NCERT solution Class 12 relations and functions

NCERT Solutions

Class 12 Maths

Relations and Functions

NCERT Questions

Ex. 1.1 Q1
Ex. 1.1 Q2
Ex. 1.1 Q3
Ex. 1.1 Q4
Ex. 1.1 Q5
Ex. 1.1 Q6
Ex. 1.1 Q7
Ex. 1.1 Q8
Ex. 1.1 Q9
Ex. 1.1 Q10
Ex. 1.1 Q11
Ex. 1.1 Q12
Ex. 1.1 Q13
Ex. 1.1 Q14
Ex. 1.1 Q15
Ex. 1.1 Q16
Ex. 1.2 Q1
Ex. 1.2 Q2
Ex. 1.2 Q3
Ex. 1.2 Q4
Ex. 1.2 Q5
Ex. 1.2 Q6
Ex. 1.2 Q7
Ex. 1.2 Q8
Ex. 1.2 Q9
Ex. 1.2 Q10
Ex. 1.2 Q11
Ex. 1.2 Q12
Ex. 1.3 Q1
Ex. 1.3 Q2
Ex. 1.3 Q3
Ex. 1.3 Q4
Ex. 1.3 Q5
Ex. 1.3 Q6
Ex. 1.3 Q7
Ex. 1.3 Q8
Ex. 1.3 Q9
Ex. 1.3 Q10
Ex. 1.3 Q11
Ex. 1.3 Q12
Ex. 1.3 Q13
Ex. 1.3 Q14
Ex. 1.4 Q1
Ex. 1.4 Q2
Ex. 1.4 Q3
Ex. 1.4 Q4
Ex. 1.4 Q5
Ex. 1.4 Q6
Ex. 1.4 Q7
Ex. 1.4 Q8
Ex. 1.4 Q9
Ex. 1.4 Q10
Ex. 1.4 Q11
Ex. 1.4 Q12
Ex. 1.4 Q13
Misc. Ex. Q1
Ex. 1.4 Q2
Ex. 1.4 Q3
Misc. Ex. Q4
Misc. Ex. Q5
Misc. Ex. Q6
Misc. Ex. Q7
Misc. Ex. Q8
Misc. Ex. Q9
Misc. Ex. Q10
Misc. Ex. Q11
Misc. Ex. Q12
Misc. Ex. Q13
Misc. Ex. Q14
Misc. Ex. Q15
Misc. Ex. Q16
Misc. Ex. Q17
Misc. Ex. Q18
Misc. Ex. Q19

Ex. 1.2 Q2

Check the injectivity and surjectivity of the following functions:

(i) f: N → N given by f(x) = x²

(ii) f: Z → Z given by f(x) = x²

(iii) f: R → R given by f(x) = x²

(iv) f: N → N given by f(x) = x³

(v) f: Z → Z given by f(x) = x³

(i) f: N → N is given by f(x) = x²

It is seen that for x, y ∈ N,

f(x) = f(y)

⇒ x²= y²

⇒ x = y

So, f is injective.

Now, 2 ∈ N. But, there does not exist any x in N such that f(x) = x² = 2.

So, f is not surjective.

Hence, function f is injective but not surjective.

(ii) f: Z → Z is given by f(x) = x²

It is seen that f(−1) = f(1) = 1, but −1 ≠ 1

So, f is not injective.

Now, −2 ∈ Z. But, there does not exist any element x ∈ Z such that

f(x) = −2 or x² = −2

So, f is not surjective.

Hence, function f is neither injective nor surjective.

(iii) f: R → R is given by f(x) = x²

It is seen that f(−1) = f(1) = 1, but −1 ≠ 1

So, f is not injective.

Now, −2 ∈ R. But, there does not exist any element x ∈ R such that

f(x) = −2 or x² = −2

So, f is not surjective.

Hence, function f is neither injective nor surjective.

(iv) f: N → N given by f(x) = x³

It is seen that for x, y ∈ N,

f(x) = f(y)

⇒ x³ = y³

⇒ x = y

So, f is injective.

Now, 2 ∈ N. But, there does not exist any element x ∈ N such that

f(x) = 2 or x³ = 2

So, f is not surjective

Hence, function f is injective but not surjective.

(v) f: Z → Z is given by f(x) = x³

It is seen that for x, y ∈ Z,

f(x) = f(y)

⇒ x³ = y³

⇒ x = y

So, f is injective.

Now, 2 ∈ Z. But, there does not exist any element x ∈ Z such that

f(x) = 2 or x³ = 2

So, f is not surjective.

Hence, function f is injective but not surjective.

Relations and Functions Class 12 Maths NCERT Chapter 1 NCERT Solutions

Solving NCERT textbook questions of Relations and Functions Class 12 Maths NCERT Chapter 1 is a crucial step to gauge your understanding of the concepts. It provides you with an opportunity to assess your grasp of the material after learning each chapter. We have already provided solutions to all the exercises in the NCERT textbook of Class 12 Maths Relations and Functions, available in various formats such as video, text, and downloadable PDFs. If you need assistance with any of the NCERT questions or any other academic topics, feel free to ask in the “Ask Questions” section of LearnoHub.com.

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Attempt to Solve Yourself: Before looking at the solution, try to solve or answer the question independently. This practice will help you test your knowledge and problem-solving skills.
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Refer to Solution Video (if needed): If you encounter difficulty or are unable to solve a question, you can refer to the NCERT solution video on Relations and Functions Class 12 Maths NCERT Chapter 1 to get a step-by-step explanation of the correct approach. Pay attention to the reasoning and methodology used in the video.
Solve Again Yourself: Once you've understood the solution, attempt to solve the question again by yourself. Repetition and practice solidify your understanding of the concepts and improve retention.
Avoid Memorization: Focus on understanding the underlying principles and concepts behind each solution. Avoid simply memorizing the solutions, as this may hinder your ability to apply the knowledge in different contexts.
Attempt All Questions: Make an effort to attempt all the questions provided in the NCERT textbook. This comprehensive practice will help you cover the entire syllabus and reinforce your understanding across various topics. You may refer Class 12 Maths Relations and Functions Online Test on LearnoHub.com.
Review and Revise: Regularly review the concepts and solutions you've learned. Revise your notes and practice regularly to retain the knowledge effectively. You may refer Relations and Functions Class 12 Maths Notes.
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NCERT solutions of Relations and Functions Class 12 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 12 Maths Relations and Functions NCERT solutions.