Exercise 9.2 Question 1 Prove that the function is everywhere continuous . Sol : When , we have We know that sin x as well as the identity function x are everywhere continuous . So , the[…]

# Category: class 12

## Rd sharma solution class 12 chapter 2 functions

Exercise 3.1 Question 1 Give an example of a function (i) which is one-one but not onto Sol : Injectivity : Let x and y be any two elements in the domain (Z) , such that […]

## Rd sharma solution class 12 chapter Relations

Exercise 1.1 Question 1 Let A be the set of all human beings in a town at a particular time. Determine whether each of the following relations are reflexive, symmetric and transitive: (i) R =[…]

## Rd sharma solution class 12 chapter Differentiation

Exercise 11.2 Question 1 Differentiate Sol : Let Differentiating y with respect to x we get, So, Question 2 Differentiate Sol : Let which can be written as Differentiating y with respect to[…]

## Rd sharma solution class 12 chapter Inverse trigonometric functions

Exercise 4.1 Question 1 Find the principal value of each of the following: (i) Sol : (ii) Sol : (iii) Sol : (iv) Sol : […]

## Rd sharma solution class 12 chapter Continuity

Exercise 9.1 Question 1 Test the continuity of the function on at the origin: Sol : Given We observe (LHL at x= 0) =-1 (RHL at x = 0) =1 Hence, is discontinuous at[…]

## Rd sharma solution class 1 chapter Indefinite integrals

Exercise 19.2 Question 1

## Rd sharma solution class 1 chapter Indefinite integrals

Exercise 19.1 Question 1 Evaluate each of the following integrals: (i) Sol : (ii) Sol : (iii) Sol : (iv) Sol : (v) Sol : (vi) Sol : (vii)[…]

## RD Sharma solution class 12 chapter 28 Straight line in space

Exercise 28.1 Question 1 Find the vector and cartesian equations of the line through the point and which is parallel to the vector Sol : We know that the vector equation of a line[…]

## RD sharma solution class 12 chapter determinants

Determinants Exercise 6.1 Question 1 Write the minors and cofactors of each element of the first column of the following matrices and hence evaluate the determinant in each case: (i) A = Sol : In[…]

## Derivative as a rate measure

Derivative as a rate measure Exercise 13.1 1. Find the rate of change of the total surface area of a cylinder of radius r and height h, when the radius varies. Sol : 2.[…]

## DIFFERENTIATION

Differentiation Exercise 11.1 Differentiate the following functions from first principles : QUESTION 1 Sol : QUESTION 2 Sol : QUESTION 3 Sol : QUESTION 4 Sol : QUESTION 5 Sol : […]

## Chapter Algebra of matrices

ALGEBRA OF MATRICES EXERCISE 5.1 1.If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements? solution: Order of matrix=number of rows \( \times \)number of column[…]