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NCERT Moments Supplementary Reader in English for Class 9th

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  • Q1
    What is the NCERT Moments Supplementary Reader?
    A1

    The NCERT Moments Supplementary Reader is an English textbook designed for 9th standard students, published by NCERT, featuring a collection of captivating stories that explore universal themes.

  • Q2
    How can this book help improve my child's English skills?
    A2

    The reader enhances language skills through engaging narratives that encourage reading comprehension, vocabulary development, and critical thinking, while also fostering emotional intelligence and empathy.

  • Q3
    Is this book aligned with the CBSE syllabus?
    A3

    Yes, the NCERT Moments Supplementary Reader is aligned with the CBSE syllabus for Class 9, serving as a complement to the main English curriculum.

  • Q4
    What subjects or themes are covered in the reader?
    A4

    The book explores a variety of themes such as childhood, adventure, compassion, resilience, and the complexities of human relationships, making it rich in both literary content and moral lessons.

  • Q5
    What types of stories are included in the reader?
    A5

    The collection includes diverse narratives, ranging from poignant tales of childhood and adventure to uplifting stories of hope, sacrifice, and moral reasoning.

  • Q6
    Who would benefit most from reading this book?
    A6

    The book is specifically tailored for 9th standard students, but it can also be valuable for teachers, parents, and anyone interested in enhancing their understanding of English literature.

  • Q7
    Can this book be used for self-study?
    A7

    Absolutely! It is a great resource for independent study, providing students with engaging content to deepen their understanding of English while enhancing their reading skills.

  • Q8
    Will this book prepare students for English exams?
    A8

    Yes, reading and analyzing the stories will improve comprehension and critical thinking skills, which are essential for performing well in English assessments.

  • Q9
    How do the stories in the reader promote critical thinking?
    A9

    The narratives contain moral dilemmas and thought-provoking situations, encouraging readers to engage in discussions, analyze characters' decisions, and reflect on their own values.

  • Q10
    Are there any illustrations or visual aids in this reader?
    A10

    While the main focus is on the text and storytelling, some editions may include illustrations or visual aids to enhance the reading experience and clarify themes.

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1. Power Series Solution of Differential Equations 
1. Power Series 
2. Ordinary and Singular Points
3. Power Series Solution about an Ordinary Point
4. Regular and Irregular in Singular Points
5. Power Series Solution about Regular Singular Point (Frobenius Method)
2. Bessel's Equations and Bessel's Funtions
1. Beta and Gamma Functions
2. Bessal's Differential Equation Bessel's Functions
3. Recurrence Relations for Bessel's Function
4. Generating Function for Bessel's Function
5. Orthogonality of Bessel's Functions
6. Integral Form of Bessel's Function
3. Legendre's Equation and Legendre's Functions
1. Legendre's Equation and Legendre's Function
1.1 Another Form of Pn (x)
2.Generating Function for Pn (x)
3. The Recurrence Relations for Pn (x)
4.Laplace's Definite Integral for Pn (x) 
5. Rodrigues' Formula
6.Orthogonal Property of Legendre's Polynimials
4. Partial Differential Equations of First Order 
1. Partial Differential Equations
2. Origin of First Order Partial Differential Equations
2.1 Formation of Partial Differential Equations by Elimination of Two Arbitary Function
2.2 Formation of Partial Differential Equation  by Elimination of Arbitary Function
3. Lagrange's Solution of The Linear Partial Differential Equations
4. Geometrical Interpretation of Lagrange's Linear Equations
5. Integral Surface Passing Through a given Curve 
6.Surfaces Orthogonal to given System of Surfaces
5.The Laplace Transforms
1. Definition of Extension of Laplace Transform 
2. Linearity Property
3. Laplace Transforms of SOme Elementary Functions
4. Shifting Properties 
5. Change of Scale Property
6. Laplace Transform of Derivatives
7. Multipilication by tn
8. Laplace Transform of Integrals
9. Division by t
10. Laplace Transform of Laplace Transform 
6. Inverse Laplace Transform 
1. Linear Property
2. Shifting Properties
3. Change of Scale Property
4. Inverse Laplace Transform of Derivatives
5. Division by s 
6. Inverse Laplace Transform of Integrals
7. Method of Partial Fractions to Evaluate Inverse Laplace Transform
8. The Convolution Property
7. Applications of Laplace Transforms 
1. Solution of Ordinary Differential Equations with Constant Coefficients
2. Solution of Ordinary Differential Equations with Variable Coefficients
3. Solution of Simultaneous Ordinary Differential Equations
DIFFERENTIAL EQUATIONS- II
Max. Marks : 30
Time : 3 Hours
Note: 1. The syllabus has been split into two Units: Unit-I and Unit-II. Four questions will be set
from each Unit.
2. A student will be asked to attempt five questions selecting at least two questions from each
Unit. Each question will carry 6 marks.
 
Unit-I
Series solution of differential equations-Power Series method, Bessel and Legendre equations.
Bessel functions of First and Second kind. Legendre function. Generating function. Recurrence
relation and orthogonality of Bessel and Legendre function.
Partial Differential Equations: Origin of first order Partial Differential Equations, Linear Equation of
first order, Integral surfaces passing through a given curve, surfaces orthogonal to a given system of surfaces.

Unit-II
Inverse Laplace transforms- Linearity property, Shifting properties, Change of Scale Property.
Inverse Laplace transforms of derivatives and integrals, Convolution theorem.
Applications of Laplace Transforms - Solution of differential equations with constant coefficients,
Solution of differential equations with variable coefficients, Solution of simultaneous differential equations.
Laplace Transformation-Linearity of the Laplace transformation. Existence theorem for Laplace
transformations, Shifting Theorems, Laplace transforms of derivatives and integrals, Multiplication of tn ,
Division by t .

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