Part-II
CLASS 12TH 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 12Th 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.