Question: Solution: Let —–(i) Let differentiate with respect to x Putting in eq (i) Divide by in numerator and denominator Let D.w.r. t.x Now OR We can do this question with another method —(i) Let Differentiate with respect to x Again taking Squaring both side Putting in (i) … Read more
EXERCISE 1.2 1. Which of the following are examples of the null set? (Ex 1.2 sets ncert maths solution class 11) (i) Set of odd natural numbers divisible by 2 (ii) Set of even prime numbers (iii) {x: x is a natural numbers, x < 5 and x > 7} (iv) {y: y is a point common to … Read more
EXERCISE 1.1 1. Which of the following are sets? Justify our answer.(Ex 1.1 ncert maths solution class 11 ) (i) The collection of all months of a year beginning with the letter J. (ii) The collection of the ten most talented writers of India. (iii) A team of eleven best-cricket batsmen of the world. (iv) The … Read more
EXERCISE 6.1 1. Find the rate of change of the area of a circle with respect to its radius r when. (class 12 maths ex 6.1 ncert solution) (a) r = 3 cm (b) r = 4 cm. Solution: We know that the area of a circle, Therefore, the rate of change … Read more
EXERCISE 4.5 (Determinant) class 12 maths exercise 4.5 ncert solution Question 1: Find the adjoint of the matrix Solution: Let Then, Thus Question 2: Find the adjoint of the matrix Solution: Let Then, Question 3: Verify for Solution: Let Then, Also, Now, Hence, Now, Also, Hence, . Question 4: verify for Solution : Let Then … Read more
EXERCISE 3.3 (Matrix) class 12 maths exercise 3.3 solution Question1: Find the transpose of each of the following matrices: (i) (ii) (iii) Solution: (i) Let Then (ii) Let Then (iii) Let Then Question2: and Then verify that (i) (ii) Solution: (i) and Now Hence (ii) Then Thus Question 5: For the matrices A and B, … Read more
Chapter 3 ( Miscellaneous) class 12 maths chapter 3 Miscellaneous solution Question 1: Let ,show that , where I is the identity matrix of order 2 and. Solution: It is given that LHS. RHS. Since, Hence, We shall prove the result by using the principle of mathematical induction. For n=1, we have: P(1): Therefore, the … Read more
Chapter 2: Miscellaneous Exercise Find the value of the following:(Class 12 ncert solution math chapter 2 Miscellaneous) Question 1: Find the value of . Solution: Question 2: Find the value of . Solution: Question 3: Prove that . Solution: Let Then, Therefore, Thus, Question 4: Prove that . Solution: Let Then, Therefore, Now, let Then, … Read more
EXERCISE 2.2 Prove the following:(Class 12 ncert solution math exercise 2.2) Question 1: Prove . Solution: Let Hence, Now, =L H S Question 2: Prove . Solution: Let Hence, Now, Question 3: Prove . Solution: Since we know that Now, Question 4:Prove . Solution: Since we know that Now, Question 5: … Read more
EXERCISE 2.1 Find the principal values of the following:(Class 12 ncert solution math exercise 2.1) Question 1: Solution : Principal value of Question 2: Solution : Principal value of Question 3: Solution: Principal value of Question 4: Solution: Principal value of Question 5: Solution :Principal value of Question 6: Solution: Principal value of … Read more