Chapter 7:Miscellaneous Exercise Integrate the functions in Exercises 1 to 24.(Chapter 7 Miscellaneous integration ncert maths solution class 12) Question 1: Solution: Let Let Let Let From equation (1), we have Now, Question 2: Solution: let Question 3: Solution: Let Question 4: Solution: Let Question 5: Solution: Let Let Dividing by denominator , we have … Read more
Fast revision(Math) class 12 revision of cbse math part-I 2022-2023 Class 12 revision of cbse math part-II 2022-2023 Integration: Chapter 7 Exercise 7.1 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) Methods of Integration:- 1. Integration by Substitution 2. Integration using Partial Fractions 3. Integration … Read more
Question : Show that right circular cone of least curve surface and given volume has an altitude equal to √2 time the radius of the base Solution: Let ‘r’ be the radius of cone and ‘h’ be the height of cone Volume of cone –(i) Curve surface area of cone Squaring both side Differentiating with … Read more
Exercise 7.11 By using the properties of definite integrals, evaluate the integrals in Exercises 1 to 19.(Ex 7.11 integration ncert maths solution class 12) Question 1: Solution : Let Adding (1) and (2), we have Question 2: Solution: Let Adding (1) and (2), we have Question 3: Solution:Let Adding (1) and (2), we have Question4: … Read more
Fast revision(Math) class 12 revision of cbse math part-I 2022-2023 Class 12 revision of cbse math part-II 2022-2023 Chapter 1: Relation and function EXERCISE 1.1(Relation) 1. Relation: If A and B are two non empty sets, then any subset R of is called relation from set A to set B. … Read more
Exercise 7.10(Integration) Evaluate the integrals in Exercises 1 to 8 using substitution.(Ex 7.10 integration ncert maths solution class 12) Question 1: Solution: Let Let When and when Question 2: Solution: Let Let When and when Question 3: Solution: Let When and when Question 4 : Solution: Let Let When and when Question 5: Solution : … Read more
Question: If 20 m of wire is available for fencing off a flower-bed in the form of a circular sector, then the maximum area(In sq m) of the flower bed is (a) 12.5 (b) 10 (c) 25 … Read more
Exercise 7.9(Integration) Evaluate the definite integrals in Exercises 1 to 20.(Ex 7.9 integration ncert maths solution class 12) Question 1: Solution: Let Question 2: Solution: Question 3: Solution: Question 4: Solution: Question 5: Solution: Question 6: Solution: Question 7: Solution : Question 8: Solution : Question 9: Solution : Question 10: Solution: Let Question 11: … Read more
EXERCISE 7.7(Integration) Integrate the functions in Exercises 1 to 9.(Ex 7.7 integration ncert maths solution class 12) Question 1: Solution: Let Since, Question 2: Solution: Let, Put, Since, Question 3: Solution: Let Since, Question 4: Solution: Let, Since, Question 5: Solution: Let, Since, Question 6: Solution: Let Since, Question 7: Solution: Put, Since, Question 8: … Read more
Question: Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is 8/27 of the volume of the sphere. Solution: Consider be the centre and be the radius of the given sphere, In ΔOBM, using pythagoras theorem BM is the radius of cone Volume of cone Differentiating … Read more