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, =R H S Question 4: Prove that . Solution: Let Then, Therefore, … 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
EXERCISE 5.6 If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find.(Class 12 ncert solution math exercise 5.6) Question 1: , Solution: Given, Then, Question 2: Solution: Given, Then, Question 3: Solution: Given, Then, Question 4: Solution: Given, Question 5: Solution: Given, Then, … Read more
Exercise 5.3 Find in the following(Class 12 ncert solution math exercise 5.3) Question 1: 2x + 3y = sin x Solution: 2x + 3y = sin x Differentiate with respect to x Question 2:- 2x + 3y = sin y Solution :- 2x + 3y = sin y Differentiate w.r.t. … Read more
f(x) = 5x^2+6x-9 prove that f is bijective. Question:- Consider given by prove that f is bijective. Solution:- To prove f is bijective,it is to prove f is one-one and onto Here, One-one: Let , such that i.e. f is one-one function. Onto:- Let f(x) = y Since, Obiviously, the value of Every value … Read more
Exercise 5.2(Continuity and differentiability) Differentiate the functions with respect to x in Exercises 1 to 8.(Class 12 ncert solution math exercise 5.2) Question 1:- Solution: Differentiate w.r.t. x Question 2:- Solution:- Differentiate w.r.t. x Question 3:- Solution:- Differentiate w.r.t. x Question 4:- Solution:- Differentiate with respect to x Question 5:- Solution: Differentiate with respect to … Read more
Exercise 5.1 (Continuity and Differentiability) Question 1: Prove that the function is continuous at and at . (Class 12 ncert solution math exercise 5.1) Solution: The given function is At Therefore, is continous at . Therefore, is continous at . Therefore, is continous at . Question 2: Examine the continuity of the function at . … Read more