NCERT Solutions for Class 11 Maths Maths Chapter 2

Relations and Functions Class 11

Chapter 2 Relations and Functions Exercise 2.1, 2.2, 2.3, miscellaneous Solutions

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Exercise 2.1 : Solutions of Questions on Page Number : 33

Q1 :  

If, find the values of xand y.


Answer :

It is given that.

Since the ordered pairs are equal, the corresponding elements will also be equal.

Therefore, and.

x= 2 and y= 1

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Q2 :  

If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A x B)?


Answer :

It is given that set A has 3 elements and the elements of set B are 3, 4, and 5.

Number of elements in set B = 3

Number of elements in (A x B)

= (Number of elements in A) x (Number of elements in B)

= 3 x 3 = 9

Thus, the number of elements in (A x B) is 9.

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Q3 :  

If G = {7, 8} and H = {5, 4, 2}, find G x H and H x G.


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Q4 :  

State whether each of the following statement are true or false. If the statement is false, rewrite the given statement correctly.

(i) If P = {m, n} and Q = {n, m}, then P x Q = {(m, n), (n, m)}.

(ii) If A and B are non-empty sets, then A x B is a non-empty set of ordered pairs (x, y) such that x A and y B.

(iii) If A = {1, 2}, B = {3, 4}, then A x (B Φ) = Φ.


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Q5 :  

If A = {-1, 1}, find A x A x A.


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Q6 :  

If A x B = {(a, x), (a, y), (b, x), (b, y)}. Find A and B.


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Q7 :  

Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that

(i) A x (B C) = (A x B) (A x C)

(ii) A x C is a subset of B x D


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Q8 :  

Let A = {1, 2} and B = {3, 4}. Write A x B. How many subsets will A x B have? List them.


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Q9 :  

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 x B, find A and B, where x, y and z are distinct elements.


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Q10 :  

The Cartesian product A x A has 9 elements among which are found (-1, 0) and (0, 1). Find the set A and the remaining elements of A x A.


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<< Previous Chapter 1 : Sets Next Chapter 3 : Trigonometric Functions >>

Exercise 2.2 : Solutions of Questions on Page Number : 35

Q1 :  

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.


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Q2 :  

Define a relation R on the set Nof natural numbers by R = {(x, y): y= x+ 5, xis a natural number less than 4; x, y N}. Depict this relationship using roster form. Write down the domain and the range.


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Q3 :  

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 xand yis odd; x A, y B}. Write R in roster form.


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Q4 :  

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?


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Q5 :  

Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by

{(a, b): a, b A, bis exactly divisible by a}.

(i) Write R in roster form

(ii) Find the domain of R

(iii) Find the range of R.


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Q6 :  

Determine the domain and range of the relation R defined by R = {(x, x+ 5): x {0, 1, 2, 3, 4, 5}}.


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Q7 :  

Write the relation R = {(x, x3): x is a prime number less than 10} in roster form.


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Q8 :  

Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.


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Q9 :  

Let R be the relation on Zdefined by R = {(a, b): a, b Z, a - bis an integer}. Find the domain and range of R.


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<< Previous Chapter 1 : Sets Next Chapter 3 : Trigonometric Functions >>

Exercise 2.3 : Solutions of Questions on Page Number : 44

Q1 :  

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)}


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Q2 :  

Find the domain and range of the following real function:

(i) f(x) = –|x| (ii)


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Q3 :  

A function fis defined by f(x) = 2x- 5. Write down the values of

(i) f(0), (ii) f(7), (iii) f(-3)


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Q4 :  

The function 't' which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by.

Find (i) t(0) (ii) t(28) (iii) t(–10) (iv) The value of C, when t(C) = 212


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Q5 :  

Find the range of each of the following functions.

(i) f(x) = 2 - 3x, x R, x> 0.

(ii) f(x) = x2+ 2, x, is a real number.

(iii) f(x) = x, xis a real number


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<< Previous Chapter 1 : Sets Next Chapter 3 : Trigonometric Functions >>

Exercise Miscellaneous : Solutions of Questions on Page Number : 46

Q1 :  

The relation f is defined by

The relation gis defined by

Show that f is a function and g is not a function.


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Q2 :  

If f(x) = x2, find.


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Q3 :  

Find the domain of the function


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Q4 :  

Find the domain and the range of the real function fdefined by.


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Q5 :  

Find the domain and the range of the real function fdefined by f(x) = |x- 1|.


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Q6 :  

Letbe a function from Rinto R. Determine the range of f.


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Q7 :  

Let f, g: R → R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f+ g, f– gand.


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Q8 :  

Let f = {(1, 1), (2, 3), (0, -1), (-1, -3)} be a function from Zto Zdefined by f(x) = ax+ b, for some integers a, b. Determine a, b.


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Q9 :  

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.


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Q10 :  

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) fis a relation from A to B (ii) fis a function from A to B.

Justify your answer in each case.


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Q11 :  

Let fbe the subset of Z x Zdefined by f = {(ab, a+ b): a, b Z}. Is fa function from Zto Z: justify your answer.


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Q12 :  

Let A = {9, 10, 11, 12, 13} and let f: A Nbe defined by f(n) = the highest prime factor of n. Find the range of f.


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<< Previous Chapter 1 : Sets Next Chapter 3 : Trigonometric Functions >>

Maths - Maths : CBSE NCERT Exercise Solutions for Class 11th for Relations and Functions ( Exercise 2.1, 2.2, 2.3, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

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