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]]>– Answer Key (Science + Diploma in Engineering)

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NEW BATCH for NEET + JEE from 23rd Nov – Register Today at our Marris Road Center, Aligarh. Call 7617733555 & 7617733444

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]]>The post DIFFERENTIATION appeared first on Turtle Tutorials.

]]>**DIFFERENTIATION LEC01**

1. Basics of Calculus

2. Concept of Differentiation

3. Slope Calculation

4. Identities used in Differentiation

5. Differentiation of single Function

6. Direct way to find differentiation

**DIFFERENTIATION LEC02**

1. Differentiation of single Function

2. Direct way to find differentiation

3. Product rule in Differentiation

4. Division rule in Differentiation

5. Concept of Increasing and decreasing Function

6. Concept of Maxima and Minima

**DIFFERENTIATION LEC03**

1. Division rule in Differentiation

2. Differentiation when one variable Function is in Degree over other

3. Differentiation of complex variables

4. JEE based question Discussion

**DIFFERENTIATION LEC04**

1. Differentiation when one variable Function is in Degree over other

2. Differentiation of complex constant degree over function

3. Differentiation of Infinite series

4. Differentiation of Equations in term of X and Y

5. Double differentiation

4. JEE previous year question Discussion

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]]>The post FUNCTION appeared first on Turtle Tutorials.

]]>**FUNCTION LEC01**

1. Definition of Function

2. Function on basis of Graph

3. Function on basis of bar diagram

4. Basics of Domain and Range

5. Domain of Function

6. Domain of Logarithmic Function

7. Inequality Calculation in Logarithm

**FUNCTION LEC02**

1. Domain of Logarithmic Function

2. Inequality Calculation in Logarithm

3. Trigonometric Inequality used in Logarithmic Function

4. JEE based question Discussion

**FUNCTION LEC03**

1. Domain of Logarithmic Function

2. Inequality Calculation in Logarithm

3. Trigonometric Inequality used in Logarithmic Function

4. Domain of Inverse Trigonometric Function

5. Domain using Modulus Inequality

**FUNCTION LEC04**

1. Domain of Square root

2. Domain when Function is in denominator

3. Domain of permutation and Combination

4. Combined domain when more than one function is combined

5. Trick used to find Domain of Function

**FUNCTION LEC05**

1. Range of Function

2. Range in Polynomial Function

3. Concept of Slope in Range

4. Range of Quadratic Equation

5. Range when one polynomial is over other

**FUNCTION LEC06**

1. Range in Polynomial Function

2. Concept of Slope in Range

3. Range of Quadratic Equation

4. Range when one polynomial is over other

5. Range of Trigonometric Function

**FUNCTION LEC07**

1. Range of Trigonometric Function

2. Solution of Inequality in case of Range

3. Maxima and Minima

4. Doubts discussion of Domain and Range

**FUNCTION LEC08**

1.Doubts discussion of Domain

2. Doubts discussion of Range

3. Assignment discussion of Differentiation

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]]>The post GRAPH AND FUNCTION appeared first on Turtle Tutorials.

]]>**GRAPH & FUNCTION LEC 01**

1. Introduction to Syllabus of IIT JEE

2. Marks distribution in JEE Mains and Advance

3. Strategy to Crack Entrance

4. What is Function

5. Function on basis of Interval

6. Function on basis of bar diagram

7. Function on basis of Graph

8. Types of Function

9. Difference between one-one and Many function on basis of Graph

**GRAPH & FUNCTION LEC 02**

1. Types of Function

2. Difference between one-one and Many function on basis of Graph

3. Onto or Into Function

4. One one or Many Function on basis of Domain and Range

5. Onto or Into Function on basis of Domain and Range

**GRAPH & FUNCTION LEC 03**

1. One one or Many Function on basis of Domain and Range

2. Onto or Into Function on basis of Domain and Range

3. JEE Level questions based on Graph

4. Number of one one Interval

5. Concept of Slope in Graph

6. Increasing and Decreasing Function

**GRAPH & FUNCTION LEC 04**

1. One one or Many Function on basis of Domain and Range

2. Onto or Into Function on basis of Domain and Range

3. Number of one one Interval

4. Increasing and Decreasing Function

5. Concept of Limits

6. Continous and Discontinuos Function

**GRAPH & FUNCTION LEC 05**

1. One one or Many Function on basis of Domain and Range

2. Onto or Into Function on basis of Domain and Range

3. Number of one one Interval

4. Increasing and Decreasing Function

5. Concept of Limits

6. Continous and Discontinuos Function

7. Differentiability in Graph

8. Concept of Maxima and Minima

**GRAPH & FUNCTION LEC 06**

1. Classification of Function

2. Graph of polynomial Function

3. General Graph of Polynomial Function

4. Detailed Analysis of Polynomial Function of degree one

5. Application of Modulus Function

**GRAPH & FUNCTION LEC 07**

2. Graph of polynomial Function

3. General Graph of Polynomial Function

4. Detailed Analysis of Polynomial Function of Degree one

5. Application of Modulus Function

6. Graph having more than Modulus Function

**GRAPH & FUNCTION LEC 08**

2. Graph of polynomial Function

3. General Graph of Polynomial Function

4. Detailed Analysis of Polynomial Function of Degree one

5. Application of Modulus Function

6. Graph having more than Modulus Function

7. Modulus on x as well as on whole Function

8. Basis of Integration in Case of Graph

9. Definite area of Graph using trick

**GRAPH & FUNCTION LEC 09**

1. Graph of polynomial Function

2. General Graph of Polynomial Function

3. Detailed Analysis of Polynomial Function of Degree two

4. Quadratic Equation

5. Graph of quadratic Equation on basis of discriminant

6. Modulus in Quadratic Equation

7. More than one Modulus in Quadratic Equation

**GRAPH & FUNCTION LEC 10**

1. Graph of Trigonometric Function

2. Shifting in Trigonometric Function

3. Modulus in Trigonometric Function

4. Multiple Modulus in Trigonometric Function

5. Graphical properties in graph of Trigonometric Function

**GRAPH & FUNCTION LEC 11**

1. Graph of Trigonometric Function

2. Shifting in Trigonometric Function

3. Modulus in Trigonometric Function

4. Multiple Modulus in Trigonometric Function

5. Graphical properties in graph of Trigonometric Function

6. Number of Solution by using Graph

**GRAPH & FUNCTION LEC 12**

1. Number of Solution in Trigonometric Function

2. Shifting in Trigonometric Function

3. Modulus in Trigonometric Function

4. Graphical properties in Trigonometric Function

5. Number of Solution by using Graph

**GRAPH & FUNCTION LEC 13**

1. Number of Solution in Trigonometric Function

2. Shifting in Trigonometric Function

3. Modulus in Trigonometric Function

4. Graphical properties in Trigonometric Function

5. Number of Solution by using Graph

6. Minimization and Maximization in Trigonometric Curve

7. Comparison in two Trigonometric curve

8. JEE previous year Question discussion

**GRAPH & FUNCTION LEC 14**

1. Graphical properties in Trigonometric Function

2. Modulus in Trigonometric Function

3. Number of Solution in Trigonometric Function

4. Minimization and Maximization in Trigonometric Curve

5. Graph of Logarithmic Function

6. Modulus in Logarithmic Function

7. Graphical properties in Logarithmic Function

8. JEE previous year Question discussion

**GRAPH & FUNCTION LEC 15**

1. Graph of Logarithmic Function

2. Modulus in Logarithmic Function

3. Graphical properties in Logarithmic Function

4. Graph of Exponential Function

5. Modulus in Exponential Function

6. Introduction to Stepwise Function

7. Graph of Greatest Integer Function

8. Integration in Greatest Integer Function

6. JEE previous year Question discussion

**GRAPH & FUNCTION LEC 16**

1. Doubt discussion of number of solution

2. Graph of Greatest Integer Function

3. Integration in Greatest Integer Function

4. Graph of Fractional Function

5. Application of Modulus in Fractional Function

6. Relation between Greatest Integer Function and Fractional Function

7. Graph of Signum Function

8. Modulus in Signum Function

8. Integration in Fractional Function

10. Integration in Signum Function

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]]>**DIFFERENTIATION LEC01 A**

1. Identity used in Differentiation

2. Complex Differentiation of single terms

3. Chain rule used in Differentiation

4. Multiplication rule in Differentiation

5. Division rule in Differentiation

6. Trick to find direct Differentiation

**DIFFERENTIATION LEC01 B**

1. Complex Differentiation of single terms

2. Differentiation of Inverse Trigonometric Function

3. Differentiation involving Trigonometric Identities

4. Discussion of JEE level Questions

**DIFFERENTIATION LEC01 C**

1. Complex Differentiation of single terms

2. Differentiation involving Trigonometric Identities

3. Differentiation involving Trigonometric Identities

4. Differentiation using logarithmic Identities

5. Differentiation when one Function is in degree over other

6. Differentiation of algebraic function having complex degree

**DIFFERENTIATION LEC02**

1. Differentiation when one Function is in degree over other

2. Differentiation of algebraic function having complex degree

3. Differentiation when Function is in degree over other and having different function is in Product

4. Differentiation of Infinite Series

**DIFFERENTIATION LEC03**

1. Differentiation when one Function is in degree over other

2. Differentiation when Function is in degree over other and having different function is in Product

3. Differentiation of Infinite Series

4. JEE Mains and Advance Question Discussion

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]]>The post INVERSE TRIGONOMETRIC FUNCTION appeared first on Turtle Tutorials.

]]>**INVERSE TRIGONOMETRIC FUNCTION LEC01**

1. Difference between Trigonometric and Inverse Trigonometric Function

2. Domain and Range of Inverse Trigonometric Function

3. Inverse Trigonometric identities and where to use

**INVERSE TRIGONOMETRIC FUNCTION LEC02 PART A**

1. JEE based Questions in Inverse Trigonometric Function

2. Inverse Trigonometric Function based on Trigonometric Identities

**INVERSE TRIGONOMETRIC FUNCTION LEC02 PART B**

1. Inverse Trigonometric Function based on series

2. JEE based Questions in Inverse Trigonometric Function

2. Inverse Trigonometric Function based on Trigonometric Identities

4. Inverse Trigonometric function outside their interval of Domain and Range

5. Graphical Analysis of Inverse Trigonometric Function

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]]>The post DETERMINANT appeared first on Turtle Tutorials.

]]>**DETERMINANT LEC01**

1. Basics of Determinant

2. Expansion of Determinant

3. Properties of Determinant

4. Elementary row Transformation in Determinant

5. Previous year Question Discussion of Determinant

**DETERMINANT LEC02**

1. Previous year Question Discussion of Determinant

2. Differentiation in Determinant

3. Question based on properties of Determinant

**DETERMINANT LEC03**

1. Question based on Differentiation of Determinant

2. Solution of Linear Equations

3. Consistent and Non Consistent Solution for two Variable

4. Consistent and Non Consistent Solution for three Variable and three Equation

5. Crammers Rule

**DETERMINANT LEC04**

1. Solution of Linear Equations

2. Consistent and Non Consistent Solution for two Variable and three Equation

3. Application of Determinant

4. Rank of Matrix

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]]>The post MATRICES appeared first on Turtle Tutorials.

]]>**MATRICES LEC01**

1. What is Matrices

2. Basic difference between Matrices and Determinant

3. Representation of Matrices and Determinant

4. Order of Matrix

5. Types of matrices

6. Algebraic operation in Matrices

**MATRICES LEC02**

1. Multiplication based problem in previous year JEE

2. Basics of Determinant

3. Transpose of Matrix

4. Symmetric and Skew Symmetric Matrix

5. Property related to Transpose of Matrices

**MATRICES LEC03**

1. Multiplication based problem in previous year JEE

2. Jee based question on Transpose of Matrix

4. Minor and Cofactor of Matrix

5. Tricks on Minor and Co-Factor of Matrix

6. Adjoint of Matrix

7. Inverse of Matrix

8. Remaining types of Matrices

9. Property related to Adjoint of Matrix

**MATRICES LEC04**

1. Multiplication based problem in previous year JEE

2. Jee based question on Transpose of Matrix

4. Minor and Cofactor of Matrix

5. Tricks on Minor and Co-Factor of Matrix

6. Adjoint of Matrix

7. Inverse of Matrix

8. Remaining types of Matrices

9. Property related to Adjoint of Matrix

**MATRICES LEC05**

1. Multiplication based problem in previous year JEE

2. Jee based question on Transpose of Matrix

3. Miscellaneous concept and Questions

**MATRICES LEC06**

1. Multiplication based problem in previous year JEE

2. Jee based question on Transpose of Matrix

3. Miscellaneous concept and Questions

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]]>Students enrolled in XI Standard (Science Subjects) will be eligible to appear for KVPY Stream SA.

A minimum of 75% (65% for SC/ST/PWD) marks in aggregate in MATHEMATICS and SCIENCE subjects in the X Standard Board examination.

The fellowship of the students selected under this stream will be activated only if they join an undergraduate course in Basic Sciences (B.Sc./B.S./B.Stat./B.Math./Int. M.Sc./Int. M.S.) after having secured a minimum of 60% (50%for SC/ST/PWD) marks in aggregate in Science subjects in the XII standard/(+2) Board Examination.

**Mode of Exam** – Online (Computer Based Test).

**Paper Language** – Both in English & Hindi Language

**Exam Duration** – 3 hours

**Maximum Marks** – 100

**Question Pattern**: Multiple choice type questions The question paper will contain two sections: PART I & PART II. There will be four sections in PART I & PART II.***All the questions are compulsory to attempt.**

In PART I of both the Stream, one mark will be awarded for the correct response& 0.25 marks will be deducted for an incorrect response. & In PART II, two marks will be awarded for correct response & 0.25 marks will be deducted for an incorrect response.

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]]>**RELATION – LEC 01 – PART A**

1. What is Relation

2. Types of Relation

3. Examples of Types of Relation

4. NCERT question Discussion

**RELATION – LEC 01 – PART **B

1. Types of Relation

2.Relation in case of given set

3. Jee Previous year Question discussion

**GRAPH AND FUNCTION**

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**GRAPH & FUNCTION – LEC01**

1. What is function

2. Types of Function

3. Graphical Analysis of Function

4. To check ONTO or INTO Function Graphically

**GRAPH & FUNCTION – LEC02**

1. Types of Function

2. One One or Many one

3. Onto or Into Function

3. Graphical Analysis of Function

4. To check ONTO or INTO Function Graphically

5. Onto or Into Function depending upon Domain and Range

**GRAPH & FUNCTION – LEC03**

1. Onto or Into Function depending upon Domain and Range

2. One One or Many one

3. Onto or Into Function

4. Number of one one interval

5. Concept of Slope

6. Increasing and Decreasing Function

7. Concept of Differentiability

**GRAPH & FUNCTION – LEC04**

1. Concept of Modulus Function

2. Concept of Modulus on X

3. Concept of Modulus on complete Function

4. Concept of shifting

4. Concept of Modulus on Y

5. Area in Modulus Function

**GRAPH & FUNCTION – LEC05**

1. Concept of Modulus Function

2. Concept of Modulus on X

3. Concept of Modulus on complete Function

4.Graph of polynomial function

5.Concept of shifting

6. Concept of Modulus on Y

7. Area in Modulus Function

8. Concept of Differentiability

**GRAPH & FUNCTION – LEC06**

1. Concept of Modulus Function

2. Concept of Modulus on X

3. Concept of Modulus on complete Function

4. Graph of polynomial function

5. Area in Modulus Function

6. Graph of Trigonometric Function

7. Modulus in Trigonometric Function

**GRAPH & FUNCTION – LEC07**

1. Graph of Trigonometric Function

2. Number of Solution by Graphical Method

3. Interval Break in Trigonometric Function

4. Intersection of two curve and their respective solution

**GRAPH& FUNCTION-LEC08-A**

1. Graph of complex Trigonometric Function

2. Number of Solution by Graphical Method

3. Solution in Trigonometric Equation

4. Intersection of two curve and their respective solution

5. Comparison in two curve

**GRAPH& FUNCTION-LEC08-B**

1. Graph of complex Trigonometric Function

2. Comparison in two trigonometric function on basis of slope

3. Solution in Trigonometric Equation with Algebraic function

4. Intersection of two curve and their respective solution

**GRAPH& FUNCTION-LEC09-A**

1. Maximization and Minimization between two curve

2. Graph of complex Trigonometric Function

3. Comparison in two trigonometric function on basis of slope

4. Solution in Trigonometric Equation with Algebraic function

5. Intersection of two curve and their respective solution

**GRAPH& FUNCTION-LEC09-B**

1. Maximization and Minimization between two curve

2.Integration in comparison of curve

3. Comparison in two trigonometric function on basis of slope

**GRAPH& FUNCTION-LEC10**

1. Introduction to Logarithm

2. Graphical property related to Logarithmic Function

3. Modulus in Logarithmic Function

4. Shifting in Logarithmic Function

5. Basic Concept of Inverse of Function

6. Introduction to Exponential Function

2. Graphical property related to ExponentialFunction

3. Modulus in Exponential Function

**GRAPH& FUNCTION-LEC11**

1. Comparison in Logarithmic Function with Exponential function

2. Maximization and Minimization in Logarithmic and Exponential Function

3. Integration in Logarithmic and Exponential function

4. Shifting in Logarithmic Function

5. Concept of Differentiability in Logarithmic and Exponential Function

**GRAPH& FUNCTION-LEC12**

1. Introduction to greatest Integer Function

2. Graph of Greatest Integer Function

3. Integration in Greatest Integer Function

4. Trick to find Area in Greatest Integer Function

**GRAPH& FUNCTION-LEC13-A**

1.Modulus in Greatest Integer Function

2. Graph of Greatest Integer Function with multiple degree on it

3. Integration in Greatest Integer Function with degree

4. Greatest Integer Function on Trigonometric Function

5. Integration in Greatest Integer Function on Trigonometric Function

6. Integration in Greatest Integer Function on Trigonometric Function

**GRAPH& FUNCTION-LEC13-B**

1.Modulus in Greatest Integer Function

2. Trick to find Area in Greatest Integer Function

3. JEE based important Questions on Greatest Integer Function

4. Integration in Greatest Integer Function

5. Integration in Greatest Integer Function with Modulus Function

**GRAPH& FUNCTION-LEC14**

1.Modulus in Greatest Integer Function

2. Trick to find Area in Greatest Integer Function

3. JEE based important Questions on Greatest Integer Function

4. Integration in Greatest Integer Function

5. Integration in Greatest Integer Function with Modulus Function

**GRAPH& FUNCTION-LEC15 A**

1.Modulus in Greatest Integer Function

2. Modulus Function with variable function on its degree

3. JEE based important Questions on Greatest Integer Function

4. Modulus Function in degree of Greatest Integer Function

5. Greatest Integer Function in degree of Modulus Function

6. Fractional Function in Degree of Modulus Function

**FUNCTION**

**FUNCTION & ITS TYPES LEC01**

1. Definition of Function

2. Theoretical and Graphical Explanation of Function

3. Function with help of bar Diagram

4. Types of Function

5. Theoretical Method to explain One one or Many function

**FUNCTION & ITS TYPES LEC02**

1. JEE Questions on One one or Many Function

2. One one or Many Function in Algebraic Function

3. Trick to find One One or Many Function

4. Slope Method to understand One One or Many function

**FUNCTION & ITS TYPES LEC03**

1. JEE Questions on One one or Many Function

2. One one or Many Function by slope Method

3. One one or Many Function when more than one Function is involved

4. Basics of Onto or Into Function

4. One one or Many one Function when domain and range is given

**FUNCTION & ITS TYPES LEC04**

1. One one or Many Function by slope Method

2. One one or Many Function when more than one Function is involved

3. Basics of Onto or Into Function

4. One one or Many one Function for Cubic Polynomial by Slope Method

**FUNCTION & ITS TYPES LEC05**

1. One one or Many Function depending on Domain and Range

2. One one or Many Function when more than one Function is involved

3. Concept of Onto or Into Function

4. One one or Many one Function for Odd degree Polynomial by Slope Method

**FUNCTION & ITS TYPES LEC06**

1. Concept of Domain and Co-domain

3. Basics of Range of Function

3. One one or Many Function depending on Domain and Range

**FUNCTION & ITS TYPES LEC0**7

1. One One or Many Function in Trigonometric Function

2. Basics of Range of Function

3. Onto or Into Function depending on Domain and Range in Trigonometric Function

4. Injective or Surjective Function

5. When function becomes Bijective

**FUNCTION & ITS TYPES LEC08**

1. Injective or Surjective Function

2. When function becomes Bijective

3. Invertible Function

4. JEE based question on Inverse of Function

**FUNCTION & ITS TYPES LEC09**

1. Invertible Function

2. Overview of covered Topic of Function

3. Odd and Even Function

4. JEE based question on Odd and Even function

**FUNCTION & ITS TYPES LEC10**

1. Domain of Function

2. Domain of Logarithmic Function

3. Domain of Square root

4. Domain of Inverse trigonometric Function

5. Domain of permutation and combination

6. Trick to find Domain of Function

7. JEE based questions on Domain of Function

**FUNCTION & ITS TYPES LEC11 – A**

1. Domain of Function

2. Trick to find domain of function

3. JEE based questions on Domain of function

4. Domain based on inequality

5. Concept of Modulus of Function

**FUNCTION & ITS TYPES LEC11 – B**

1. Domain of Function

2. Range of Function

3. Composition of Function

4. Question based on Composition and Inverse of Function

5. Value of Function

**FUNCTION & ITS TYPES LEC11 – C**

1. Value of function

2. Composition of Function

3. JEE based question on value of function

4. Range of Complex Function

5. Miscellanous question based on concept of slope

6. Range of Algebraic Function

**FUNCTION & ITS TYPES LEC12 **

1. Range of Algebraic Function in different form

2. Range of Modulus Function

3. JEE based Question on Algebraic Function

4. Range of Complex Function

**FUNCTION & ITS TYPES LEC13**

1. Range of Complex Function

2. JEE based Questions on Range of Function

3. Range of Greatest Integer Function

4. Range of fractional Function

**FUNCTION & ITS TYPES LEC14**

1. Range of Complex Function

2. JEE based questions on Range of Function

3. Period of Function

4. Period of Trigonometric Function

5. Effect of Modulus Function on Period of Function

6. Period of Stepwise Function

7. Period of more than one combined Function

**FUNCTION & ITS TYPES LEC15**

1. Range of Complex Trigonometric Function

2. Properties of Periodic Function

3. Exception in Period of Function

4. JEE based question in Period of Function

5. Period of Function in value based Function

**FUNCTION & ITS TYPES LEC16**

1. Miscellaneous concept in Composition of Function

2. Jee previous year Question Discussion

3. Complex Question in Value of Function

4. Odd and Even Function

**FUNCTION & ITS TYPES LEC17**

1. Miscellaneous question of Function

2. Jee Previous year question

3. Tricks to find Period of Function

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