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NTA CUET Mathematics With Fully Solved 2023 Papers by Pearson

by Prakash Gupta, Prashant Jain

April 2024

Intermediate to advanced

432 pages

16h 41m

English

Pearson India

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CUET Mathematics (UG) 2022
RelationsOrdered Pair Cartesian Product Relation Domain and Range of a Relation Types of Relations FunctionDefinition Algebraic Operations on Functions Methods of Determining Range Classification of Functions One-one Function Many-one Function Onto Function Into Function Equal or Identical Functions Composite Function Properties of Composite Functions Odd and Even Functions Properties of Even/Odd Function Periodic Functions Properties of Periodic Functions Inverse of a Function Properties of Inverse Function Inverse Trigonometry Functions Introduction Property 1: T(T −1) Property 2: T −1(T)Property 3: ‘−x’Property 4: ‘π/2’Interconversion and Simplification Identities on Addition and SubtractionTest Your Knowledge Answer Key Hints and Explanations
Fundamental Theorems on LimitsIndeterminate FormsMethods of RemovingIndeterminacy Factorisation MethodRationalisation Method Standard LimitsUse of Substitution in Solving Limit Problems Limits Using Expansion Limit when x → ∞Limits of form 1∞, 0°, ∞°Sandwich Theorem or Squeeze Play TheoremContinuity and DerivabilityTheorems on ContinuityContinuity of Composite FunctionsContinuity in an IntervalIntermediate Value TheoremDifferentiability of a Function at a PointConcept of Tangent and its Association with DerivabilityRelation Between Differentiability and ContinuityDifferentiability Over an IntervalProblems of Finding Functions Satisfying Given ConditionsTest Your Knowledge Answer Key Hints and Explanations
Tangent and NormalGeometrical Meaning of dy/dxEquation of Tangent and NormalTangent and Normal from an External PointLengths of Tangent, Normal, Subtangent and SubnormalDerivative as Rate of ChangeError and ApproximationMonotonicity of a FunctionApplication of Differentiation for Detecting Monotonicity Monotonicity of Function About a PointTest for Increasing and Decreasing Functions About a PointGlobal MaximumLocal MaximaGlobal MinimumLocal MinimaExtremaMaxima, Minima for Differentiable FunctionsStationary PointsFirst Derivative TestMaxima, Minima for Continuous FunctionsCritical PointsGlobal Extrema for Continuous FunctionsMaxima, Minima by Higher Order DerivativesSecond Derivative TestApplication of Maxima, MinimaUseful Formulae of Mensuration to RememberRolle’s TheoremAlgebraic Interpretation of Rolle’s TheoremLagrange’s Mean Value Theorem (LMVT)Geometrical Interpretation of LMVTTest Your KnowledgeAnswer Key Hints and Explanations

IndefiniteStandard FormulaeTheorems on Integration Integration by SubstitutionIntegration by Parts Integration of Rational Algebraic Functions by Using Partial FractionsIntegration of Trigonometric FunctionsDefiniteNewton-Leibnitz FormulaProperties of Definite IntegrationEstimation of IntegralsLeibnitz TheoremDefinite Integral as a Limit of SumWalli’s Formula Test Your KnowledgeAnswer Key Hints and Explanations
Area Under the Curve Test Your Knowledge Answer Key Hints and Explanations
Introduction Order and Degree of a Differential EquationFormation of Differential Equation Solving a Differential EquationSolution Methods of First Order and First Degree Differential Equations Exact Differential EquationGeometrical Application of Differential EquationTest Your KnowledgeAnswer Key Hints and Explanations
DefinitionType of MatricesMultiplication of Matrix by Scalar Addition of MatricesSubtraction of MatricesProperties of Addition and Scalar MultiplicationMultiplication of Matrices Properties of Matrix Multiplication Transpose of a MatrixSymmetric and Skew-symmetric MatrixSubmatrixCofactor Matrix and Adjoint MatrixProperties of Cofactor A and adj AInverse of a Matrix (Reciprocal Matrix)Characteristic Polynomial and Characteristic Equation Cayley-Hamilton TheoremTest Your KnowledgeAnswer Key Hints and Explanations
Vectors and their RepresentationZero VectorUnit VectorEqual VectorsCollinear VectorsCoplanar VectorsMultiplication of a Vector by aScalarAddition of VectorsPosition Vector of a PointDistance FormulaSection FormulaDistance FormulaDistance of a Point P from Coordinate AxesCentroid of a TriangleIncentre of Triangle ABCDirection Cosines and Direction RatiosScalar Product (Dot Product) of Two VectorsGeometrical Interpretation of Scalar Product Properties of Dot ProductVector Product (Cross Product) of Two VectorsScalar Triple Product (Box Product) (S.T.P.)Volume of Parallelopiped/Tetrahedron and their PropertiesVector Triple ProductLinear CombinationsTest of CollinearityTest of CoplanarityTest Your KnowledgeAnswer Key Hints and Explanations
A LineEquation of a LineFoot, Reflection, Length of Perpendicular from a Point to a LineAngle Between Two LineSkew LinesShortest Distance Between Two LinesA PlaneEquation of a PlanePosition of Point with Respect to PlaneA Plane and a PointAngle Between Two PlanesDistance Between Parallel PlanesAngle BisectorsFamily of PlanesAngle Between a Plane and a LineCondition for a Line to Lie in a PlaneNon-symmetrical Form of LineTest Your Knowledge Answer Key Hints and Explanations
Important TerminologiesClassical (A Priori) Definition of Probability Addition Theorem of Probability De Morgan’s LawsDistributive LawsConditional Probability Independent and DependentEvents Independency of Three or More EventsTotal Probability Theorem Bayes’ Theorem Binomial Probability Theorem Probability Distribution Expectation Statistics Measures of Central TendencyMean (Arithmetic Mean)Properties of Arithmetic MeanGeometric MeanMedianHarmonic MeanModeMeasure of DispersionArithmetic MeanMedianTest Your KnowledgeAnswer Key Hints and Explanations
OverviewAn Optimisation ProblemA Linear Programming Problem (LPP)Objective FunctionDecision VariablesConstraints Feasible RegionFeasible SolutionsInfeasible SolutionsOptimal (Feasible) SolutionCorner Point Method for Solving LPPMultiple Optimal PointsTest Your KnowledgeAnswer Key Hints and Explanations
Modular ArithmeticModulo OperatorProperties of Modulo OperatorAddition Modulo mSubtraction Modulo m Multiplication Modulo m Congruence ModuloEquivalence ClassSimple Arithmetic FunctionsTypes of Simple Arithmetic FunctionEuler’s Totient Function or Euler’s Phi FunctionProperties of Euler’s Totient FunctionNumber of Divisor Function τ(n)Divisor Sum Function σ(n)Alligation and MixtureMixtureAlligationMean PriceRule of AlligationBoats and Streams Upstream and DownstreamPipes and CisternsRaces and GamesTerms Related to Races and GamesPartnershipNumerical InequalitiesRelationship between AM and GMRules for Operations on InequalitiesPropertiesTest Your KnowledgeAnswer Key Hints and Explanations
Inferential StatisticsPopulation and SampleSamplingSimple Random SamplingSystematic Random SamplingRepresentative and Unrepresentative SampleUnbiased and Biased Sampling Unbiased SamplingBiased Sampling Types of Biasness Sampling Errors Parameter and StatisticsStatistical Significance and Sampling DistributionSampling DistributionCentral Limit Theorem (CLT)Confidence Interval (CI)Test (A Test of Difference for Parametric Data) Standard Error of Mean (σM)Degrees of FreedomOne Sample t-testIndex Numbers Time-based Data Index NumberConstruction of Index NumberRelative Index NumberSimple (Unweighted) Aggregative MethodWeighted Aggregative MethodLaspeyres’ Index Paasche IndexFisher’s Ideal MethodMarshall-Edgeworth’s MethodWeighted Average of Relatives Types of Index NumbersIndex SeriesTest of Adequacy of Index NumbersUnit TestTime-reversal TestTime SeriesTime Series Analysis Trend Analysis by Fitting Linear Trend LinePerpetuitySinking FundValuation of BondsBondCalculation of EMI or Amortization of LoansMeaning of EMI Methods of Calculation of EMI or InstalmentNominal and Effective Rate of InterestCompound Annual Growth RateMeaning of Compound Annual Growth Rate Formula for Calculation of CAGR Stock, Shares and Debentures: Important Facts and FormulaeFeatures of Equity Shares Features of DebenturesDepreciationMethods of Computing the Annual Depreciation Linear or Straight Line MethodTest Your KnowledgeAnswer Key Hints and Explanations

Content preview from NTA CUET Mathematics With Fully Solved 2023 Papers by Pearson

CHAPTER 6 Differential Equations

CHAPTER AT A GLANCE

Introduction

An equation involving independent and dependent variables and the derivatives of the dependent variables is called a differential equation. There are two kinds of differential equations:

Ordinary Differential Equation: If the dependent variables depend on one independent variable x, then the differential equation is said to be ordinary.
For example, + = y + z,

+ xy = sin ...