Class 12 Ch-2,3;4 and 5 test

Test Paper of Class 12 

This test is just for Students who wants to practice for CBSE Mathematics in order to score more marks.

I have made this test for practice purpose for students.

And Paper contains many previous year and important questions from Board perspective.

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Set assignment

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CLASS 12TH MATHEMATICS PART (II) IMPORTANT QUESTIONS OF NCERT

Part-II

CLASS 12^TH MATHEMATICS PART (II)

IMPORTANT QUESTIONS LIST OF NCERT

Some of the quotations for Mathematics

1. “Do not worry about your difficulties in mathematics. I can assure you mine are still greater.” – Albert Einstein

2. “The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.” – Charles Caleb Colton

3. “Without mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is numbers.” – Shakuntala Devi

4. “In mathematics, the art of proposing a question must be held of higher value than solving it.” – Georg Ferdinand Ludwig Philipp Cantor

5. “The only way to learn mathematics is to do mathematics.” – Paul Halmos

All the above quotations suggest that Mathematics is easy and scoring subject so do practice to improve it.

For making your practice easy I have provided you important questions of Class 12^Th Mathematics NCERT Part(II) with weight age.

Chapter-7: INTEGRATION

Weight age of Chapter= 13 Marks

This Chapter carries 13 Marks which comprising of one 1 mark and Three 4 Mark questions.

For 1 Mark:

Examples: 3, 7, 9, 14, 18, 19,

Ex. 7.1: Whole exercise

Ex. 7.2: Q 1 to 9, 18, 19, 21, 38, 39

Ex. 7.3: Q 1, 2, 4, 5, 7, 8, 12, 24

Ex 7.4: Q 1, 2, 3, 4, 6

Ex 7.6: Q 1 to 9

Ex 7.7: Q 1, 2, 3, 10, 11

Ex 7.9: Q 1 to 12, 21, 22

Ex 7.10: Q 1, 3, 4, 5, 7

Ex 7.11: Q 1 to 4, 13, 20

For 4 Mark:

Examples:  6, 10, 15, 16, 22, 25, 27, 30, 35, 36, 40, 41, 43, 44,

Ex. 7.2: Q 9, 12, 32, 34, 37

Ex. 7.3: Q 3, 4, 10, 16, 19, 22

Ex 7.4: Q 15, 18, 21, 22, 23

Ex 7.5: Q 3, 6, 9, 16, 17, 18,

Ex 7.6: Q 14, 17, 18, 20

Ex 7.8: Q 2, 4, 6

Ex 7.11: Q 8, 10, 16

Miscellaneous: Q 10, 14, 18, 19, 20, 23, 25, 30, 33, 40, 42

Chapter-8: APPLICATIONS OF INTEGRALS

Weight age of Chapter= 6 Marks

This Chapter carries 6 Marks which comprising of only one 1 questions.

For 6 Mark:

Examples: Q 3, 4, 5, 7, 8, 9, 10, 13

Ex 8.1: Q 4 to 9

Ex 8.2: Q 1, 2, 4, 5, 6

Miscellaneous: Q 4 to 11, 13, 14

Chapter-9: DIFFERENTIAL EQUATIONS

Weight age of Chapter= 6-8 Mark

This Chapter carries 6-8 Marks which comprising of two 4 Mark or One 6 Mark questions.

Examples: Q 12, 13, 15, 16, 17, 18, 20, 21, 22, 27, 28

Ex 9.4: Q 4, 5, 11, 14

Ex 9.5: Q 7, 9, 10, 13, 14

Ex 9.6: Q 5, 6, 8. 13, 14, 15

Miscellaneous: Q 7, 9, 10, 11 to 16

 

Chater-10: VECTORS

Weight age of Chapter= 8 Marks

This Chapter carries 8 Marks which comprising of TWO 1 Marks and One 4 Mark questions.

For 1 Mark:

Examples: 3, 4, 6, 9, 10 to 17, 21, 23, 24, 25

Ex 10.2: Q 7 to 17

Ex 10.3 Q 1 to 10, 16, 17

Ex 10.4: Q 1, 2, 5, 9, 10, 11

Miscellaneous: Q 5, 11, 17, 18, 19 

For 4 Marks:

Examples: 29, 30

Ex 10.3 Q 11, 13

Miscellaneous: Q 8, 9, 10, 12, 13, 14, 15

Chapter-11: THREE DIMENSIONAL GEOMETRY

Weight age 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: 1, 5, 8, 9, 10, 19

Ex 11.1: Q 1, 3, 4

Ex 11.2; Q 2 to 8

Ex 11.3: Q 3, 7, 8

For 4 and 6 Marks:

Examples: 20, 22, 23, 25, 27, 28,

Ex 11.2: Q 12 to 17

Ex 11.3: Q 6, 9 to 12

Miscellaneous: Q 8 to 15, 18, 20, 21

Chater-12: LINEAR PROGRAMMING

Weight age of Chapter= 6 Marks

This Chapter carries 6 Marks which comprising of only one 1 questions.

For 6 Marks:

Examples: 2, 4, 6, 8, 9, 10, 11

Ex 12.1: Q 5 to 9

Ex 12.2: Q 2, 3, 5, 7, 10

Miscellaneous: Q 2, 3, 4, 6, 8, 10

Chater-13: PROBABILITY

Weight age of Chapter= 10 Marks

This Chapter carries 10 Marks which comprising of One 4 Marks and One 6 Mark questions.

For 4 Marks:

Examples: 7, 25, 26, 27, 29, 31, 36, 37

Ex 13.1: Q 10, 11, 12, 13

Ex 13.2: Q 8, 11, 14, 16

Ex 13.4: Q 8, 9, 14, 15

Ex 13.5: Q 4 to 10

Miscellaneous: Q 4, 5, 6, 8, 10, 11, 15

For 6 Marks:

Examples: 16 to 21

Ex 13.3: Q 1, 4, 5, 7, 8, 10, 11

Miscellaneous: Q 3, 12, 13, 16

TIPS FOR EXAMINATIONS:

You are now on the verge to give the last and lengthiest paper of your School. So 

1. Try to solve the first questions which you know in the paper and do it as fast as possible to you.

2. Put your legs on accelerators from the very first questions.

3. Do not waste time on that questions in which have doubt and which think take time.

4. Make belief in you.

5. Do not rush in the examinations.

6. Try to keep yourself calm.

7.  Try to give brief solutions to questions.

8.  Make selections on choose questions as per its length and your ability to answer better.

9.  Check the calculations in the last 15 minutes especially in 6 marks questions.

10.  Try to maintain your handwriting neat and clean.  

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CLASS 12TH MATHEMATICS PART (I) NCERT IMPORTANT QUESTIONS

CLASS 12^TH MATHEMATICS PART (I)

IMPORTANT QUESTIONS LIST OF NCERT

 

Every Student thinks Mathematics as a difficult subject especially Class 12^th 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 12^th 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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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 = Ф ⊃ 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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