Exercise 2.1 Question 1 (i) If find the values of and Sol : By the definition of equality of ordered pairs, we have: and and and b = 1 (ii) If find the values[…]

# Category: Class 11

## 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[…]

## 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, ,[…]

## 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.[…]

## 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[…]

## 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 :[…]

## 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[…]

## Circle

EXERCISE 24.3 QUESTION 1 Find the equation of the circle, the end points of whose diameter are $(2,-3)$ and $(-2,4)$ . Find its center and radius. Sol : $(2,-3)$ and $(-2,4)$ are the ends points[…]

## Combination

EXERCISE 17.2 QUESTION 1 From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done? Sol : Required number of ways =[…]

## Circle

EXERCISE 24.2 QUESTION 1 Find the co-ordinates of the center and radius of each of the following circles: (i) Sol : The given equation can be rewritten as Center And, radius = 7 (ii)[…]

## Circle

EXERCISE 24.1 QUESTION 1 Find the equation of the circle with : (i) Center $(-2,3)$ and radius 4 Sol : Let $(h, k)$ be the centre of a circle with radius a. Thus, its equation[…]

## Permutation

Exercise 16.2 QUESTION 1 In a class there are 27 boys and 14 girls . The teacher wants to select 1 boy and 1 girl to represent the class in a function . In how[…]

## 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[…]

## 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[…]

## Quadratic equations

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 : […]

## 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 : , ,[…]

## 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[…]

## Rd sharma solution of chapter 13 Complex numbers

Complex numbers Exercise 13.1 QUESTION 1 Evaluate the following: (i) Sol : (ii) Sol : =1 (iii) Sol : = -1 (iv) Sol : (v) Sol : = 0[…]

## Hydrocarbons

HYDROCARBONS Organic compound are composed of only carbons and hydrogen are called hydrocarbons. ON THE BASIS OF STRUCTURE HYDROCARBONS ARE OF TWO TYPES 1. Acyclic or open chain hydrocarbons 2. Cyclic or closed chain hydrocarbons[…]

## WORK, ENERGY AND POWER

WORK, ENERGY AND POWER In your daily life you have seen many things like person pushing heavy box , a teacher teaching students , mom cooking food , all are said to be working .[…]

## REDOX REACTIONS

REDOX REACTIONS Chemical reaction in which electron transfer from one chemical substance to another are termed as oxidation-reduction reactions or redox reactions. You can see many examples from your daily life like production of electricity[…]

## Thermodynamics

Thermodynamics The word “thermodynamics” is derived from Greek words therme (heat) and dinamics (flow or motion) . Thermodynamics mainly deals with the transformation of heat into mechanical energy and vice versa . LIMITATIONS OF THERMODYNAMICS[…]

## straight line

Straight line EXERCISE 23.1 1. Find the slopes of the lines which make the following angles with the positive direction of x-axis : (i) \( -\dfrac{\pi}{4} \) sol: m=tan\( \theta \) =tan(\( -\dfrac{\pi}{4} \)) = -1[…]

## Chapter Some Basic Concepts of Chemistry

SOME BASIC CONCEPT OF CHEMISTRY Classification of matter on the basis of chemical properties: Matter classified into two groups pure substances and mixtures.Pure substances further divided into elements and compounds. 1. Elements : it is[…]

## Chapter classification of elements and periodicity in properties

CLASSIFICATION OF ELEMENTS AND PERIODICITY IN PROPERTIES Brief Historical Development Of Periodic Table 1.Johann Dobereiner’s (Law of triads) In between 1815 and 1829 he gave law of triads.According to which group of three elements which[…]

## Chapter Kinematics

KINEMATICS The branch of physics which deals with the study of the objects at rest and in motion is called mechanics. It is further divided into two parts are: 1.Statics Statics is the branch of[…]

## Chapter Unit and measurement

UNIT AND MEASUREMENT Units of measurement are vital parts of any physical quantity. Just as the person is known by his or her name, the physical quantities are known by the units of measurement. System[…]