NCERT Class 11 Mathematics Chapter 2 – Relations and Functions Solutions

Exercise 2.1 1. If (x/3 + 1, y – 2/3) = (5/3, 1/3) then find values of x and y. Comparing both sides of this equation we get Simplifying x/3 + 1 = 5/3 Simplifying y – 2/3 = 1/3 Thus if (x/3 + 1, y – 2/3) = (5/3, 1/3) then value x = …

NCERT Class 11 Mathematics Chapter 2 – Relations and Functions Miscellaneous Exercise Solutions

Question 1 Question 2 Question 3 Question 4 5. Find the domain and the range of the real function f defined by f (x) = |x –1| We know that absolute or modulus of a function is defined for all of Real values of xHence Domain of f(x) = |x – 1| is Real Numbers …

NCERT Class 11 Mathematics Chapter 2 – Relations and Functions Exercise 2.3 Solutions

1. Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.(i) {(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)}As every first element in the ordered pairs (2,1), (5,1), (8,1), (11,1), (14,1), (17,1) is mapped uniquely to other numbers that’s why relation {(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)} is …

NCERT Class 11 Mathematics Chapter 2 – Relations and Functions Exercise 2.2 Solutions

1. Let A = {1, 2, 3,…,14}Define a relation R from A to A byR = {(x, y) : 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range. R = Relation from A to A = {(x, y) : 3x – y = 0 where x, y …

NCERT Class 11 Mathematics Chapter 2 – Relations and Functions Exercise 2.1 Solutions

1. If (x/3 + 1, y – 2/3) = (5/3, 1/3) then find values of x and y. Comparing both sides of this equation we get Simplifying x/3 + 1 = 5/3 Simplifying y – 2/3 = 1/3 Thus if (x/3 + 1, y – 2/3) = (5/3, 1/3) then value x = 2 and …

NCERT Class 11 Mathematics Chapter 1 – Sets Solutions

Exercise 1.1 1. Which of the following are sets? Justify your answer.(i) The collection of all the months of a year beginning with the letter JThe collection of all months of a year beginning with letter J is January, June, July which is a well defined collection of objects(words) that’s why it will be a …

NCERT Class 11 Mathematics Chapter 1 – Sets Miscellaneous Exercise Solutions

1. Decide among the following sets which sets are subsets of one and another: A = {x : x ∈ R and x satisfy x2 – 8x + 12 = 0}B = {2, 4, 6}C = {2, 4, 6, 8, . . .}D = {6} Let’s first simplify these sets and then find out which …

NCERT Class 11 Mathematics Chapter 1 – Sets Exercise 1.6 Solutions

1. If X and Y are two sets such that n(X) = 17, n(Y) = 23 and n(X ∪ Y) = 38 Find n(X ∩ Y)We know thatn(X ∪ Y) + n(X ∩ Y) = n(X) + n(Y)Replacing given values in this formula38 + n(X ∩ Y) = 17 + 2338 + n(X ∩ Y) …

NCERT Class 11 Mathematics Chapter 1 – Sets Exercise 1.5 Solutions

1. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9} A = {1, 2, 3, 4}B = {2, 4, 6, 8}C = {3, 4, 5, 6}Find (i) A′ A′ = {1, 2, 3, 4}’ = {5, 6, 7, 8, 9}A’ = {5, 6, 7, 8, 9} (ii) B′ B′ = {2, 4, …

NCERT Class 11 Mathematics Chapter 1 – Sets Exercise 1.4 Solutions

1. Find the union of each of the following pairs of sets: (i) X = {1, 3, 5} Y = {1, 2, 3}X ∪ Y = {1, 2, 3, 5} (ii) A = [ a, e, i, o, u} B = {a, b, c}A ∪ B = {a, b, c, e, i, o, u} (iii) …