DISTANCE
	NORTH EAST
	BEARINGS OF A POINT
	SOME PROPERTIES RELATED TO TRIANGLE
	SOME PROPERTIES RELATED TO CIRCLE
	SOME IMPORTANT RESULTS
	PRACTICE EXERCISES
Chapter 18 Mathematical Reasoning
	MATHEMATICAL REASONING
	STATEMENT
	THE CONNECTING WORD ‘OR’
	QUANTIFIERS
	IMPLICATIONS
	NCERT EXEMPLARS
	PRACTICE EXERCISES