## 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 :[…]

## 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[…]

## 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[…]

## 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 =[…]

## Combination

EXERCISE 17.1 QUESTION 1 Evaluate the following : (i) Sol :   (ii) Sol :   (iii) Sol :   (iv) Sol :       (v) Sol : = 31   QUESTION 2 If[…]

## 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[…]

## 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[…]

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 : , ,[…]