book

NTA CUET Mathematics With Fully Solved 2023 Papers by Pearson

Name: NTA CUET Mathematics With Fully Solved 2023 Papers by Pearson
ISBN: 9788196874308

by Prakash Gupta, Prashant Jain

April 2024

Intermediate to advanced

432 pages

16h 41m

English

Pearson India

Read now

Unlock full access

Cover
Title Page
Contents
Preface
Acknowledgement
About the Authors
Memory-based Paper CUET Mathematics (UG) 2023
CUET Mathematics (UG) 2022
Chapter 1 Sets, Relations and Functions
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
Chapter 2 Limits Continuity and Differentiability
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
Chapter 3 Differentiation and its Application
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

Chapter 4 Integration
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
Chapter 5 Application of Integrals
Area Under the Curve Test Your Knowledge Answer Key Hints and Explanations
Chapter 6 Differential Equations
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
Chapter 7 Matrices
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
Chapter 8 Vectors
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
Chapter 9 Three Dimensional Geometry
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
Chapter 10 Probability and Statistics
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
Chapter 11 Linear Programming
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
Chapter 12 Numbers, Quantification and Numerical Application
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
Chapter 13 Financial Mathematics
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
Copyright

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

CHAPTER 7 Matrices

CHAPTER AT A GLANCE

Definition

Any rectangular arrangement of numbers (real or complex) (or of real-valued or complex-valued expressions) is called a matrix. If a matrix has m rows and n columns then the order of the matrix is written as m × n and we call it as order m by n.

The general m × n matrix is:

A =

where a_ij denote the element of i^th row and j^th column. The above matrix is usually denoted as [a_ij]_m _× _n.

Notes:

The elements a₁₁, a₂₂, a₃₃, … are called as diagonal elements. Their sum is called trace of A denoted as tr(A)
Capital letters of English alphabets are used to denote matrices.
Order of a matrix: If ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.

Read now

Unlock full access

More than 5,000 organizations count on O’Reilly

O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.

Julian F.

Head of Cybersecurity

I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.

Addison B.

Field Engineer

I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.

Amir M.

Data Platform Tech Lead

I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.

Mark W.

Embedded Software Engineer

NTA CUET- UG 2024 Physics | Fully solved 2023 paper | Chapterwise summed pointers for revision | Digital Question Bank & Mock Tests

Prashant Jain, Ajit Lulla

What Successful Brick-and-Mortar Retailers Get Right

Publisher Resources

ISBN: 9788196874308

Cloud Computing

Data Engineering

Data Science

AI & ML

Programming Languages

Software Architecture

IT/Ops

Security

Design

Business

Soft Skills

NTA CUET Mathematics With Fully Solved 2023 Papers by Pearson

by Prakash Gupta, Prashant Jain

CHAPTER 7