Thursday, February 28, 2019

CLASS 12TH MATHEMATICS PART (I) NCERT IMPORTANT QUESTIONS

CLASS 12TH MATHEMATICS PART (I)

IMPORTANT QUESTIONS LIST OF NCERT

 

Every Student thinks Mathematics as a difficult subject especially Class 12th Mathematics. But in my opinions, it is one of the most scoring subjects in class 12. It just demands concentrations and more and more practice to improve score in Mathematics.
C.B.S.E Class 12th board exam will be held in the month of March. For all students who appearing and preparing for this exam, I have given some important Chapter wise questions of NCERT with the respective marking scheme of those chapters.
It is recommended to take these questions as important questions perspective, not as questions out of which whole paper is set.  

 

Chapter-1: RELATIONS AND FUNCTIONS


Weightage of Chapter= 5 Marks
This Chapter carries 5 Marks which comprising of one 1 mark and 4 Mark questions.

For One Mark:

Important questions of NCERT are:
Ex. 1.1: Q 15, 16 Examples: 4, 10, 11 and 14
Ex1.2: Q 6 Examples: 28
Ex1.3: Q 3,5,13 Examples: 35
Miscellaneous: Q 3, 16, 17, 30

For 4 Marks:

Examples: 2, 3, 12
Ex1.1: 8, 11, 12, 13, 14, 17, 25
Ex1.2: Q 2, 7, 9, 10
Ex1.3: Q 7, 8, 9, 14
Ex1.4: Q 5, 6, 9
Miscellaneous: Q 4

Chapter-2: INVERSE FUNCTIONS


Weightage of Chapter= 5 Marks
This Chapter carries 5 Marks which comprising of one 1 mark and 4 Mark questions.

For One Mark:

Important questions of NCERT are:
Questions related to Principal Values as in Ex 2.1
Ex2.2: Q 16, 17, 18, 19, 21
Examples: 9

For 4 Marks:

Ex2.2: Q 8, 11, 13, 14, 15
Examples: 10, 11, 12
Miscellaneous: Q 7, 10, 11, 12, 16, 17

Chapter-3: MATRICES


Weightage of Chapter= 8 Marks
This Chapter carries 8 Marks which comprising of one 2 mark and 8 Mark questions.

For 2 Marks:

Important questions of NCERT are:
Examples: 8, 9, 10, 17, 21, 25
Ex 3.1: Q 7, 9
Ex 3.2: Q 8, 9, 10, 11, 12, 13
Ex 3.3: Q 6, 7, 9, 12
Miscellaneous: Q 5, 6, 7, 9, 13, 14, 15

For 6 Marks:

Examples: 22, 24, 26, 28
Ex 3.2: Q 15, 16, 17, 18
Ex 3.3: Q 10
Ex 3.4: Q 15, 16, 17

  

Chapter-4: DETERMINANTS


Weightage of Chapter= 5 Marks
This Chapter carries 5 Marks which comprising of one 1 mark and 4 Mark questions.

For 1 Mark:

Important questions of NCERT are:
Examples: 4, 5, 9, 12, 17, 18, 31
Ex 4.1: Q 3, 4, 7, 8
Ex 4.2: Q 15
Ex 4.3: Q 1, 3, 5
Ex 4.4: Q 3, 4
Ex 4.5: Q 1, 17, 18       Miscellaneous: Q 19

For 4 Marks:

Examples: 11, 13, 14, 15, 16, 22, 24, 25, 32, 33
Ex 4.2: Q 11, 12, 13, 14
Ex 4.5: Q 13, 15, 16
Ex 4.6: Q 11, 13, 14, 15
Miscellaneous: Q 4, 6, 12, 13, 16 

Chapter-5: CONTINUITY AND DIFFERENTIABILITY


Weightage of Chapter= 8 Marks
This Chapter carries 8 Marks which comprising of two 4 Mark questions.

For 4 Marks:

Examples: 30, 32, 33, 37, 40. 41, 42, 43, 45(iii), 47, 48
Ex 5.1: Q 8, 14, 17, 18, 23, 24, 26 to 30
Ex 5.5: Q 1, 2, 5, 6, 8 to 15
Ex 5.6: Q 6, 8, 11
Ex 5.7: Q 12 to 17
Ex 5.8: Q 1, 4, 5
Miscellaneous: Q 6, 9, 10, 11, 12, 14, 15, 16, 17, 23 

Chapter-6: APPLICATIONS OF DERIVATIVES


Weightage of Chapter= 11 Marks
This Chapter carries 11 Marks which comprising of One 1 Marks, One 4 Mark, and One 6 Mark questions.

For 1 Mark:

Examples: 2, 4, 5, 14, 15, 20, 24, 25
Ex. 6.1: Q2, 5, 7, 8, 10, 11, 14, 16
Ex. 6.2:Q1, 2,
Ex. 6.3: Q2, 3, 6, 7, 8, 26, 27

For 4 Marks:

Examples: 11, 12, 13, 16, 17, 19, 22, 23, 32, 40, 41, 43, 45, 47
Ex. 6.2: Q3, 5, 8, 9, 14, 16
Ex. 6.3: Q10, 11, 12, 16, 18, 19, 20, 23, 25
Ex. 6.4: Q1, 3, 8
Ex. 6.5: Q3, 6, 7, 10
Misc.: Q1, 4, 6, 9, 13, 20, 24

For 4 Marks:

Examples: 11, 12, 13, 16, 17, 19, 22, 23, 32, 40, 41, 43, 45, 47
Ex. 6.2: Q3, 5, 8, 9, 14, 16
Ex. 6.3: Q10, 11, 12, 16, 18, 19, 20, 23, 25
Ex. 6.4: Q1, 3, 8
Ex. 6.5: Q3, 6, 7, 10
Misc.: Q1, 4, 6, 9, 13, 20, 24

For 6 Marks:

Examples:  50
Ex. 6.5: Q17 to Q26
Misc.: Q10, 11, 12, 15, 17, 18

At last, it is your hard work which helps you to score good marks in your examinations,

So, keep going your hard work and ALL THE BEST for your examinations. 
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Tuesday, February 12, 2019

Previous Year Paper Maths Class 12 2019


CLASS 12th Maths 2019 Solved Papers

I have just given a Solved paper of CBSE 2019 for all students who were appearing for Class 12th.
It is just to help students so that they were able to understand what kind of questions asked in examination.
And they have to prepare for them to get more marks in CBSE Mathematics Exam.



































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Chapter wise Notes


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Types of Relation


What are the Types of Relations?


1. Empty Relation
2. Universal Relation
3. Reflexive Relation
4. Symmetric Relation
5. Transitive Relation




1   1.     What is Empty Relation?

                       A Relation R in any set say A is said to be Empty Relation if no elements of                               Set A is related no elements of itself.
                              i.e.  R = ะค  A×A.

2.      What is Universal Relation? 

                                  A Relation R in any set say A is said to be Universal Relation if all elements of Set A is related to its all elements.
                            i.e.  R = A×A.

     3.  What is Reflexive Relation? 

                             A Relation R in any set say A is said to be Reflexive Relation if all same elements present in any Relation.
     i.e. if (a, a) R, for every a A.
     For Example R = {(1, 1), (2, 2), (a, a), (x, x)}
    

         4.   What is Symmetric Relation?

                            A Relation R in any set say A is said to be Symmetric Relation if all same elements present in any Relation R then its mirror image also presents in that Relation.
      i.e. if (a, b) R,  then it implies (b, a)  R for all a, b A.
      For Example R = {(1, 2), (2, 1), (a, b), (b, a), (x, y), (y, x)}
    

     5. What is Transitive Relation?  

                              A Relation R in any set say A is said to be Transitive Relation 
       i.e. if (a, b) R,  (b, c)  R then it implies (a, c)  R for all a, b, c A.
       For Example R = {(1, 2), (2, 1), (1, 1), (b, a), (a, y), (b, y)}
      

        Note:    Equivalence Relation:

                        A Relation R which is Reflexive, Symmetric and Transitive said to be equivalence Relation.



                                  

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