Team Gmath Chapter 5 Miscellaneous (differentiation ) Differentiate w.r.t. x the function in Exercises 1 to 11.(Class 12 ncert solution math chapter 5 miscellaneous) Question 1: Solution: Let Differentiate with respect to x Question 2: Solution: Let Differentiate with respect to x Question 3: Solution: Let Taking ‘log’ both side Question 4: Solution: Let Differentiate with respect … Read more
Exercise 5.7 ( Differentiation) Find the second order derivatives of the functions given in Exercises 1 to 10.(Class 12 ncert solution math exercise 5.7 differentiation) Question:1 Solution: Let y = Then, differentiate with respect to x Again differentiate w.r. to x Question 2: Solution: Let Diffrentiate with respect to x Again d.w.r. to x … Read more
EXERCISE 4.3 (Determinants) Question 1: Find area of the triangle with vertices at the point given in each of the following:(Class 12 ncert solution math exercise 4.3 determinants) (i) (ii) (iii) Solution: (i) The area of the triangle with vertices is given by the relation, Hence, area of the triangle is square units. (ii) … Read more
EXERCISE 4.6 ( Determinants ) Question 1: Examine the consistency of the system of equations:(Class 12 ncert solution math exercise 4.6) Solution: The given system of equations is: The given system of equations can be written in the form of , where Hence, =3-4 So, is non-singular. Therefore, exists. Thus, the given system … Read more
EXERCISE 4.1 ( Determinants ) Evaluate the determinant:(Class 12 ncert solution math exercise 4.1) Question 1: Solution: Let Hence, Question 2: Evaluate the determinants: (i) (ii) Solution: (i) (ii) Question 3: If , then show that Solution: The given matrix is Therefore, Hence, Now, Therefore, Thus, proved. Question 4: If , then show … Read more
EXERCISE 4.4 (Determinants) Write Minors and Cofactors of the elements of following determinants:(Class 12 ncert solution math exercise 4.4) Question 1: (i) (ii) Solution: (i) The given determinant is Minor of element is minor of element minor of element minor of element minor of element Cofactor of is (ii) The given determinant is Minor of … Read more
EXERCISE 5.4 ( Differentiation ) Differentiating the following w.r.t.(Class 12 ncert solution math exercise 5.4) Question 1: . Solution:Let By using the quotient rule, we get Question 2: Solution:Let By using the quotient rule, we get Question 3: Solution:Let By using the quotient rule, we get Question 4: Solution:Let By using the … Read more
Three friends go for coffee. They decide who will pay the bill, by each tossing a coin and and then letting the “odd person” pay. There is no odd person if all three tosses produce the same result. It there is no odd person in the first round , they make a second … Read more
Exercise 1.2 Question 1: Show that the function defined by is one-one and onto, where the set of all non-zero real numbers. Is the result true, if the domain is replaced by with codomain being same as (Class 12 ncert solution math exercise 1.2 ) Solution: For one-one: … Read more
Exercise 1.1 Question 1: Determine whether each of the following relations are reflexive, symmetric and transitive.(Class 12 ncert solution math exercise 1.1) (i) Relation in the set defined as (ii) Relation in the set of natural numbers defined as (iii) Relation in the set defined as (iv) Relation in the … Read more