Intermediate Course in MEC

Intermediate Course in MEC

Paper I A - Algebra: 65 Periods

1 Functions of Mappings 9
2 Surds 6
3 Logs 6
4 Mathematical Induction 14

VECTOR ALGEBRA:

5 Addition of Vectors 24
6 Multiplication of Vectors 25

Trigonometry: 60 Periods

7 Graphs & Periodic Functions )
(Trigonometric ratios of Compound
angles ) (Multiple & Sub-multiple
angles ) ( Transformations 9
8 Trigonometric Equations 16
9 Inverse Trigonometric functions 5
10 Hyperbolic functions 5
11 Properties of triangles 10
12 Heights and distances in single plane 7
13 Complex Numbers 6
14 De-movires Theorem 5
15 Trignometric expansions 3

Intermediate Mathematics -1a (Algebra, Vector Algebra & Trignometry) : 10 Periods

S. No Topics/Chapter

Sub-topics/Sections/Sub-sections

Periods of Instructions
1 Functions or Mappings A. Definitions of one-one, onto, bijection functions, Identity and constant functions Equality of two functions 9 periods
B. Definitions of Inverse function, composite Function and Inverse of composite Function Theorems with proofs

1. F:A->B, g:B->C are bijective functions, then gof:A->C is also a bijection.
2. Let A & B be two sets. If f:A->B is a Bijective then f -1 :B-A is also a bijective function
3. If f:A->B and g:B->C are two Bijective functions then (gof) -1 =f -1 -1og -1 -1.
4. If f:A->B and g:B->C are two Bijective functions then (gof) -1 =f -1 -1og -1 -1.
5. If f:A->B is a function and IA: A->A, IB: IB: B->2B are identity functions then foIA= f=IBof
6. If f: A->B is a bijective function Then / f -1 = IA, fof -1 = IB
7. If f:A->B, g:B->Cand h:C->D are any 3 functions then ho(gof) = (hog) of or composition of functions is associative

C. Definition of real valued function

1. Definition of domain, Range
2. Algebra of real valued functions

2 Surds Evaluating Surds of the form

Cube root of the surds of the form

Rationalizing factors (upto 3rd degree)
3 Logarithms Definitions Introduction of common
logarithms

6 periods

Theorems:

log mn=log m+log n
log (m/n) = log m - log n
log m k = Klog m
log a m = log b m . log a b
Nature of Logarithms through graphs,
Logarithms functions
Types of Logarithms
4 Mathematical Induction Principle of Mathematical Induction;
Theorem of Principle of finite Mathematical Induction
Application of Mathematical Induction
S n, S n2, S n3 etc.,
x-y devides x"-y" for all positive integral
values of n and other divisibility problems

6 Periods

Vector Algebra 14 Periods

Addition Of Vector

1. Introduction of Vector as an ordered triad of real numbers- Representation of a vector as a directed line segment - Free and localized Vectors.
2. Classification of Vectors - Collinear or parallel, like, unlike vectors, Co-initial vectors, coplanar and non-coplanar vectors, position vector, unit vector etc.,
3. Addition of vectors - parallelogram and triangle laws - Properties of additions .
4. Multiplication of Vector by Scalar
5. Angle between two Non-Zero vectors. Vector of the points of division - Concurrence of Medians of a Triangle by Vector Method
6. Linear combination of Vectors - linearly dependent and independent vectors
7. Components of Vector in three dimension - Direction consines,
8. modulus of a vector, Right and Left hand systems - Orthogonal triad of Vectors.
9. Vector equation of line and plane in parametric from co linearity of three points and co planarity of four points.
10. Multiplication Of Vectors
Definition of the Scalar or dot product of two vectors its geometrical representation and Orthogonal projection of
11. Properties of Scalar product - Commutative, and distributive laws - condition for perpendicularity of two vectors a, b are perpendicular vectors, Then a.b = o.
12. Analytic expressions for scalar product in terms of i, j, k, angle between the two vectors. Some identities such as (a+b) 2 etc.
13. Proof by Vector Method of
14. angle in a semi-circle is a right angle
15. laws of cosines and projection formula in a triangle
16. Concurrency of the altitudes and perpendicular bisectors of sides of a triangle
17. = cos A cos B + sin A sin B formal form - Angle between two planes.
18. Vector equation of a plane in the normal form of two types:
Vector equation of sphere, angle between two planes.
19. Vector or Cross product of two vectors - Non-commutative vector product is distribution over addition
20. Vector product among i, j, k, sine or the angle between two Vectors, Unit vector perpendicular to a given pair of Vectors
21. Vector area of a parallelogram and a triangle - Proofs by vector method
(i) sin rule

22. Triple Products - Scalar triple product and its geometric interpretation. Co planarity of three vectors and deductions volume of a tetrahedron.
23. Vector area of a plane in different parts, skew lines - simple problems.
24. Vector triple product and its results.
25. Product of Four vectors - Scalar and vector product of Four vectors

Trigonometry

Topics/Chapter

Sub-topics/Sections/Sub-sections

Periods of Instructions
Graph & Periodicity Definition of Trigonometric functions
with the help of unit circle

3 periods
Particular values - Variation of sinq ,
cos ? ,tanq ? , Variation 3 periods
in values as changes periodicity and
extreme values, trigonometric ratio
of any angle

Graphs y=sin ? , Y=cos ? , y=tan ?
Trigonometric ratios of compound angles Trigonometric Ratios of compound
angles such as Summation Formulae
Sin(A+B),
Cos(A+B), Tan (A+B)

5 periods
Trigonometric ratios of Multiple and submultiples Angles Triogonometric ratios of 2A, 3A and A/2 (Multiple and submultiple Angles angles

4 periods
Transformations and Identities Transformation from sum to products Transformation from products to sums

4 periods

Trigonometric Equations Trigonometric Equations
Solving simple Trigonometric Equations
Inverse of all the six Trigonometric functions, domains, ranges-graphs.
Solving simple Equations involving Inverse trigonometric functions

5 periods

Hyperbolic functions Meaning of e, exponential of
the series
Definitions Domain and Range of
Hyperbolic and Inverse Hyperbolic functions
Addition formulae of Hyperbolic functions Sinh(x±y), Cosh(x±y) etc.,

3 periods
Properties of triangles Relation between the sides and angles of an triangle.
Half angle formulae and area of a triangle
Incircle and ex-circle of a triangle

10 periods
Heights & Distances Angles of Elevation and Depression
Problems involving one plane

10 periods
Complex Numbers Complex number as an ordered pair
of real numbers. Representation in the
form of a+ib, real and imaginary part equality of Complex Numbers
Fundamental operations on Complex Numbers.
Conjugate Complex Numbers
Modulus and amplitude of a Complex Numbers
Geometrical Representation of a complex number, Argand Plane and Argand diagram

6 periods
Demovieris Theorem Demovier's theorem for integral index and for rational index.
nth root of unity and its geometrial representation.
Cube roots of unity
Trigonometric Expansions Expansion of Trigonometric functions,
Sin n ? , Cos n ? as series, expansion of Tann n ? and Cos n ?
Expressing Sinnq and Cosq interms of Sines and Cosines of multiples of ?

7 periods

Mathematics IB
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Revised Syllabus Intermediate I Year
Mathematics Ib
(Coordinate Geometry And Calculus)

Coordinate Geometry
Dimensions: 65 Periods)
Locus 4
Translation and rotation of axes 5
Straight lines 20
Pair of Straight lines 20
Dimensional;
Coordinates 8
Direction cosines and ratios 8

Calculus:
Functions, Limits and Continuity 16
Derivatives, first order and second order derivatives 16
Applications of derivatives 20
Partial differentiation 8

Co-Ordinate Geometry - 2D

Locus Definition of locus
Equation of locus
Illustrations
Translation & Rotation of axes Translation of axes
Rotation of axes
Illustrations
Straight line General equation of a straight line and Forms of equation of a straight line
slope intercept form
Intercepts form
Point-slope form
Two point form
Normal form xCosx+ySinx=p
Symmetric form x-x 1 /sinq = y-y 1 /sinq = r
To reduce the general equation into different forms
Point of intersection of two straight lines
Family of straight lines passing through the point of intersection of two given
lines.
Pair of straight lines ax 2 +2hxy+by 2 =0 a pair of line through the origin

Angle between the lines ax 2 +2hyx+by 2 =0 conditions for coincidence perpendicularities
Bi-sector of the angles between the lines L 1 =0, L 2 =0

Combined equation of the bisectors of the angles between the lines ax 2
+2hxy+by 2 =0

If the general equation of the second degree in x & y i.e. ax 2 +2nxy+by 2 +2gx+2fy+c=0 represents a pair of straight lines then

abc+2fgh-af 2 -bg 2 - ch 2 =0, h 2 >ab, g 2 >ac and f 2 >bc
Converse of 4.5 without proof.

If S=ax 2 +2hxy+by 2 +2gx+2fy+c=0 represents a pair of straight lines then
ax 2 +2hxy+by 2 =0 represents the line through the origin, parallel to the above lines. Angle between the lines S=0 condition for these line to be (I) Parallel (ii) Perpendicular
Point of intersection of the lines S=0
Homogenization of the second degree equation with a first degree equation in
x and y
Co-Ordinate Geometry - 3D
Co-ordinates Co-ordinate planes - Co-ordinates of a point - Distance between two points in space.
To find the Co-ordinates of a point which divides the join of two points

(x, y, z), (x1 y1 z1) internally in the ratio m:n - centroid of a triangle and
tetrahedron
Direction cosines and ratios Direction cosines of a line, relation between the cosines l 2 +m 2 +n 2 =1
Direction cosines of a line, to find the direction cosines when direction ratios are given

Calculus
Functions, Limits and Continuity Function, Domain and Range of Continuity Function-Algebraic, Trigonometric,

Inverse Trigonometric, Hyperbolic, Step function and construction of graphs of logx, e l, lxl, (x)

Concepts of intervals and neighborhood
Limits - Definition of right hand limit, left hand limit, limit. Limits of f+g, f/g,
fog (without proof) Standard limits

(Limits 3,4, and 5 without proof)
Continuity - Definition and simple
illustration
Differentiation Introduction - Definition
Differentiation of a function at a point and on an Interval - Derivative of a
function - Differentiation of sum, difference, product and quotient of
functions.
Differentiation of algebraic, circular, exponential, logarithmic functions.

Derivatives of composite, implicit, parametric, inverse circular, hyperbolic
and inverse hyperbolic functions.

Logarithmic differentiation, Derivative of a function with respect of another
function.
Derivatives of first and second order
Application of
Derivative Infinitesimal - Differentials
Errors and approximations
Geometrical interpretation of a derivative
Equations of tangent, normal sub tangent, sub-normal at a point
Lengths of tangent, normal sub-tangent, sub-normal at a point.
Angle between two curves, orthogonally
Derivative as a rate measurer
Increasing and decreasing functions
Maxima and minima
Partial Differentiation Partial derivatives - First and second orders only

Homogeneous functions - Euler's theorem on homogeneous functions - functions - simple applications.

Economics
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Intermediate First Year Syllabus
(With Effect From 2003-2004)
Paper-I Introductory Economic Theory

UNIT-I: Nature And Scope Of Economics 14 Periods

1. Brief explanation of the concepts - Origin of the word Economics - Economic problem, Economic activity - Economics as a study of wants, efforts and satisfaction. Subject matter of Economics - Broad division
Consumption, production, exchange and distribution. Income and Employment, Planning and Development.
2. Definition of Economics:
Explanation and criticism of: Wealth definition of Adam Smith - Welfare definition of Alfred Marshall
Scarcity definition of Lionel Robbins - Development definition of Paul Samuelson.
3. Divisions of Economic theory:
Micro Economics - meaning, subject matter and importance.
Macro Economics - meaning, subject matter and importance.

UNIT-II: Basic Concepts: 10 Periods

1. Goods: Free and Economic goods. Consumption goods and Capital goods - Intermediate goods - Perishable and Non-perishable goods, Single use goods and durable goods.
2. Wealth: Meaning, Characteristics and Classification.
3. Income: A flow concept.
4. Welfare: Meaning, difference between wealth & welfare.
5. Utility: Meaning and classification.
6. Value: Value in use and value in exchange.
7. Price: Meaning.
8. Wants: Characteristics and classification.

UNIT-III: Analysis Of Demand: 10 Periods

1. Meaning of cordinal and ordinal utility.
2. The Law of Diminishing marginal utility - Statement of the Law, Illustration, assumptions, exceptions and importance.
3. Law of equi-marginal utility - Statement of the Law - Illustration, Assumptions and importance.
4. Demand - Concept of Demand, direct and derived demand, Demand function, determinants of demand, Individual demand schedule and curve, market demand schedule and curve, Law of demand and diagrammatic explanation - exceptions of the law, explanation of the downwards sloping demand curve, Income and cross demand with diagrams.
5. Price elasticity of demand - meaning - Measurement and Importance.

UNIT-IV: Theory Of Production: 15 Periods

1. Production Function - Simple illustrations.
2. Law of variable proportions - Statement of the Law, illustrations, assumptions and importance.
3. Returns to Scale - Mention of increasing, constant, diminishing returns only.

UNIT-V: Analysis Of Supply: 10 Periods

1. Concept of Supply - supply function - determinants of supply - Law of supply - supply schedule supply curve.
2. Cost and Revenue Analysis: Concept of cost - Real, money and opportunity cost - Fixed, Variable, total, average and marginal costs Average and Marginal costs Curves (short run only) concept of revenue - Total, Average and Marginal revenue - Average and Marginal Revenue Curves.

UNIT-VI: Price Determination: 25 Periods

1. Market: Meaning of market, types of market on the basis of area, period of time and competition.
2. Perfect Competition:
Features of Perfect competition and Imperfect competitions. Price Determination - Equilibrium of the Firm and Industry. Time element in Price determination (No diagrammatic representation).
3. Monopoly: Meaning - Features of Monopoly - Price determination.

UNIT-VII: Distribution: 10 Periods

1. Distribution of National Income among the four factors of production.
2. Rent: Meaning of economic rent, contract rent, rent as a differential surplus (Ricardo) - Scarcity rent, transfer earnings- Quasi rent.
3. Wages: Meaning of wages - Types of wages - Money wages, real wages and piece wages - Time wage - Factors affecting real wages.
4. Interest: Meaning of interest - Gross interest and Net interest.
5. Profit: Meaning of Profit - Gross profit and Net profit.

UNIT-VIII: National Income: 15 Periods

1. Definitions and concepts of National Income - Gross national Product - Gross Domestic Product Net National product - National Income at Factor prices - Personal income - Disposable income and per capita
income - Relationship between population and per capita income.
2. Components of National Income Consumption expenditure - Investment expenditure - Government
expenditure - net income in Foreign Trade.
3. Measurement of National Income :
Value added Method - Income Method - Expenditure Method.

UNIT-IX: Macro Economic Aspects: 30 Periods

1. Basic features of Classical theory of Employment - Basic Features of Keynesian theory of Employment.
2. Role of Government in Economic activities - Components of public revenue - Public Expenditure - Public Debt. (Elementary concepts only).
3. Role of International Trade in Economic Activities - Exports and Imports and Balance of payments (Elementary concepts only).

UNIT-X: Money And Inflation: 15 Periods

1. Concept of Money, Liquidity and Near Money - Functions of Money activities of Commercial Banks, Concepts of Primary Deposit, Secondary Deposit, Demand Deposit and Time Deposit - Types of Money.
2. Concept of Inflation - Types of Inflation - Economic Effects of Inflation.

[ Top ]
Intermediate First Year Syllabus
(With Effect From 2003-2004)
Economics-I

Paper-I Introductory Economic Theory

UNIT-I: Nature And Scope Of Economics: 15 Periods

1. Brief explanation of the concepts - Origin of the word Economics - Economic problem, Economic activity - Economics as a study of wants, efforts and satisfaction. Subject matter of Economics - Broad division
- Consumption, production, exchange and distribution. Income and Employment, Planning and Development.
2. Definition of Economics:
Explanation and criticism of: Wealth definition of Adam Smith - Welfare definition of Alfred Marshall
- Scarcity definition of Lionel Robbins - Development definition of Paul Samuelson.
3. Divisions of Economic theory:
Micro Economics - meaning, subject matter and importance.
Macro Economics - meaning, subject matter and importance.

UNIT-II: Basic Concepts: 10 Periods

1. Goods: Free and Economic goods. Consumption goods and Capital goods - Intermediate goods - Perishable and Non-perishable goods, Single use goods and durable goods.
2. Wealth: Meaning, Characteristics and Classification.
3. Income: A flow concept.
4. Welfare: Meaning, difference between wealth & welfare.
5. Utility: Meaning and classification.
6. Value: Value in use and value in exchange.
7. Price: Meaning.
8. Wants: Characteristics and classification.

UNIT-III: Analysis Of Demand: 25 Periods

1. Meaning of cordial and ordinal utility.
2. The Law of Diminishing marginal utility - Statement of the Law, Illustration, assumptions, exceptions and importance.
3. Law of equi-marginal utility - Statement of the Law - Illustration, Assumptions and importance.
4. Demand - Concept of Demand, direct and derived demand, Demand function, determinants of demand, Individual demand schedule and curve, market demand schedule and curve, Law of demand and
diagrammatic explanation - exceptions of the law, explanation of the downwards sloping demand curve, Income and cross demand with diagrams
5. Price elasticity of demand - meaning - Measurement and Importance.

UNIT-IV: Theory Of Production: 15 Periods

1. Production Function - Simple illustrations.
2. Law of variable proportions - Statement of the Law, illustrations, assumptions and importance.
3. Returns to Scale - Mention of increasing, constant, diminishing returns only.

UNIT-IV: Theory Of Production: 15 Periods

1. Production Function - Simple illustrations.
2. Law of variable proportions - Statement of the Law, illustrations, assumptions and importance.
3. Returns to Scale - Mention of increasing, constant, diminishing returns only.

UNIT-V: Analysis Of Supply: 10 Periods

1. Concept of Supply - supply function - determinants of supply - Law of supply - supply schedule supply curve.
2. Cost and Revenue Analysis:
Concept of cost - Real, money and opportunity cost - Fixed, Variable, total, average and marginal costs Average and Marginal costs Curves (short run only) concept of revenue - Total, Average and Marginal
revenue - Average and Marginal Revenue Curves.

UNIT-VI: Price Determination: 10 Periods

1. Market: Meaning of market, types of market on the basis of area, period of time and competition.
2. Perfect Competition:
Features of Perfect competition and Imperfect competitions. Price Determination - Equilibrium of the Firm and Industry. Time element in Price determination (No diagrammatic representation).
c) Monopoly: Meaning - Features of Monopoly - Price determination.

UNIT-VII: Distribution: 10 Periods

1. Distribution of National Income among the four factors of production.
2. Rent: Meaning of economic rent, contract rent, rent as a differential surplus (Ricardo) - Scarcity rent, transfer earnings- Quasi rent.
3. Wages: Meaning of wages - Types of wages - Money wages, real wages and piece wages - Time wage - Factors affecting real wages.
4. Interest: Meaning of interest - Gross interest and Net interest.
e) Profit: Meaning of Profit - Gross profit and Net profit.

UNIT-VIII: National Income: 15 Periods

1. Definitions and concepts of National Income - Gross national Product - Gross Domestic Product Net National product - National Income at Factor prices - Personal income - Disposable income and per capita
income - Relationship between population and per capita income.
2. Components of National Income Consumption expenditure - Investment expenditure - Government
expenditure - net income in Foreign Trade.
3. Measurement of National Income :
Value added Method - Income Method - Expenditure Method

UNIT-IX: Macro Economic Aspects: 30 Periods

1. Basic features of Classical theory of Employment - Basic Features of Keynesian theory of Employment.
2. Role of Government in Economic activities - Components of public revenue - Public Expenditure - Public Debt. (Elementary concepts only).
3. Role of International Trade in Economic Activities - Exports and Imports and Balance of payments (Elementary concepts only).

UNIT-X: Money And Inflation: 15 Periods

1. Concept of Money, Liquidity and Near Money - Functions of Money activities of Commercial Banks, Concepts of Primary Deposit, Secondary Deposit, Demand Deposit and Time Deposit - Types of Money.
2. Concept of Inflation - Types of Inflation - Economic Effects of Inflation.

English
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Syllabus:

Objective
To equip the learners with the skills (language, study, communication, and literary) required to function fluently, accurately, and appropriately in the target language in a variety of academic and real-life situations.
Main Reader

Part-A
Literary appreciation skills shall be imparted and tested for 50 Marks. Language skills, Study skills, and Communication skills shall be imparted and tested for 50 Marks.

Part-B
The total number of prose lessons shall be eight (8). Of the eight, one shall be a skit or one-act play in modern English and the other seven selections from modern prose. The maximum length of each lesson shall not exceed six pages.
The four prose passages and one skit / one-act play shall be on the following themes:
Empowerment of women /Information technology/bio-technology / scientific temper / Human emotions/qualities/values such as courage, love, honesty etc., Indian Culture and tradition / Human rights /
humanism.

Three lessons shall be customized for teaching language skills, communication skills, and study skills exclusively. The customized lessons shall focus on the teaching / learning of:
Skimming
Scanning
Reference skills
Information transfer
Listening (listen and repeat, listen and draw, listen and complete, listen and do, listen for gist, listen for specific information etc.,)
Writing (paragraph writing etc.,)
Speaking (greeting, introducing, thanking, leave-taking, requesting, seeking permission, asking for / giving information, agreeing, disagreeing)

Part-C
The total number of poems shall be give (5). The poems chosen shall be modern and native or non-native. The maximum length of each poem shall not exceed thirty lines. The themes for the poems shall be:
Values (human/moral)
Culture and heritage
Patriotism and world view
Adventure
Emotions
Triumph of good over evil

Part-D
All Lessons (Prose-8 and Poetry-5) in the main reader shall be exploited to the extent possible to teach the language skills study skills, literary appreciation skills, and communicative functions specified in this document.
All selections shall be culturally familiar, and of relevance to the learner.
The teacher shall present and give practice in the grammatical items relevant to each lesson in a graded manner.
Selections wherever possible may be preceded by a brief write-up about the author. All selections shall be accompanied by a glossary and relevant types of tasks / activities (essay writing, answering comprehension questions, dialogues, games, role playing, information gap, problem solving etc.,) The
teacher shall employ participatory, and interactive techniques to teach the
lessons.
First Book: " Petals Of Poetry And Prose "
Lessons:
Prose

1. Visionary Teachers and Scientists - Abdul Kalam From Ignited Minds.
2. Energy - Isaac Asimov
3. A Nation's Strength - Karan Singh
4. An ordinary Man in an Extraordinary Way - Gandhi - Humayun Kabir.
5. The Never-Never Nest (One act play) - Cedric Mount

Customized passages

1. TV. should never be held out as a carrot
2. The name spells Magic - Kapil Dev
3. She Ignited Aspirations: Kalpana Chawla

Poetry

1. All the World Is a Stage - Shakespeare
2. The Road Not Taken - Robert Frost
3. The Gift of India - Sarojini Naidu
4. The Talisman - Har Prasad Sharma
5. Character of Happy Life - H. Wotton

Second Book:
Non-detailed Text Book " Insights - A Collection Of Short Stores "
- A Flowering Tree
- A Hero
- The Cherry Tree
- Lalajee
- After Twenty Years
- Marriage is a Private Affairs

Third Book:
"Intermediate English Grammar" - Grammar, Study Skills & Communication skil

Sanskrit
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First Book: " Gyrvani Vilasah "

A. Poetry:

1. Epic Litt. - Valmiki Ramayana - Ayodhya Kanda 75th Canto 25 Slokas.
2. Descriptive Poetry - Kalidasa - Kumara Sambhavam 1 Canto - 17 Slokas.
3. Subhashitas - Bhatrihari - 15 Slokas.
4. Modern Poetry - Vasa Suryanarayana Sastry - Lokamanya Charitam - 25
Slokas.
5. Modern Poetry - Dr. Arka Somayaji - Purabharata Medini - 8 Slokas.
6. Selected Verses for Translation - Recitation - 15 Slokas

B. Prose:

1. Ancient Sanskrit Literature Bhoja Prabandha - 2 Stores 5 pages
2. 6 stories from selected Katha Vali - 5 pages

1. Scientific Story - Antariksha Vijayaha (Sansmskrita Bhasha Prachara Samithi) Dr. P. Sri Ramachandrudu - 4 Pages
2. Patriotic Lesson - Story - Manava Sevaiva Madhava Seva
3. Communication Skills - Yuktisali Vanik - Comedy Satire - 6 pages

C. Grammar

1. Sabdas - 15
2. Conjugations - 15
3. Sandhis - 06

Second Book: Non-detailed Text Book " NETAJI "