# RD sharma

## RD Sharma Solution CLass 12 Mathematics Chapter 33 Binomial Distribution

Chapter 33 – Binomial Distribution Exercise Ex. 33.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Required Probability = Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 …

## RD Sharma Solution CLass 12 Mathematics Chapter 32 Mean and Variance of  a Random Variable

Chapter 32 – Mean and variance of a random variable Exercise Ex. 32.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 …

## RD Sharma Solution CLass 12 Mathematics Chapter 31 Probability

Chapter 31 – Probability Exercise Ex. 31.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Chapter 31 – Probability Exercise Ex. 31.2 Question 1 Solution 1 Question …

## RD Sharma Solution CLass 12 Mathematics Chapter 30 Linear Programming

Chapter 30 – Linear programming Exercise Ex. 30.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution …

## RD Sharma Solution CLass 12 Mathematics Chapter 29 The Plane

Chapter 29 – The plane Exercise Ex. 29.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Chapter 29 – The plane Exercise Ex. 29.10 Question 1 Solution 1 Question 2 Solution …

## RD Sharma Solution CLass 12 Mathematics Chapter 28 Straight Line in Space

Chapter 28 – Straight line in space Exercise Ex. 28.1 Question 1 Solution 1 Question 2 Find the vector equation of the line passing through the points (-1, 0, 2) and (3, 4, 6). Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution …

## RD Sharma Solution CLass 12 Mathematics Chapter 27 Direction Cosines and Direction Ratios

Chapter 27 – Direction Cosines and Direction Ratios Exercise Ex. 27.1 Question 1 If a line makes angles of 90°, 60° and 30° with the positive direction of x,y and z-axis respectively, find its direction cosines. Solution 1 Let l, m and n be the direction cosines of a line. l = cos 90° = …

## RD Sharma Solution CLass 12 Mathematics Chapter 26 Scalar Triple Product

Chapter 26 – Scalar Triple Product Exercise Ex. 26.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 …

## RD Sharma Solution CLass 12 Mathematics Chapter 25 Vectors or Cross Product

Chapter 25 – Vector or Cross Product Exercise Ex. 25.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question …

## RD Sharma Solution CLass 12 Mathematics Chapter 24 Scalar or Dot Product

Chapter 24 – Scalar Or Dot Product Exercise Ex. 24.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question …

## RD Sharma Solution CLass 12 Mathematics Chapter 23 Algebra of Vectors

Chapter 23 – Algebra of vectors Exercise Ex. 23.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Chapter 23 – Algebra of Vectors Exercise Ex. 23.2 Question 1 Solution 1 Question 2 Solution 2      …

## RD Sharma Solution CLass 12 Mathematics Chapter 22 Differential Equations

Chapter 22 – Differential Equations Exercise Ex. 22.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6   Solution 6   Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question …

## RD Sharma Solution CLass 12 Mathematics Chapter 21 Areas of Bounded Regions

Chapter 21 – Areas of bounded regions Exercise Ex. 21.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Thus, Required area = square units Question 8 Solution 8 Question 9 Solution 9 Question 10   …

## RD Sharma Solution CLass 12 Mathematics Chapter 20 Definite Integrals

Chapter 20 – Definite Integrals Exercise Ex. 20.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution …

## RD Sharma Solution CLass 12 Mathematics Chapter 19 Indefinite Integrals

Chapter 19 – Indefinite Integrals Exercise Ex. 19.1 Question 1 integrate each of the following functions with respect to x: Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Chapter 19 – Indefinite Integrals Exercise Ex. 19.10 Question 1 Solution 1 Question …

## RD Sharma Solution CLass 12 Mathematics Chapter 18 Maxima and Minima

Chapter 18 – Maxima and Minima Exercise Ex. 18.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Chapter 18 – Maxima and Minima Exercise Ex. 18.2 …

## RD Sharma Solution CLass 12 Mathematics Chapter 17 Increasing and Decreasing Functions

Chapter 17 – Increasing and Decreasing Functions Exercise Ex. 17.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Chapter 17 – Increasing and Decreasing Functions Exercise Ex. …

## RD Sharma Solution CLass 12 Mathematics Chapter 16 Tangents and Normals

Chapter 16 – Tangents and Normals Exercise Ex. 16.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question …

## RD Sharma Solution CLass 12 Mathematics Chapter 15 Mean Value Theorems

Chapter 15 – Mean Value Theorems Exercise Ex. 15.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 …

## RD Sharma Solution CLass 12 Mathematics Chapter 14 Differentials , Errors and Approximations

Chapter 14 – Differentials, Errors and Approximations Exercise Ex. 14.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question …

## RD Sharma Solution CLass 12 Mathematics Chapter 13 Derivative as Rate Measurer

Chapter 13 – Derivative as a Rate Measurer Exercise Ex. 13.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 The money to be spent for …

## RD Sharma Solution CLass 12 Mathematics Chapter 12 Higher Order Derivatives

Chapter 12 – Higher Order Derivatives Exercise Ex. 12.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Find the second order derivative of log(sinx). Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution …

## RD Sharma Solution CLass 12 Mathematics Chapter 11 Differentiation

Chapter 11 – Differentiation Exercise Ex. 11.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Chapter 11 – Differentiation Exercise Ex. 11.2 Question …

## RD Sharma Solution CLass 12 Mathematics Chapter 10 Differentiability

Chapter 10 – Differentiability Exercise Ex. 10.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Find whether the following functions is differentiable at  x = 1 and x = 2 or not: Solution 6 Question 7 Solution 7 Question 8 Solution …

## RD Sharma Solution CLass 12 Mathematics Chapter 9 Continuity

Chapter 9 – Continuity Exercise Ex. 9.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution 12 …

## RD Sharma Solution CLass 12 Mathematics Chapter 8 Solution of Simultaneous Linear Equations

Chapter 8 – Solution of Simultaneous Linear Equations Exercise Ex. 8.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 …

## RD Sharma Solution CLass 12 Mathematics Chapter 7 Adjoint and Inverse of a Matrix

Chapter 7 – Adjoint and Inverse of a Matrix Exercise Ex. 7.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution …

## RD Sharma Solution CLass 12 Mathematics Chapter 6 Determinants

Chapter 6 – Determinants Exercise Ex. 6.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution 12 …

## RD Sharma Solution CLass 12 Mathematics Chapter 5 Algebra of Matrices

Chapter 5 – Algebra of Matrices Exercise Ex. 5.1 Question 1 If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements? Solution 1 We know that if a matrix is of the order , it has mn elements. Thus, to find all the possible orders of …

## RD Sharma Solution CLass 12 Mathematics Chapter 4 Inverse Trigonometric Functions

Chapter 4 – Inverse Trigonometric Functions Exercise Ex. 4.1 Question 1 Find the value of each of the following : Solution 1 Question 2 Find the value of each of the following : Solution 2 Question 3 Find the value of each of the following : Solution 3 Question 4 Find the value of each …

## RD Sharma Solution CLass 12 Mathematics Chapter 3 Binary Operations

Chapter 3 – Binary Operations Exercise Ex. 3.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Determine whether the following operation defines a binary operation on the Solution 6 We have, A ⊙ b = ab + ba for all a, …

## RD Sharma Solution CLass 12 Mathematics Chapter 2 Functions

Chapter 2 – Functions Exercise Ex. 2.1 Question 1 Give an example of function which is one-one but not onto. Solution 1 Question 2 Give an example of a function which is not one-one but onto. Solution 2 Question 3 Given an example of a function which is neither one-one nor onto. Solution 3 Question …

## RD Sharma Solution CLass 12 Mathematics Chapter 1 Relations

Chapter 1 – Relations Exercise Ex. 1.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution 12 …

## RD Sharma Solution CLass 11 Mathematics Chapter 33 Probability

Chapter 33 – Probability Exercise Ex. 33.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 An experiment consists of tossing a coin and then tossing …

## RD Sharma Solution CLass 11 Mathematics Chapter 32 Statistics

Chapter 32 – Statistics Exercise Ex. 32.1 Question 1 Calculate the mean deviation on the following income groups of five and seven members from their medians: I Income in Rs. II income in Rs. 4000 3800 4200 4000 4400 4200 4600 4400 4800 4600 4800 5800 Solution 1 Note: Answer given in the book is …

## RD Sharma Solution CLass 11 Mathematics Chapter 31 Mathematical Reasoning

Chapter 31 – Mathematical Reasoning Exercise Ex. 31.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 It is not a statement. The sentence “This sentence is a …

## RD Sharma Solution CLass 11 Mathematics Chapter 30 Derivatives

Chapter 30 – Derivatives Exercise Ex. 30.2 Question 1 Differentiate -x using first principles. Solution 1 Question 2 Differentiate (-x)-1 using first principles. Solution 2 Question 3 Differentiate sin(x + 1) using first principles. Solution 3 Question 4 Differentiate cos using first principles. Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 …

## RD Sharma Solution CLass 11 Mathematics Chapter 29 Limits

Chapter 29 – Limits Exercise Ex. 29.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3   Question 4 Solution 4 Question 5 Solution 5 Question 6   Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 …

## RD Sharma Solution CLass 11 Mathematics Chapter 28 Introduction to 3D Coordinate Geometry

Chapter 28 – Introduction to 3-D coordinate geometry Exercise Ex. 28.1 Question 1 Name the octants in which the following points lie:  (i) (5, 2, 3)           Solution 1 All are positive, so octant is XOYZ   Question 2 Name the octants in which the following points lie: (ii) (-5, 4, …

## RD Sharma Solution CLass 11 Mathematics Chapter 27 Hyperbola

Chapter 27 – Hyperbola Exercise Ex. 27.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution 12 …

## RD Sharma Solution CLass 11 Mathematics Chapter 26 Ellipse

Chapter 26 – Ellipse Exercise Ex. 26.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Find the eccentricity, coordinates of foci, length of the latus-rectum …

## RD Sharma Solution CLass 11 Mathematics Chapter 24 The Circle

Chapter 24 – The Circle Exercise Ex. 24.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution …

## RD Sharma Solution CLass 11 Mathematics Chapter 23 The Straight Lines

Chapter 23 – The Straight Lines Exercise Ex. 23.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 …

## RD Sharma Solution CLass 11 Mathematics Chapter 22 Brief Review of Cartesian System of Rectangular Coordinates

Chapter 22 – Brief Review of Cartesian System of Rectangular Coordinates Exercise Ex. 22.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Chapter 22 – Brief Review of Cartesian System of …

## RD Sharma Solution Class 11 Mathematics Chapter 21 Some Special Series

Chapter 21 – Some Special Series Exercise Ex. 21.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 …

## RD Sharma Solution Class 11 Mathematics Chapter 20 Geometric Progressions

Chapter 20 – Geometric Progressions Exercise Ex. 20.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution …

## RD Sharma Solution Class 11 Mathematics Chapter 19 Arithmetic Progressions

Chapter 19 – Arithmetic Progressions Exercise Ex. 19.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Find the first four terns of the sequence defined by a1 = 3 and, an = 3an– 1 + 2, for all n > 1 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 …

## RD Sharma Solution Class 11 Mathematics Chapter 18 Binomial Theorem

Chapter 18 – Binomial Theorem Exercise Ex. 18.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution …

## RD Sharma Solution Class 11 Mathematics Chapter 17 Combinations

Chapter 17 – Combinations Exercise Ex. 17.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution 12 …

## RD Sharma Solution Class 11 Mathematics Chapter 16 Permutations

Chapter 16 – Permutations Exercise Ex. 16.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution 12 …

## RD Sharma Solution Class 11 Mathematics Chapter 15 Linear Inequations

Chapter 15 – Linear Inequations Exercise Ex. 15.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution …

## RD Sharma Solution Class 11 Mathematics Chapter 14 Quadratic Equations

Chapter 14 – Quadratic Equations Exercise Ex. 14.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution …

## RD Sharma Solution Class 11 Mathematics Chapter 13 Complex Numbers

Chapter 13 – Complex Numbers Exercise Ex. 13.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution …

## RD Sharma Solution Class 11 Mathematics Chapter 12 Mathematical Induction

Chapter 12 – Mathematical Induction Exercise Ex. 12.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Chapter 12 – Mathematical Induction Exercise Ex. 12.2 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution …

## RD Sharma Solution Class 11 Mathematics Chapter 11 Trigonometric Equations

Chapter 11 – Trigonometric Equations Exercise Ex. 11.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution …

## RD Sharma Solution Class 11 Mathematics Chapter 10 Sine and Cosine Formulae and Their Applications

Chapter 10 – Sine and Cosine Formulae and Their Applications Exercise Ex. 10.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 …

## RD Sharma Solution CLass 11 Mathematics Chapter 9 Trigonometric Ratios of Multiple and Submultiple Angles

Chapter 9 – Trigonometric Ratios of Multiple and Submultiple Angles Exercise Ex. 9.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 …

## RD Sharma Solution CLass 11 Mathematics Chapter 8 Transformation Formulae

Chapter 8 – Transformation Formulae Exercise Ex. 8.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 prove that ten 20o tan …

## RD Sharma Solution CLass 11 Mathematics Chapter 7 Trigonometric Ratios of Compound Product

Chapter 7 – Trigonometric Ratios of Compound Angles Exercise Ex.7.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question …

## RD Sharma Solution CLass 11 Mathematics Chapter 6 Graphs of Trigonometric Functions

Chapter 6 – Graphs of Trigonometric Functions Exercise Ex. 6.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Sketch the graph of the following pairs of functions on the same axes: y = sin x, y = …

## RD Sharma Solution CLass 11 Mathematics Chapter 5 Trigonometric Functions

Chapter 5 – Trigonometric Functions Exercise Ex. 5.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution …

## RD Sharma Solution CLass 11 Mathematics Chapter 4 Measurement of Angle

Chapter 4 – Measurement of Angles Exercise Ex. 4.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 …

## RD Sharma Solution CLass 11 Mathematics Chapter 3 Functions

Chapter 3 – Functions Exercise Ex. 3.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution 12 …

## RD Sharma Solution CLass 11 Mathematics Chapter 2 Relations

Chapter 2 – Relations Exercise Ex. 2.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution 12 …

## RD Sharma Solution Class 11 Mathematics Chapter 1 Sets

Chapter 1 – Sets Exercise Ex. 1.1 Question 1 Solution 1 Question 2 Solution 2 Question 3 If A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then insert the appropriate symbol or in each of the following blank spaces: 4…A -4 …A 12 ….A 9 …A 0 …..A -12 ….A …

## Rd sharma solution 2019 class 9 chapter 14 Areas of paralllelograms and triangles

Exercise 14.3 QUESTION 1 In the given f‌igure, compute the area of quadrilateral ABCD. Sol : Given : Here from the given figure we gwt (1) ABCD is a quadrilateral with base AB . (2) ΔABD is a right angled triangle. (3) ΔBCD is a right angled triangle with base BC right angled at B …

## Rd sharma solution 2019 class 9 chapter 14 Areas of paralllelograms and triangles

Exercise 14.1    Exercise 14.2 Exercise 14.2 QUESTION 1  lf the given f‌igure, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm. AE = 8 cm and CF =10 cm, f‌ind AD. Sol : Given: Here in the question it is given (1) ABCD is a parallelogram, (2) …

## Rd sharma solution 2019 class 9 chapter 14 Areas of paralllelograms and triangles

Exercise 14.1    Exercise 14.2 Exercise 14.1 QUESTION 1  Which of the following f‌igures lie on the same base and between the same parallels. In such a case, write the common base and two parallels: (i) Sol : (i) ΔAPB and trapezium ABCD are on the same base CD and between the same parallels AB …

## RD sharma solution class 9 chapter 1 number system (2018)

EXERCISE 1.1 QUESTION 1 Is zero a rational number? Can you write it in the form   where p and q are integers and ? Sol : Yes, zero is  a rational number because it is either terminating or non-terminating so we can write in the form of , where p and q are natural numbers and …

## Geometric progression

EXERCISE 20.3 QUESTION 1 Find the sum of the following geometric progressions: (i) to 7 terms; Sol : Here, a=2 and r=3 = 2787 – 1 = 2186   (ii) to 8 terms Sol : Here, a=1 and r=3 = 3280   (iii) to 9 terms; Sol : Here, a=1 and   (iv) to n …

## Geometric progression

EXERCISE 20.2 QUESTION 1 Find three numbers in G.P. whose sum is 65 and whose product is 3375 . Sol : Let the terms of the the given G.P. be , a and Then, product of the G.P. =3375 a = 15 Similarly, sum of the G.P. Substituting the value of a Hence, the G.P.for …

## Geometric Progressions

EXERCISE 20.1 QUESTION 1 Show that each one of the following progressions is a G.P. Also, find the common ratio in each case: (i) Sol : We have : ,, , , , Thus, , , and are in G.P., where a=4 and   (ii) Sol : We have : ,, , Thus, , and …

## Arithmetic progression

EXERCISE 19.6 QUESTION 1 Find the A.M. between: (i) 7 and 13 Sol : Let be the A.M. between 7 and 13 = 10   (ii) 12 and -8 Sol : Let be the A.M. between 12 and -8 = 2   (iii) (x – y) and (x + y) Sol : Let be the …

## Arithmetic progression

EXERCISE 19.4 QUESTION 1 Find the sum of the following arithmetic progressions: (i) to 10 terms Sol : We have : a = 50 d = (46 -50) = -4 n = 10 = 320   (ii) to 12 terms Sol : We have : a = 1 d = (3 – 1) = 2 …

## Arithmetic progression

EXERCISE 19.3 QUESTION 1 The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms. Sol : Let the three terms of the A.P. be  ,  a , Then , we have   Also ,     …

## Arithmetic progression

EXERCISE 19.2 QUESTION 1 Find : (i) 10 th term of the A.P. Sol : We have  a = 1 d = 4 – 1 = 3   = 28   (ii) 18 th term of the A.P. Sol : We have :   (iii) n th term of the A.P. Sol : We have …

## Arithmetic progression

EXERCISE 19.1 QUESTION 1 If the term of a sequence is given by write down its first five terms. Sol : Given : For = 1 For = 2 For = 3 For = 13 For = 21 Thus, the first five terms of the sequence are   QUESTION 2 A sequence is defined by …

## Rd sharma solution of class 11 chapter 16 permutation

EXERCISE 16.1 QUESTION 1 Compute : (i) Sol : = 870   (ii) Sol : = 100   (iii) L.C.M. Sol : Therefore, and can be rewritten as: LCM of and   QUESTION 2 Prove that Sol : Hence , proved   QUESTION 3 Find in each of the following: (i) Sol :   (ii) …

## complex number

Exercise 13.4 QUESTION 1 Find the modulus and argument of the following complex number and hence express each of them in the polar form : (i) Sol : Let Since point lies in the first quadrant , the argument of z is given by Polar form   (ii) Sol : Let Since point lies in the …

Exercise 14.1 QUESTION 1 Sol : Hence , the roots of the equation are i and -i    QUESTION 2 Sol : Hence, the roots of the equation are   QUESTION 3 Sol :   Hence, the roots of the equation are    QUESTION 4 Sol : Hence , the roots of the equation are …

## Rd sharma solution of class 11 chapter 13 complex number

Exercise 13.3 QUESTION 1 (i) Sol : , and   (ii) Sol : ,   , ṇṇ   (iii) Sol : , ,   (iv) Sol : , ,   (v) Sol : , ,   (vi) Sol : , ,   (vii) Sol : , ,   (viii) Sol : , ,   (ix) …

## Rd sharma solution of chapter 13 complex number class 11

Exercise 13.2 QUESTION 1 Express the following complex numbers in the standard form a+ib : (i) Sol :   (ii) Sol :   (iii) Sol :     (iv) Sol :     (v) Sol :     (vi) Sol :   (vii) Sol :       (viii) Sol :   (ix) 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 the origin.   Question 2 A function is defined as  Show that is continuous that Sol : Given We observe …

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