Chapters
Chapter 2 - Relations and Functions
Chapter 3 - Trigonometric Functions
Chapter 4 - Principle of Mathematical Induction
Chapter 5 - Complex Numbers and Quadratic Equations
Chapter 6 - Linear Inequalities
Chapter 7 - Permutations and Combinations
Chapter 8 - Binomial Theorem
Chapter 9 - Sequences and Series
Chapter 10 - Straight Lines
Chapter 11 - Conic Sections
Chapter 12 - Introduction to Three Dimensional Geometry
Chapter 13 - Limits and Derivatives
Chapter 14 - Mathematical Reasoning
Chapter 15 - Statistics
Chapter 16 - Probability
Chapter 2 - Relations and Functions
Pages 33 - 34
If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A × B)?
if `(x/3 + 1, y - 2/3) = (5/3, 1/3)` find the values of x and y.
If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.
State whether the following statement are true or false. If the statement is false, rewrite the given statement correctly.
If P = {m, n} and Q = {n, m}, then P × Q = {(m, n), (n, m)}.
State whether the following statement are true or false. If the statement is false, rewrite the given statement correctly.
If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x ∈ A and y ∈ B.
State whether the following statement are true or false. If the statement is false, rewrite the given statement correctly.
If A = {1, 2}, B = {3, 4}, then A × (B ∩ Φ) = Φ.
If A = {–1, 1}, find A × A × A.
If A × B = {(a, x), (a, y), (b, x), (b, y)}. Find A and B.
Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that A × (B ∩ C) = (A × B) ∩ (A × C)
Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that A × C is a subset of B × D
Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.
Let A and B be two sets such that n(A) = 3 and n (B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y and z are distinct elements.
The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0, 1). Find the set A and the remaining elements of A × A.
Pages 35 - 36
Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range.
Define a relation R on the set N of natural numbers by R = {(x, y): y = x + 5, x is a natural number less than 4; x, y ∈ N}. Depict this relationship using roster form. Write down the domain and the range.
A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.
The given figure shows a relationship between the sets P and Q. write this relation
(i) in set-builder form (ii) in roster form.
What is its domain and range?
Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a, b ∈ A, b is exactly divisible by a}.
(i) Write R in roster form
(ii) Find the domain of R
(iii) Find the range of R.
Determine the domain and range of the relation R defined by R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}.
Write the relation R = {(x, x3): x is a prime number less than 10} in roster form.
Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.
Let R be the relation on Z defined by R = {(a, b): a, b ∈ Z, a – b is an integer}. Find the domain and range of R.
Page 44
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)}
(ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
(iii) {(1, 3), (1, 5), (2, 5)}
Find the domain and range of the given real function:
f(x) = –|x|
Find the domain and range of the following real function:
f(x) = `sqrt(9 - x^2)`
A function f is defined by f(x) = 2x – 5. Write down the values of
(i) f(0), (ii) f(7), (iii) f(–3)
The function ‘t’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by `t(C) = "9C"/5 + 32`
Find
(i) t(0)
(ii) t(28)
(iii) t(–10)
(iv) The value of C, when t(C) = 212.
Find the range of each of the following functions.
f(x) = 2 – 3x, x ∈ R, x > 0.
Find the range of each of the following functions.
f(x) = x, x is a real number
Find the range of each of the following functions.
f(x) = x2 + 2, x, is a real number.
Pages 46 - 47
The relation f is defined by f(x) = `{(x^2,0<=x<=3),(3x,3<=x<=10):}`
The relation g is defined by g(x) = `{(x^2, 0 <= x <= 2),(3x,2<= x <= 10):}`
Show that f is a function and g is not a function.
If f(x) = x2, find `(f(1.1) - f(1))/((1.1 - 1))`
Find the domain of the function f(x) = `(x^2 + 2x + 1)/(x^2 - 8x + 12)`
Find the domain and the range of the real function f defined by `f(x)=sqrt((x-1))`
Find the domain and the range of the real function f defined by f (x) = |x – 1|.
Let `f = {(x, x^2/(1+x^2)):x ∈ R}` be a function from R into R. Determine the range of f.
Let f, g: R → R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and `f/g`
Let f = {(1, 1), (2, 3), (0, –1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.
Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b2}. Are the following true?
(i) (a, a) ∈ R, for all a ∈ N
(ii) (a, b) ∈ R, implies (b, a) ∈ R
(iii) (a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R.
Justify your answer in each case.
Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true?
(i) f is a relation from A to B (ii) f is a function from A to B.
Justify your answer in each case.
Let f be the subset of Z × Z defined by f = {(ab, a + b): a, b ∈ Z}. Is f a function from Z to Z: justify your answer.
Let A = {9, 10, 11, 12, 13} and let f: A → N be defined by f(n) = the highest prime factor of n. Find the range of f.
Textbook solutions for Class 11
NCERT solutions for Class 11 Mathematics chapter 2 - Relations and Functions
NCERT solutions for Class 11 Mathematics chapter 2 (Relations and Functions) include all questions with solution and detail explanation from Mathematics Textbook for Class 11. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has created the CBSE Mathematics Textbook for Class 11 solutions in a manner that help students grasp basic concepts better and faster.
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Concepts covered in Class 11 Mathematics chapter 2 Relations and Functions are Relation, Pictorial Diagrams, Functions, Pictorial Representation of a Function, Some Functions and Their Graphs, Exponential Function, Logarithmic Functions, Ordered Pairs, Equality of Ordered Pairs, Cartesian Product of Sets, Graph of Function, Algebra of Real Functions.
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