Chapter 7 ( Miscellaneous Exercise) Chapter 7 Miscellaneous Ncert math solution class 11 Question 1: How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER? Solution: The word DAUGHTER has 3 vowels, A, E, U and 5 consonants D, G, H, … Read more
EXERCISE 7.4(Permutations and Combinations) Exercise 7.4 ncert solutions maths class 11 Question 1: If , find . Solution: Given that We know that if then either or If On rearranging we get Now, Question 2: Determine if (i) (ii) Solution: (i) Given that: Substituting the formula we get On multiplying we get (ii) Given that: … Read more
Exercise 7.3(Permutations and Combinations) Chapter 7 Exercise 7.3 ncert solutions maths class 11 Question 1: How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated? Solution: Total number of digit Number of places where the digit can fill If repetition of digit not allowed, Then number … Read more
Exercise 7.2(Permutations and Combinations) Exercise 7.2 ncert solutions maths class 11 Question 1: Evaluate (i) 8! (ii) 4! – 3! Solution: (i) Given 8! We know that 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320 (ii) Given 4!-3! 4! – 3! = (4 × 3!) … Read more
Exercise 7.1(Permutations and Combinations) Ncert math solution(Exercise 7.1 ncert solutions maths class-11) Question 1: How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5, assuming that (i) Repetition of the digits is allowed? (ii) Repetition of the digits is not allowed? Solution: 3-digit numbers can be formed from the … Read more
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
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 $I=\int_0^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} … 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
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