2021

Sem -1 Solutions Polytechnic Engineering Maths

Sem -1 Solutions – Polytechnic Engineering Mathematics

Sem -1 Solutions

Polytechnic Engineering Mathematics – Sem -1 Solutions

Sem -1 Solutions

Education is the acquisition of knowledge, skill value, etc.    
Education contributes to the development of society.
www.basicsinmaths.com website has been given material for mathematics Polytechnic Students.

Polytechnic Engineering Mathematics – Sem -1 Solutions solutions in PDF Files are designed by the ‘Basics In Maths” Team. These Pdf Files are very useful for students who are prepared for polytechnic examinations.


TRANSFORMATIONS

Transformations  PDF File is designed by the ‘Basics In Maths” Team. This Pdf File is very useful for students who are prepared for polytechnic examinations.

PART – 1

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PART – 2

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INVERSE TRIGONOMETRIC FUNCTIONS

The inverse trigonometric functions solutions  PDF File is designed by the ‘Basics In Maths” Team. This Pdf File is very useful for students who are prepared for polytechnic examinations.

 

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SOLUTIONS OF SIMULTANEOUS EQUATIONS

Solutions of simultaneous equations  PDF File is designed by the ‘Basics In Maths” Team. This Pdf File is very useful for students who are prepared for polytechnic examinations.

 

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SOLUTIONS OF TRIANGLES

 

Solutions of triangles  PDF File is designed by the ‘Basics In Maths” Team. This Pdf File is very useful for students who are prepared for polytechnic examinations.

 

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Sem - 2 Concept Polytechnic Engineering Mathematics Feature Image for Sem 2 Concept

Sem – 2 Concept – Engineering Mathematics

Sem – 2 Concept – Engineering Mathematics

Sem – 2 Concept

Education is the acquisition of knowledge, skill value, etc.    
Education contributes to the development of society.
www.basicsinmaths.com website has been given material for math Polytechnic Students.

Engineering Maths  Sem – 2 Concept solutions in PDF Files are designed by the ‘Basics In Maths” Team. These Pdf Files are very useful for students who are prepared for polytechnic examinations.

TS 6th Class Maths Concept


Polytechnic-Engineering Mathematics -SEM-2-Concept.pdf

 

 

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Sem -2 Solutions Polytechnic Engineering Maths Feature Image for Sem 2 solutions

Sem -2 Solutions – Polytechnic Engineering Mathematics

Sem -2 Solutions – Polytechnic Engineering Mathematics

Sem -2 Solutions

Education is the acquisition of knowledge, skill value, etc.    
Education contributes to the development of society.
www.basicsinmaths.com website has been given material for mathematics Polytechnic Students.

Polytechnic Engineering Mathematics – Sem -2 Solutions in PDF Files are designed by the ‘Basics In Maths” Team. These Pdf Files are very useful for students who are prepared for polytechnic examinations.


Tangents and Normals

Tangents and Normals solutions  PDF File is designed by the ‘Basics In Maths” Team. This Pdf File is very useful for students who are prepared for polytechnic examinations.

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Maxima and Minima

The Maxima and Minim solutions  PDF File is designed by the ‘Basics In Maths” Team. This Pdf File is very useful for students who are prepared for polytechnic examinations.

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TS Inter Practice Papers 2021

TS Inter Maths 1A &1B Practice papers (Reduced Syllabus)

TS Inter Maths 1A &1B Practice papers (Reduced Syllabus)

 

TS Inter Maths 1A and 1B Practice papers as per reduced syllabus were designed by the ‘Basics in Maths‘ team.

These Practice papers to do help the intermediate First-year Maths students.

TS Inter Maths 1A and 1B Practice papers as per reduced syllabus are very useful in IPE examinations.

 


 

MATHS 1A PRACTICE PAPER – 1

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TS Inter Maths 1A and 1B Practice papers as per reduced syllabus were designed by the ‘Basics in Maths‘ team.

These Practice papers to do help the intermediate First-year Maths students.

TS Inter Maths 1A and 1B Practice papers as per   syllabus are very useful in IPE examinations.


 

 

MATHS 1B PRACTICE PAPER – 1

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PDF Files

PDF Files || Inter Maths 1A &1B || (New)

Inter Maths 1A &1B|| PDF Files (New)

 

What is PDF?

pdf . png

PDF, or Portable Document Format, is an open file format used for exchanging electronic documents. Documents, forms, images, and web pages encoded in PDF can be correctly displayed on any device, including smartphones and tablets. If you distribute your reports in PDF, you can be sure that all of your pupils or friend will be able to open and read it on their PCs, Macs or Android smartphones.

Inter Mathematics 1A ands 1B Pdf Files|  these   Files were designed by the ‘Basics in Maths‘ team. These notes to do help the intermediate First-year Maths students.

Inter Maths – 1A & 1B   PDF Files are very useful in IPE examinations.

These notes cover all the topics covered in the intermediate First-year Maths syllabus and include plenty of solutions to help you solve all the major types of Math problems asked in the

IPE examinations.  

 


MATHEMATICS 1A

 

Addition Of Vectors SAQ’S

Matrices

 

TS 10th class maths concept (E/M)

 

 

MATHEMATICS 1B 

DC’s and Dr’s

Tangents and Normals

Maxima and Minima

 

 

 

TS 6th Class Maths Concept


 

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English Grammar Feature Image

English Grammar 4 Competitive Exams & School Education

english grammar

This content is designed by the ‘Basics in Maths‘ team.

English language:

The English Language is important to communicate and interact with other people around us. It keeps us in contact with other people.
An example of the importance of a language is the ‘English language’ because it is the international language and has become the most important language to people in many parts of the world.
British brought with them their language English to India.

ఇంగ్లీష్ భాష:

మన చుట్టూ ఉన్న ఇతర వ్యక్తులతో సందేశించాదానికికి  మరియు మన చుట్టూ ఉన్న ఇతర వ్యక్తులతో సంభాషించడానికి భాష ముఖ్యం. ఇది మనల్ని ఇతర వ్యక్తులతో సంప్రదించుటకు దోహదపడుతుంది.
ఒక భాష యొక్క ప్రాముఖ్యతకు ఒక ఉదాహరణ ‘ఆంగ్ల భాష’ ఎందుకంటే ఇది అంతర్జాతీయ భాష మరియు ప్రపంచంలోని అనేక ప్రాంతాల ప్రజలకు అత్యంత ముఖ్యమైన భాషగా మారింది.
బ్రిటిష్ వారు తమ భాష ఇంగ్లిష్ ను భారతదేశానికి తీసుకువచ్చారు.

English Grammar:

Grammar is the way we arrange words to make proper sentences. Grammar rules about how to speak and write in a language. english grammar is the grammar of the English language. English grammar started out based on Old English,

ఇంగ్లిష్ వ్యాకరణం:

వ్యాకరణం అనేది సరైన వాక్యాలు చేయడానికి పదాలను ఏర్పాటు చేసే విధానం. వ్యాకరణం అనగా  ఒక భాషలో ఎలా మాట్లాడాలి మరియు ఎలా రాయాలి అనే నియమాలు. ఆంగ్ల వ్యాకరణం ఆంగ్ల భాష యొక్క వ్యాకరణం. ఓల్డ్ ఇంగ్లిష్ ఆధారంగా ఇంగ్లిష్ గ్రామర్ ప్రారంభమైంది,


Introduction

There are 26 letters in the English Language. Those are called as ‘Alphabet’

There are two parts to Alphabet.

  • Vowels (a, e, i, o, u) [ 5 letters]
  • Consonants (Remaining 21 letters)

Without vowel (sound or structure) we cannot create even a single word in English.

enhlish grammar

PARTS OF SPEECH (భాషాభాగాలు)

 

NOUN (నామవాచకం):

A noun is a naming word. The noun means the name of the person, things, places, or animals

(నామవాచకం ఒక వ్యక్తి యొక్క, ఒక వస్తువు యొక్క లేదా జంతువు యొక్క పేరును తెలుపుతుంది)

Ex: Ramu goes to college by car

Seetha went to school by bus        → underlined words are nouns

Kinds of Nouns (According to their usage):

Proper Noun: A proper noun denotes one particular person, place, or thing.

(Proper Noun, ఒక ప్రత్యేక వ్యక్తి, వస్తువు లేదా జంతువు యొక్క పేరును తెలుపుతుంది)

Ex: Raju, Hyderabad, The Ganga, etc.

Common Noun: A common noun is a name given commonly to a person, place or thing.

(CommonNoun, ఒకే జాతికి చెందిన వ్యక్తి, వస్తువు లేదా జంతువు యొక్క పేరును తెలుపుతుంది)

Ex: boy, girl, animal, river, city, etc.

Collective noun:  A collective noun denotes a group or collection of persons or things taken as one.

(Collective Noun, వ్యక్తుల, వస్తువుల లేదా జంతువుల యొక్క గుంపును తెలుపుతుంది)

Ex: herd, army, committee, flock, etc.,

Material noun: A Material noun denote the name of a particular kind of metal, liquid, or substance.

(Material Noun, ఒక నిర్దిష్ట రకం లోహం, ద్రవం లేదా పదార్థం యొక్క పేరును తెలియజేస్తుంది)

Ex: salt, sand, gold, rice, paddy, etc.,

Kinds of Nouns (According to their Meaning):

Concrete Noun:  A Concrete noun denotes something that can be tasted, something that can be touched or seen, something that exists physically.

(కాంక్రీట్ నామవాచకం దేనినైనా రుచి చూడవచ్చు, ఏదైనా తాకవచ్చు లేదా చూడవచ్చు, భౌతికంగా ఉన్నదాన్ని సూచిస్తుంది.)

Ex: Pencil, boy, girl, gold, silver, rice, etc.,

Note: Proper nouns and Material nouns are Concrete nouns.

Abstract Noun: An Abstract noun denotes something maybe an idea or emotion.

Ex: born, sad, joy, bravery, freedom, etc.,

PRONOUN (సర్వనామం):

A pronoun is a word that is used instead of a noun.

సర్వనామం ను నామవాచకానికి బదులుగా వాడుతాము.

Ex:      Ramu went to the Ground, he played cricket.

పై వాక్యం లో రాము కు బదులుగా he వాడబడినది.

Types of Pronouns:

Personal Pronouns: Personal pronoun refers to a particular person or thing. (దీనిని వ్యక్తి పేరు కి బదులుగా ఉపయోగిస్తారు)

These are three types

ఇవి మూడు రకాలు

I person: Talks about himself (తన గురించి చెప్పేది. ఉదా : నేను, నాకు, మేము , మాకు, మొ ||)

Ex:  I – we – my – us etc.,

II person: what it says about others (ఎదుటి వారి గురించి చెప్పేది. ఉదా : నీవు , మీరు , మీకు  మొ ||)

Ex: you, yours

III Person: Talks about the third person between the discussion of two people (ఇద్దరి వ్యక్తుల సంభాషణ మధ్య మూడో వ్యక్తి గురించి చెప్పే ది. ఉదా : అతను , ఆమె , అతనికి  , ఆమెకి , వారికి  మొ ||)

Ex: he, she, it, they. Etc.,

Reflexive Pronoun:

Reflexive Pronouns are used when the subject and the object of a sentence are the same. They can act as either objects or indirect objects. (ఒక వ్యక్తి చేసిన పని ఫలితాన్ని తానే పొందినప్పుడు వీటిని వాడుతారు)  

Ex: myself, himself, themself, yourselves

Relative Pronouns:

A relative pronoun introduces a clause. It refers to some noun going before and also joins two sentences together.  (రెండు వాక్యములను కలుపుటకు వాడుతాము లేదా ఒక వాక్యములో అంతకుముందే చెప్పబడిన nouns ను refer చేస్తాయి)

Ex: who ……. Persons కు

       Which ……. Places కు

       That …… Things కు వాడుతారు

Demonstrative Pronoun: Demonstrative pronouns always identify nouns, whether those nouns are named specifically or not (ఇది, దేనినైనా లేక వేనినైన ఎత్తి చూపడానికి ఉపయోగపడుతుంది)

Ex: this, that, those, these, etc.,

Distributive Pronoun: Distributive pronouns refer to persons or things one at a time. (ఒకే సమయం లో ఎందరికో చెందేవి)

Ex; each, either, neither, etc.,

Indefinite Pronouns: Indefinite pronouns refer to people or things without saying exactly who or what they are. (ఫలానా వ్యక్తీ, ఫలానా వస్తువు గురించి కాకుండా ఎవరో ఒక వ్యక్తి, ఎదో ఒక వస్తువు గురించి Indefinite Pronouns తెలియజేస్తాయి)

Ex: somebody, none, all, nobody, etc.,

Interrogative Pronouns: These are used to ask questions (ప్రశ్నలు అడగడానికి వాడుతాము)

Ex: What, who, why

Subject (కర్త ): Subject means noun or pronoun or noun and pronoun.

Adjective (విశేషణం)

An adjective is used with a noun to add something to its meaning (ఒక విశేషణం నామవాచకంతో దాని అర్థానికి ఏదైనా జోడించడానికి ఉపయోగించబడుతుంది)

Ex: large, big, small, honest, wise, etc.,

Kinds Of Adjectives:

Qualitative Adjective: It indicates the characteristic of a person or an object (ఇది ఒక వ్యక్తి లేదా ఒక వస్తువు యొక్క లక్షణాన్ని తెలుపుతుంది)

Ex: honest, wise, small, big, etc.,

Quantitative adjective: It shows how much of a thing is (ఇవి ఎంత అనే అర్థంలో వాడుతాము)

Ex: some, much, little, enough, etc.,

Numeral Adjectives:  It shows how many things are meant (సంఖ్యాత్మకమైనవి. ఎన్ని అనే పదానికి సమాధానంగా వచ్చేవి)

Ex: few, many, most, five, three, etc.,

Demonstrative Adjectives:

These, that, those, this వంటి నామవాచకం తో కలిపి వస్తే వాటిని Demonstrative Adjectives అంటారు.

Ex: This boy is tall

That girt is clever

 Verb (క్రియ)

Verb (క్రియ) లేకుండా ఇంగ్లీష్ లో వాక్యము లు ఉండవు. ఇంగ్లీష్ వాక్యానికి ‘క్రియ’ ప్రాణం ‍వంటిది.

A verb is a word that tells something about an action or state.

Verb (క్రియ) లేకుండా ఇంగ్లీష్ లో వాక్యము లు ఉండవు. ఇంగ్లీష్ వాక్యానికి ‘క్రియ’ ప్రాణం ‍వంటిది.

A verb is a word that tells something about an action or state. (పనులను తెలియజేయు పదాలను verbs అంటారు)

Ex: I go to school

I am a student

He plays Cricket

We sit at the table

There are two kinds of verbs:

  1. Main verb
  2. Helping verb

Main verbs:

A verb that has an individual meaning is called the Main verb (వ్యక్తిగత అర్థాన్ని కలిగి ఉన్న క్రియను ప్రధాన క్రియ అని అంటారు)

Ex: go, come, take, sing, play, etc.,

Helping verbs:

A verb that does not have any individual meaning is called Helping verb (వ్యక్తిగత అర్థం లేని క్రియను Helping verb అని అంటారు)

Helping verb is mainly used to identify the tense. (ప్రధానంగా టెన్స్ గుర్తించడానికి Helping verb ఉపయోగించబడుతుంది)

Ex: do, does, Is, am, are, have, has, had, will, shall, etc.,

Types of Verbs:

Transitive Verb: A transitive verb is a verb that denotes an action that passes over from the subject to an object. (Object ను కలిగి యుండే   verb ను transitive verb అంటారు)

Ex: He writes a letter

Raju sings a song

In Transitive Verb:  An intransitive verb is a verb that denotes an action that does not pass over to an object. (Object లేని verb ను Intransitive verb అంటారు)

Ex: the boy plays

The Bird sings

 Adverb (క్రియా విశేషణం)

An Adverb is a word that modifies the meaning of a verb, an adjective, or another adverb. (ఒక వాక్య్తం లోని ఒక verb, adjective లేదా adverb గురించి తెలిపేది)

Ex: quickly, very, quietly, clearly etc.,

Preposition (విభక్త్యర్థ పదం)

A preposition is a word that is placed before a noun or pronoun to show the relation between a person, place, or thing. (ఒక నామవాచకముకు లేదా సర్వనామమునకు ముందున్చబడి వాక్యంలోని ఇతర పదం లేక పదాలతో అ నామవాచకం లేదా సర్వనామం యొక్క సంబందాన్ని తెలిపే పదం)

Kinds of Prepositions

Simple Prepositions:  at, by, in, for, off, of, up, to, with, etc., are Simple Prepositions

Compound Prepositions: about, across, along, among, behind, before, below, besides, inside, within, without, etc., are called Compound Prepositions.

Phrase Prepositions: according to, Infront of, in favor of, because of, with regard to, etc., are known as Phrase Prepositions.

Conjunction (సముచ్చయం):

Conjunction combines sentences or words together. (కొన్ని వాక్యాలను లేదా పదాలను కలిపే పదం)

Ex: and, or, but, so, if, as, since, when, etc.,

Interjection (భావోద్వేగ ప్రకటన):

An Interjection is a word that expresses some sudden feelings or emotions.

(మానసిక భావాలను లేక ఉద్రేకాలను తెల్పుటకు వాడే మాటలను Interjections అని అంటారు).

Note: Interjections తరువాత ఆశ్చర్యార్ధకము (!) అనే గుర్తు ఉంచి దాని తరువాత వచ్చేమాట మొదటి అక్షరము Capital letters తో ప్రారంభించవలెను.

Ex: Hello! What are you doing here?

Alas! He  injured

Hurrah! I won the game


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Polytechnic Engineering Maths Feature Image for Sem 1 Concept

Engineering Mathematics SEM – 1Concept

Mathematics Notes for Polytechnic SEM – 1 is Designed by the ” Basics in Maths” team. Here we can learn Concepts in Basic Engineering mathematics Polytechnic Sem – I.

 This Material is very Useful for Basic Engineering Mathematics Polytechnic Sem – I Students.

By learning These Notes, Basic Engineering Mathematics Polytechnic Sem – I Students can Write their Exam successfully and fearlessly.


Engineering Mathematics SEM – 1Concept

 

LOGARITHMS

Logarithm: For ant two positive real numbers a, b, and a ≠ 1. If the real number x such then ax = b, then x is called logarithm of b to the base a. it is denoted by Polytechnic SEM - I image 1

Polytechnic SEM - I image 2Standard formulae of logarithms:

Polytechnic SEM - I image 3

Logarithmic Function:

Let a be a positive real number and a ≠ 1. The function f: (o, ∞) → R Defined by f(x) = Polytechnic SEM - I image 4

Polytechnic SEM - I image 5

Polytechnic SEM - I image 6


PARTIAL FRACTIONS

Fractions:

If f(x) and g(x) are two polynomials, g(x) ≠ 0, then Polytechnic SEM - I Partial Fractions1  is called rational fraction.

Ex:

Polytechnic SEM - I Partial Fractions 2   etc.  are rational fractions.

Proper Fraction:

A rational fractionPolytechnic SEM - I Partial Fractions1 is said to be a Proper fraction if the degree of g(x) is greater than the degree of f(x).

Ex:

Polytechnic SEM - I Partial Fractions 3  etc. are the proper fractions.

Improper Fraction:

A rational fractionPolytechnic SEM - I Partial Fractions1 is said to be an Improper fraction if the degree of g(x) is less than the degree of f(x).

Ex:

Polytechnic SEM - I Partial Fractions 4 etc. are the Improper fractions.

Partial Fractions:

Expressing rational fractions as the sum of two or more simpler fractions is called resolving a given fraction into a partial fraction.

∎ If R(x) =Polytechnic SEM - I Partial Fractions1  is proper fraction, then

Case(i): – For every factor of g(x) of the form (ax + b) n, there will be a sum of n partial fractions of the form:

Polytechnic SEM - I Partial Fractions 5

Case(ii): – For every factor of g(x) of the form (ax2 + bx + c) n, there will be a sum of n partial fractions of the form:

Polytechnic SEM - I Partial Fractions 6

∎ If R(x) =Polytechnic SEM - I Partial Fractions1 is improper fraction, then

Case (i): – If degree f(x) = degree of g(x),Polytechnic SEM - I Partial Fractions 6   where k is the quotient of the highest degree term of f(x) and g(x).

Case (ii): – If f(x) > g(x)

R(x) = Polytechnic SEM - I Partial Fractions 8

 

 

 MATRICES AND DETERMINANTS

 

Matrix: A set of numbers arranged in the form of a rectangular array having rows and columns is called Matrix.

•Matrices are generally enclosed by brackets like

•Matrices are denoted by capital letters A, B, C, and so on

•Elements in a matrix are real or complex numbers; real or complex real-valued functions.

Oder of Matrix: A matrix having ‘m’ rows and ‘n’ columns is said to be of order m x n read as m by n.

Ex:

Polytechnic SEM - I Matrices 1

Types Of Matrices

Rectangular Matrix: A matrix in which the no. of rows is not equal to the no. of columns is called a rectangular matrix.                 

Polytechnic SEM - I Matrices 2

 Square Matrix: A matrix in which the no. of rows is equal to no. of columns is called a square matrix.

Polytechnic SEM - I Matrices 3

Principal diagonal (diagonal) Matrix: If A = [a ij] is a square matrix of order ‘n’ the elements a11, a22, a33, ………. An n is said to constitute its principal diagonal.

Polytechnic SEM - I Matrices 4

Trace Matrix: The sum of the elements of the principal diagonal of a square matrix A is called the trace of the matrix. It is denoted by Tr (A).

Polytechnic SEM - I Matrices 5

Diagonal Matrix: If each non-diagonal element of a square matrix is ‘zero’ then the matrix is called a diagonal matrix.

Polytechnic SEM - I Matrices 6

Scalar Matrix: If each non-diagonal element of a square matrix is ‘zero’ and all diagonal elements are equal to each other, then it is called a scalar matrix.

Polytechnic SEM - I Matrices 7

Identity Matrix or Unit Matrix: If each of the non-diagonal elements of a square matrix is ‘zero’ and all diagonal elements are equal to ‘1’, then that matrix is called unit matrix

Polytechnic SEM - I Matrices 29

Null Matrix or Zero Matrix: If each element of a matrix is zero, then it is called a null matrix.

Polytechnic SEM - I Matrices 8

Row matrix & column Matrix: A matrix with only one row s called a row matrix and a matrix with only one column is called a column matrix.

Polytechnic SEM - I Matrices 9

Triangular matrices:

A square matrix A = [aij] is said to be upper triangular if aij = 0   ∀ i > j

A square matrix A = [aij] is said to be lower triangular matrix aij = 0  ∀ i < j

 

Equality of matrices:


matrices A and B are said to be equal if A and B are of the same order and the corresponding elements of A and B are equal.

Polytechnic SEM - I Matrices 11

Addition of matrices:

If A and B are two matrices of the same order, then the matrix obtained by adding the corresponding elements of A and B is called the sum of A and B. It is denoted by A + B.

Polytechnic SEM - I Matrices 12

Subtraction of matrices:

If A and B are two matrices of the same order, then the matrix obtained by subtracting the corresponding elements of A and B is called the difference from A to B.

Polytechnic SEM - I Matrices 13

Product of Matrices:

Let A = [aik]mxn and B = [bkj]nxp be two matrices, then the matrix C = [cij]mxp   where

Polytechnic SEM - I Matrices 14

Note: Matrix multiplication of two matrices is possible when no. of columns of the first matrix is equal to no. of rows of the second matrix.

A m x n  . Bp x q = AB mx q; n = p

Transpose of Matrix: If A = [aij] is an m x n matrix, then the matrix obtained by interchanging the rows and columns is called the transpose of A. It is denoted by AI or AT.

Note: (i) (AI)I = A     (ii) (k AI) = k . AI    (iii)  (A + B )T = AT + BT  (iv)  (AB)T = BTAT

Symmetric Matrix: A square matrix A is said to be symmetric if AT =A

If A is a symmetric matrix, then A + AT is symmetric.

Skew-Symmetric Matrix: A square matrix A is said to be skew-symmetric if AT = -A

If A is a skew-symmetric matrix, then A – AT is skew-symmetric.

 Minor of an element: Consider a square matrix Polytechnic SEM - I Matrices 16

the minor element in this matrix is defined as the determinant of the 2×2 matrix obtained after deleting the rows and the columns in which the element is present.

Ex: – minor of a3 is Polytechnic SEM - I Matrices 17    = b1c2 – b2c1

Minor of b2 is   = a1c3 – a3c1

Cofactor of an element: The cofactor of an element in i th row and j th column of A3×3 matrix is defined as its minor multiplied by (- 1) i+j.

Properties of determinants:

If each element of a row (column) f a square matrix is zero, then the determinant of that matrix is zero.

Ex: –    A = Polytechnic SEM - I Matrices 19   ⇒ det(A) = 0

If A is a square matrix of order 3 and k is scalar then.

If two rows (columns) of a square matrix are identical (same), then Det. Of that matrix is zero.

Ex: –    A =   Polytechnic SEM - I Matrices 20  ⇒ det(A) = 0

If each element in a row (column) of a square matrix is the sum of two numbers then its determinant can be expressed as the sum of the determinants.

Ex: –  Polytechnic SEM - I Matrices 21

If each element of a square matrix are polynomials in x and its determinant is zero when x = a, then (x-a) is a factor of that matrix.

For any square matrix A Det(A) = Det (AI).

Det (AB) = Det(A). Det(B).

For any positive integer n Det (An) = (DetA)n.

Singular and non-singular matrices:

A Square matrix is said to be singular if its determinant is is zero, otherwise it is said to be non-singular matrix.

Ex: –   A =  Polytechnic SEM - I Matrices 22    det(A) = 4 – 4 = 0

∴ A is singular matrix

B = Polytechnic SEM - I Matrices 23

Det(B) = 4 + 4 = 8≠ 0

∴ B is non-singular

 Adjoint of a matrix: The transpose of the matrix formed by replacing the elements of a square matrix A with the corresponding cofactors is called the adjoint of A.

Let A = Polytechnic SEM - I Matrices 24 and     cofactor matrix of A = Polytechnic SEM - I Matrices 25

Then adj (A) =Polytechnic SEM - I Matrices 26

 Invertible matrix: Let A be a square matrix, we say that A is invertible if there exists a matrix B such that AB =BA = I, where I is a unit matrix of the same order as A and B.

  1. (A– I)– I = A
  2. (AI)– I = (A-I)I
  3. (AB)-I = B-I A-I
  4. A-I =Polytechnic SEM - I Matrices 27

 

Compound Angles

The algebraic sum of two or more angles is called a ‘compound angle’. Thus, angles A + B, A – B, A + B + C etc., are Compound Angles

For any two real numbers A and B

sin (A + B) = sin A cos B + cos A Cos B

sin (A − B) = sin A cos B − cos A Cos B

cos (A + B) = cos A cos B − sin A sin B

cos (A − B) = cos A cos B + sin A sin B

tan (A + B) =Polytechnic SEM - I Compound Angles 1

tan (A − B) =Polytechnic SEM - I Compound Angles 2

cot (A + B) =Polytechnic SEM - I Compound Angles 3

cot (A − B) = Polytechnic SEM - I Compound Angles 4

tan (Polytechnic SEM - I Compound Angles 5 + A) = Polytechnic SEM - I Compound Angles 6

tan ( Polytechnic SEM - I Compound Angles 5− A) =Polytechnic SEM - I Compound Angles 7

cot (Polytechnic SEM - I Compound Angles 5+ A) =Polytechnic SEM - I Compound Angles 8

cot (Polytechnic SEM - I Compound Angles 5− A) =

sin (A + B + C) = ∑sin A cos B cos C − sin A sin B sin C  

cos (A + B + C) = cos A cos B cos C− ∑cos A sin B sin C 

tan (A + B + C) =Polytechnic SEM - I Compound Angles 10

⋇ cot (A + B + C) =Polytechnic SEM - I Compound Angles 11

⋇ sin (A + B) sin (A – B) = sin2 A – sin2 B = cos2 B – cos2 A

⋇ cos (A + B) cos (A – B) = cos2 A – sin2 B = cos2 B – sin2 A

Polytechnic SEM - I Compound Angles 12

 

Multiple and Sub Multiple Angles

If A is an angle, then its integral multiples 2A, 3A, 4A, … are called ‘multiple angles ‘of A and the multiple of A by fraction like are called ‘submultiple angles.

Polytechnic SEM - I Multiple and Submultiple Angles 1

∎ If Polytechnic SEM - I Multiple and Submultiple Angles 2  is not an add multiple of Polytechnic SEM - I Multiple and Submultiple Angles 3

Polytechnic SEM - I Multiple and Submultiple Angles 4 Polytechnic SEM - I Multiple and Submultiple Angles 5

Polytechnic SEM - I Multiple and Submultiple Angles 8

Polytechnic SEM - I Multiple and Submultiple Angles 7

 

 

PROPERTIES OF TRIANGLES

 

In ∆ABC,

Polytechnic SEM - I Properties of triangles 1

Lengths AB = c; BC = a; AC =b

The area of the triangle is denoted by ∆.

Perimeter of the triangle = 2s = a + b + c

A = ∠CAB; B = ∠ABC; C = ∠BCA.

R is circumradius.

Sine rule:

In ∆ABC,

Polytechnic SEM - I Properties of triangles 2

⟹ a = 2R sin A; b = 2R sin B; c = 2R sin C

Where R is the circumradius and a, b, c, are lengths of the sides of ∆ABC.

Cosine rule:

In ∆ABC,

Polytechnic SEM - I Properties of triangles 3

Projection rule:

In ∆ABC,

a = b cos C + c cos B

b = a cos C + c cos A

c = a cos B + b cos A

Tangent rule (Napier’s analogy):

Polytechnic SEM - I Properties of triangles 4

 Area of the triangle:

Polytechnic SEM - I Properties of triangles 7

In ∆ABC, a, b, and c are sides

S = Polytechnic SEM - I Properties of triangles 5and area of the triangle Polytechnic SEM - I Properties of triangles 11

 

 

HYPERBOLIC FUNCTIONS

Polytechnic SEM - I Hyperbolic Functions 1

The function f: R→R defined by f(x) =Polytechnic SEM - I Hyperbolic Functions 2 ∀ x ∈ R is called the ‘hyperbolic sin’ function. It is denoted by Sinh x.

∴Sinh x =Polytechnic SEM - I Hyperbolic Functions 2

Similarly,

Polytechnic SEM - I Hyperbolic Functions 3

Identities:

cosh2x – sinh2 x = 1

cosh2x = 1 + sinh2 x

sinh2 x = cosh2 x – 1

sech2 x = 1 – tanh2 x

tanh2 x = 1 – sesh2 x

cosech2 x = coth2 x – 1

coth2 x = 1 + coth2 x

Addition formulas of hyperbolic functions:

Sinh (x + y) = Sinh x Cosh y + Cosh x Sinh y

Sinh (x − y) = Sinh x Cosh y − Cosh x Sinh y

Cosh (x + y) = Cosh x Cosh y + Sinh x Sinh y  

Cosh (x − y) = Cosh x Cosh y − Sinh x Sinh y 

tanh (x + y) = Polytechnic SEM - I Hyperbolic Functions 4

tanh (x − y) = Polytechnic SEM - I Hyperbolic Functions 5

coth (x + y) = Polytechnic SEM - I Hyperbolic Functions 6

sinh 2x = 2 sinh x cosh 2x =Polytechnic SEM - I Hyperbolic Functions 7

cosh 2x = cosh2x + sinh2 x = 2 cosh2x – 1 = 1 + 2 sinh2x =Polytechnic SEM - I Hyperbolic Functions 8

tanh 2x =Polytechnic SEM - I Hyperbolic Functions 9

 

Inverse hyperbolic functions:

Sinh−1x = Polytechnic SEM - I Hyperbolic Functions 10 ∀ x ∈ R

Cosh−1x = Polytechnic SEM - I Hyperbolic Functions 11  ∀ x ∈ (1, ∞)

Tanh−1x = Polytechnic SEM - I Hyperbolic Functions 15   ∀ < 1

Polytechnic SEM - I Hyperbolic Functions 13

 

 

COMPLEX NUMBERS

The equation x2 + 1 = 0 has no roots in real number system.

∴ scientists imagined a number ‘i’ such that i2 = − 1.

Complex number:

if x, y are any two real numbers then the general form of the complex number is

z = x + i y; where x real part and y is the imaginary part.

3 + 4i, 2 – 5i, – 3 + 2i are the examples for Complex numbers.

  • z = x +i y can be written as (x, y).
  • If z1 = x1 + i y1, z2 = x2 + i y2, then
  • z1 + z2 = (x1 + x2, y1 + y2) = (x1 + x2) + i (y1 + y2)
  • z1 − z2 = (x1 − x2, y1 − y2) = (x1 − x2) + i (y1 − y2)
  • z1∙   z2 = (x1 x2 −y1 y2, x1y2 + x2y1) = (x1x2 −y1 y2) + i (x1y2 +x2 y1)
  • z1/ z2 = (x1x2 + y1 y2/x22 +y22, x2 y1 – x1y2/ x22 +y22)

= (x1x2 + y1 y2/x22 +y22) + i (x2 y1 – x1y2/ x22 +y22)

  Multiplicative inverse of complex number:

   The multiplicative inverse of the complex number z is 1/z.

z = x + i y then 1/z = x – i y/ x2 + y2

Conjugate complex numbers:

The complex numbers x + i y, x – i y are called conjugate complex numbers.

Conjugate of z is denoted byPolytechnic SEM - I Complex Numbers 1

The sum and product of two conjugate complex numbers are real.

If z1, z2 are two complex numbers then

Polytechnic SEM - I Complex Numbers 2

 Modulus and amplitude of complex numbers:

Modulus: – If z = x + i y, then the non-negative real numberPolytechnic SEM - I Complex Numbers 3 is called modulus of z and it is denoted byPolytechnic SEM - I Complex Numbers 4 or ‘r’.

Amplitude: – The complex number z = x + i y represented by the point P (x, y) on the XOY plane. ∠XOP = θ is called amplitude of z or argument of z.

x = r cos θ, y = r sin θ

x2 + y2 = r2 cos2θ + r2 sin2θ = r2 (cos2θ + sin2θ) = r2(1)

⇒ x2 + y2 = r2

⇒ r =Polytechnic SEM - I Complex Numbers 3  and Polytechnic SEM - I Complex Numbers 4 = r.

• Arg (z) = tan−1(y/x)

• Arg (z1.z2) = Arg (z1) + Arg (z2) + nπ for some n ∈ { −1, 0, 1}

• Arg(z1/z2) = Arg (z1) − Arg (z2) + nπ for some n ∈ { −1, 0, 1}

Note:

∎ e = cos θ + i sin θ

∎ e−iθ = cos θ − i sin θ

De- Moiver’s theorem

For any integer n and real number θ, (cos θ + i sin θ) n = cos n θ + i sin n θ.

cos α + i sin α can be written as cis α

cis α.cis β= cis (α + β)

1/cisα = cis(-α)

cisα/cisβ = cis (α – β)

(cos θ + i sin θ) -n = cos n θ – i sin n θ

(cos θ + i sin θ) (cos θ – i sin θ) = cos2θ – i2 sin2θ = cos2θ + sin2θ = 1.

cos θ + i sin θ = 1/ cos θ – i sin θ and cos θ – i sin θ = 1/ cos θ + i sin θ

(cos θ – i sin θ) n = (1/ (cos θ –+i sin θ)) n = (cos θ + i sin θ)-n = cos n θ – i sin n θ

nth root of a complex number: let n be a positive integer and z0 ≠ 0 be a given complex number. Any complex number z satisfying z n = z0 is called an nth root of z0. It is denoted by z01/n orPolytechnic SEM - I Complex Numbers 5

let z = r (cos θ + i sin θ) ≠ 0 and n be a positive integer. For k∈ {0, 1, 2, 3…, (n – 1)}

letPolytechnic SEM - I Complex Numbers 6 Then a0, a1, a2, …, an-1 are all n distinct nth roots of z and any nth root of z is coincided with one of them.

nth root of unity:  Let n be a positive integer greater than 1 andPolytechnic SEM - I Complex Numbers 7 

Note:

  • The sum of the nth roots of unity is zero.
  • The product of nth roots of unity is (– 1) n – 1.
  • The nth roots of unity 1, ω, ω2, …, ωn-1 are in geometric progression with common ratio ω.
Cube root of unity:      

x3 – 1 = 0 ⇒ x3 = 1

x =11/3

cube roots of unity are: 1 Polytechnic SEM - I Complex Numbers 8    Polytechnic SEM - I Complex Numbers 9

ω = Polytechnic SEM - I Complex Numbers 8 , ω2 =Polytechnic SEM - I Complex Numbers 9

ω2 +ω + 1 = 0 and ω3 = 1

 

 

TRANSFORMATIONS

 

For A, B∈ R

⋇ sin (A + B) + sin (A – B) = 2sin A cos B

⋇ sin (A + B) −sin (A – B) = 2cos A sin B

⋇ cos (A + B) + cos (A – B) = 2 cos A cos B

⋇ cos (A + B) − cos (A – B) = − 2sin A sin B

For any two real numbers C and D

⋇ sin C + sin D = 2sinPolytechnic SEM - I Transformations 1 cosPolytechnic SEM - I Transformations 2

 

⋇ sin C −sin D= 2cosPolytechnic SEM - I Transformations 1  sinPolytechnic SEM - I Transformations 2

⋇ cos C + cos D = 2 cosPolytechnic SEM - I Transformations 1   cosPolytechnic SEM - I Transformations 2

⋇ cos C − cos D = − 2sinPolytechnic SEM - I Transformations 1   sin Polytechnic SEM - I Transformations 2

If A + B + C = π or 1800, then

⋇ sin (A + B) = sin C; sin (B + C) = sin A; sin (A + C) = sin B

⋇ cos (A + B) = − cos C; cos (B + C) = −cos A; cos (A + C) = − cos B

If A + B + C = 900 or Polytechnic SEM - I Transformations 3then

⋇ sinPolytechnic SEM - I Transformations 4   = cosPolytechnic SEM - I Transformations 9;   sinPolytechnic SEM - I Transformations 5   = cosPolytechnic SEM - I Transformations 8 ;  sinPolytechnic SEM - I Transformations 6   = cosPolytechnic SEM - I Transformations 7

⋇ cos Polytechnic SEM - I Transformations 4  = sinPolytechnic SEM - I Transformations 9; cosPolytechnic SEM - I Transformations 5   = sinPolytechnic SEM - I Transformations 8; cosPolytechnic SEM - I Transformations 6   = sinPolytechnic SEM - I Transformations 7

IfPolytechnic SEM - I Transformations 1    then

⋇ sin (A + B) = cos C; sin (B + C) = cos A; sin (A + C) = cos B

⋇ cos (A + B) = sin C; cos (B + C) = sin A; cos (A + C) = sin B

 

 

 

 

INVERSE TRIGONOMETRIC RATIOS

 

If A, B are two sets and f: A→ B is a bijection, then f-1 is existing and f-1: B → A is an inverse function.

Polytechnic SEM - I Inverse Trigonometric Ratios 1

Polytechnic SEM - I Inverse Trigonometric Ratios 2

Properties of Inverse Trigonometric functions:

Polytechnic SEM - I Inverse Trigonometric Ratios 3 Polytechnic SEM - I Inverse Trigonometric Ratios 4 Polytechnic SEM - I Inverse Trigonometric Ratios 5 Polytechnic SEM - I Inverse Trigonometric Ratios 6 Polytechnic SEM - I Inverse Trigonometric Ratios 7

Polytechnic SEM - I Inverse Trigonometric Ratios 8

 

Solutions of Simultaneous Equations

 

Matrix Inversion Method:

Let a system of simultaneous equations be

a1 x + b1 y + c1z = d1

a2 x + b2 y + c2z = d2

a3 x + b3 y + c3z = d3

The matrix form of the above equations is

Polytechnic SEM - I Equations In Matrices 1

Therefore, the matrix equation is AX = B

If Det A ≠ 0, A-1 is exists

X = A-1 B

By using above Condition, we get the values of x, y and z

This Method is called as Matrix Inversion Method

Cramer’s Method:

Let system of simultaneous equations be

a1 x + b1 y + c1z = d1

a2 x + b2 y + c2z = d2

a3 x + b3 y + c3z = d3

Polytechnic SEM - I Equations In Matrices 2

1 is obtained by replacing the coefficients of x (1st column elements of ∆) by constant values

Polytechnic SEM - I Equations In Matrices 3

2 is obtained by replacing the coefficients of y (2nd column elements of ∆) by constant values

Polytechnic SEM - I Equations In Matrices 4

3 is obtained by replacing the coefficients of z (3rd column elements of ∆) by constant values

Now Polytechnic SEM - I Equations In Matrices 5

This method is called Cramer’s Method

Gauss-Jordan Method:

Let a system of simultaneous equations be

a1 x + b1 y + c1z = d1

a2 x + b2 y + c2z = d2

a3 x + b3 y + c3z = d3

Augmented matrix: The coefficient matrix (A) augmented with the constant column matrix (B) is called the augmented matrix. It is denoted by [AD].

[AD] = Polytechnic SEM - I Equations In Matrices 6

This Matrix is reduced to the standard form ofPolytechnic SEM - I Equations In Matrices 7by using row operations

  1. Interchanging any two rows
  2. Multiplying the elements of any two elements by a constant.
  3. Adding to the elements of one row with the corresponding elements of another row multiplied by a constant.

∴ The solution of a given system of simultaneous equations is x = α, y = β, and z = γ.

Procedure to get the standard form:
  1. Take the coefficient of x as the unity as a first equation.
  2. If 1 is there in the first-row first column, then make the remaining two elements in the first column zero.
  3. After that, if one element in R2 or R3 is 1, then make the remaining two elements in that column C2 or C3 as zeroes.
  4. If any row contains two elements as zeros and only non-zero divide that row elements with the non-zero element to get unity and make the remaining two elements in that column as zeros.

 

 

PDF FILE: Mathematics Notes 4 Polytechnic SEM – I


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>Compatible with all smartphones. Charge for 10 minutes, enjoy for 10 hours on your OnePlus Bullets Wireless Z that comes equipped with the Bluetooth v5.0 QCC3024 chipset.                                                                                                                                                 > Battery charge method : USB Type-C
>The Bullets Wireless Z comes with Warp Charge technology. Sweat and water-resistant:IP55. Bluetooth range : Up to 33ft (10m)
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Canon EOS 1500D 24.1 Digital SLR Camera (Black) with EF S18-55 is II Lens:

Sensor: APS-C CMOS Sensor with 24.1 MP (high resolution for large prints and image cropping)
ISO: 100-6400 sensitivity range (critical for obtaining grain-free pictures, especially in low light)
Image Processor: DIGIC 4+ with 9 autofocus points (important for speed and accuracy of autofocus and burst photography)
Video Resolution: Full HD video with fully manual control and selectable frame rates (great for precision and high-quality video work)
Connectivity: WiFi, NFC and Bluetooth built-in (useful for remotely controlling your camera and transferring pictures wirelessly as you shoot)
Lens Mount: EF-S mount compatible with all EF and EF-S lenses (crop-sensor mount versatile and compact, especially when used with EF-S lenses)

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Amazon Product

 

Oppo A 31

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Boult Audio Bass Buds Q2

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Redmi 9 ( Sky Blue)

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Samsun Galaxy M12

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Samsun Galaxy M31

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AS Tutorial For Math Classes / YouTube new no. 1 Channel

AS Tutorial తెలుగులో

Hi, This is [email protected] Satyanarayana Reddy, Welcome To My Channel AS Tutorial తెలుగులో.
In ASTutorialతెలుగులో I will share with you the concepts of Maths in inter.
AS Tutorialతెలుగులో Provides Concepts and Problems for Inter Maths Students In Telugu.


హాయ్, ఇది అనిత @ సత్యనారాయణ రెడ్డి, వెల్ కమ్ మై ఛానల్ AS Tutorial తెలుగులో,
AS Tutorial తెలుగులో ఇంటర్ లో మ్యాథ్స్ భావనలను మీతో పంచుకుంటాను.
AS Tutorial తెలుగులో ఇంటర్ మ్యాథ్స్ విద్యార్థులకు తెలుగులో కాన్సెప్ట్స్ అండ్ ప్రాబ్లమ్స్ ను అందిస్తోంది.


MY APP: https://play.google.com/store/apps/details?id=mobi.androapp.basicsinmaths.c9507


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My Links:

My Youtube Channel: https://www.youtube.com/channel/UCtL8sDWcUlJX_7Npr9460lA

Simple Equations | LHS to RHS and RHS to LHS, RULE ||AS Tutorial తెలుగులో || 2021|| : https://youtu.be/2Vkb_jYx_YM

Trigonometry// ALL-SILVER-TEA-CUPS Rule ||ASTutorialతెలుగులో || 2021|| :https://youtu.be/UqwfCBsJVMY

‘Locus’ Concept and Problems For Inter First Year Maths 1B||AS Tutorial తెలుగులో || 2021||(PART – 1):https://youtu.be/RAtxfld4ywQ

‘Locus’ Concept and Problems For Inter First Year Maths 1B||AS Tutorial తెలుగులో || 2021||(PART – 2): https://youtu.be/E6IaE09YsbM

Trigonometry Introduction, Sides of Right Triangle and Trigonometry Ratios |ASTutorialతెలుగులో 2021:https://youtu.be/Elt7Uy_yfLU

Trigonometry || How To Prove Specific Angles In Trigonometry| || AS Tutorialతెలుగులో|| || 2021|: https://youtu.be/Fh4Vc66swQQ

Trigonometry| How to remember Specific Angles Table in Trigonometry |ASTutorialతెలుగులో || 2021||: https://youtu.be/D3CZ1ijq7OM

Trigonometry| Trigonometric Identities In Trigonometry|ASTutorialతెలుగులో || 2021|| :https://youtu.be/r1NZyagpN90

‘Transformation Of Axes’ Concept and Problems For Inter Maths 1B||AS Tutorial తెలుగులో || 2021|| P 1: https://youtu.be/9qJJuZzKtJ8

‘Transformation Of Axes’ Concept and Problems For Inter Maths 1B||AS Tutorial తెలుగులో || 2021|| P 2 :https://youtu.be/lAfuMQ1YU3c

Playing With Numbers||Divisibility Rules In Telugu ||AS Tutorial తెలుగులో || || 2021|| : https://youtu.be/8I1izylDH_o

Playing With Numbers||Even| Odd|Prime|Composite|Co-Prime &Twin- Prime Numbers|| AS Tutorial తెలుగులో : https://youtu.be/TZeleb6vd1I

Logarithms|| Product Rule| Quotient Rule| and Power Rule||AS Tutorial తెలుగులో || || 2021||: https://youtu.be/ssYCXUc0Hf8

Periodic Functions| Trigonometric Ratios Up To Transformations ||AS Tutorial తెలుగులో || || 2021|| : https://youtu.be/aeOEDgQpVu0

TS TET Child Developmentt & Pedagogi Part 2: https://youtu.be/qyB5pImDg8c
TS TET Child Developmentt & Pedagogi Part 3: https://youtu.be/m3ui0jFIgmc
TS TET Child Developmentt & Pedagogi Part 4: https://youtu.be/sULWOJctF8k
TS TET Child Developmentt & Pedagogi Part 5: https://youtu.be/J-huGDv7cUs

TS TET 2022, Mathematics Methods, paper 2, Practice Bits p – 1: https://youtu.be/HPBN6WdgbBc

TS TET 2022, Mathematics Methods, paper 2, Practice Bits, part 3:https://youtu.be/DZzgHljDklA

TS TET 2022, Mathematics Methods, paper 2, Practice Bits, part 4:https://youtu.be/2Bdu_dWIH7U

TS TET 2022, Mathematics Methods, paper 2, Practice Bits, part 5: https://youtu.be/INWN_23gXDc

TS TET – 2022: VI Class Maths, Chapter 1, మనసంఖ్యలను తెలుసుకుందాం , Practice Bits:https://youtu.be/wVMzcpNWyPc

TS TET – 2022: VI Class Maths, Chapter 1, మనసంఖ్యలను తెలుసుకుందాం , Practice Bits: https://youtu.be/3-1MEbi6z9E

TS TET – 2022: VI Class Maths, Chapter 2,పూర్ణాంకాలు , Practice Bits: https://youtu.be/Z7w4p2naP7Y

TS TET 2022: VI Class Maths, Chapter 2, Wole Numbers , Practice Bits: https://youtu.be/I2BKs3YBLT8

TS TET – 2022: X Class Maths, Chapter 11, Trigonometry , Practice Bits: https://youtu.be/5xwtndJLhPs

TS TET – 2022: X Class Maths, Chapter 11, త్రికోణమితి , Practice Bits:https://youtu.be/oHbOZPTeWuo

TS TET 2022 , X Class Maths, Chapter 1,Real Numbers , Practice Bits, Practice Bits: https://youtu.be/iUWXfxF3pz4

TS TET 2022,10 th Maths, chapter 1, Real numbres – Logorithms: https://youtu.be/6HoIeoATswY

TS TET 2022, Paper 2, 10 th Maths, chapter 2, SETS, Practicew bits : https://youtu.be/VYypC4xC6Jc
TS TET 2022, Paper 2, 10 th Maths, chapter 14, Statistics, Practicew bits: https://youtu.be/RA6jDQQaRXw

Matrices Basic Concepts: https://youtu.be/_Gqg07ZquN0
Trace of Matrix, Addition of Matrices, Equality of Matrices: https://youtu.be/Hycj-UITfD8
Multiplication of two matrices P – 1:https://youtu.be/rMp96I6ag8s
Multiplication of two matrices P – 2:https://youtu.be/Axu5BbGKkbs
Multiplication of two matrices P – 3:https://youtu.be/1aSVztz9TII
transose of matrices: https://youtu.be/D8nhjYQJqm0
Smmetric and Skew Symmetric Matrices:https://youtu.be/JUv2RT35DaA

Adjoint and Inverse of Matrices P – 1:https://youtu.be/mPnkSkxKaxo

Adjoint and Inverse of Matrices P – 2:https://youtu.be/4fpvFTNpXC0

Adjoint and Inverse of Matrices P – 3:https://youtu.be/Ge-jHQRF4SM



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My YouTube Videos Play List

  Simple Mistakes Done by Maths Students

 Inter Maths Concept & Solutions

 10th Class Maths Concept & Solutions

 

 

AS Tutorial In Telugu - QR code

Reduced Syllabus 2021 Reduced Syllabus

Reduced Syllabus 2021 Telangana BIE Maths

Reduced Syllabus 2021 Telangana BIE Maths

Reduced Syllabus 2021

This content is designed by the ‘Basics in Maths‘ team.

Telangana BIE Maths Reduced Syllabus(2021) very useful  I.P.E  exam.

 

PDF Files || Inter Maths 1A &1B || (New)

6th maths notes|| TS 6 th class Maths Concept

TS 10th class maths concept (E/M)

 


Inter 1st year Maths Reduced SyllabusClick Here
Inter 2nd  year Maths Reduced Syllabus Click Here

 

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