Careers360 Logo
School
Search Colleges, Exams, Schools & more
NCERT Solutions for Exercise 1.2 Class 12 Maths Chapter 1 - Relations and Functions

NCERT Solutions for Exercise 1.2 Class 12 Maths Chapter 1 - Relations and Functions

Edited By Ramraj Saini | Updated on Dec 03, 2023 01:18 PM IST | #CBSE Class 12th

NCERT Solutions For Class 12 Maths Chapter 1 Exercise 1.2

NCERT Solutions for Exercise 1.2 Class 12 Maths Chapter 1 Relations and Functions are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. NCERT Solutions for Class 12 Maths chapter 1 exercise 1.2 is the most important exercise of chapter Relations and Functions and it includes topics like types of relations, functions, binary operations etc. Exercise 1.2 Class 12 Maths exposes students to questions like proving one to one functions etc. Such questions are generally asked in Board examinations. Solving NCERT syllabus for Class 12 Maths chapter 1 exercise 1.2 is recommended to students to score well in CBSE Class 12 board exam. The contribution of chapter Relations and Functions is high in competitive exams also like JEE main and NEET. There are many questions asked in previous years which are based on concepts of Class 12 Maths chapter 1 exercise 1.2.

This Story also Contains
  1. NCERT Solutions For Class 12 Maths Chapter 1 Exercise 1.2
  2. Assess NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.2
  3. NCERT Solutions For Class 12 Maths Chapter 1 Relations And Functions: Exercise 1.2
  4. More About NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.2
  5. Benefits of NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.2
  6. Key Features Of NCERT Solutions for Exercise 1.2 Class 12 Maths Chapter 1

12th class Maths exercise 1.2 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all NCERT exercise together using the link provided below.

Tallentex 2025 - ALLEN's Talent Encouragement Exam

Register for Tallentex '25 - One of The Biggest Talent Encouragement Exam

Apply

Assess NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.2

Download PDF

NCERT Solutions For Class 12 Maths Chapter 1 Relations And Functions: Exercise 1.2

Question:1 Show that the function f: R_* \longrightarrow R_{*} defined by f(x) = \frac{1}{x} is one-one and onto,where R ∗ is the set of all non-zero real numbers. Is the result true, if the domain R ∗ is replaced by N with co-domain being same as R ∗ ?

Answer:

Given, f: R_* \longrightarrow R_{*} is defined by f(x) = \frac{1}{x} .

One - One :

f(x)=f(y)

\frac{1}{x}=\frac{1}{y}

x=y

\therefore f is one-one.

Onto:

We have y \in R_* , then there exists x=\frac{1}{y} \in R_* ( Here y\neq 0 ) such that

f(x)= \frac{1}{(\frac{1}{y})} = y

\therefore f is \, \, onto .

Hence, the function is one-one and onto.

If the domain R ∗ is replaced by N with co-domain being same as R ∗ i.e. g: N \longrightarrow R_{*} defined by

g(x)=\frac{1}{x}

g(x_1)=g(x_2)

\frac{1}{x_1}=\frac{1}{x_2}

x_1=x_2

\therefore g is one-one.

For 1.5 \in R_* ,

g(x) = \frac{1}{1.5} but there does not exists any x in N.

Hence, function g is one-one but not onto.

Question:2(i) Check the injectivity and surjectivity of the following functions:

(i) f : N\rightarrow N given by f(x) = x^2

Answer:

f : N\rightarrow N

f(x) = x^2

One- one:

x,y \in N then f(x)=f(y)

x^{2}=y^{2}

x=y

\therefore f is one- one i.e. injective.

For 3 \in N there is no x in N such that f(x)=x^{2}=3

\therefore f is not onto i.e. not surjective.

Hence, f is injective but not surjective.

Question:2(ii) Check the injectivity and surjectivity of the following functions:

(ii) f : Z \rightarrow Z given by f(x) = x^2

Answer:

f : Z \rightarrow Z

f(x) = x^2

One- one:

For -1,1 \in Z then f(x) = x^2

f(-1)= (-1)^{2}

f(-1)= 1 but -1 \neq 1

\therefore f is not one- one i.e. not injective.

For -3 \in Z there is no x in Z such that f(x)=x^{2}= -3

\therefore f is not onto i.e. not surjective.

Hence, f is neither injective nor surjective.

Question:2(iii) Check the injectivity and surjectivity of the following functions:

(iii) f: R \rightarrow R given by f(x) = x^2

Answer:

f: R \rightarrow R

f(x) = x^2

One- one:

For -1,1 \in R then f(x) = x^2

f(-1)= (-1)^{2}

f(-1)= 1 but -1 \neq 1

\therefore f is not one- one i.e. not injective.

For -3 \in R there is no x in R such that f(x)=x^{2}= -3

\therefore f is not onto i.e. not surjective.

Hence, f is not injective and not surjective.

Question:2(iv) Check the injectivity and surjectivity of the following functions:

(iv) f: N \rightarrow N given by f(x) = x^3

Answer:

f : N\rightarrow N

f(x) = x^3

One- one:

x,y \in N then f(x)=f(y)

x^{3}=y^{3}

x=y

\therefore f is one- one i.e. injective.

For 3 \in N there is no x in N such that f(x)=x^{3}=3

\therefore f is not onto i.e. not surjective.

Hence, f is injective but not surjective.

Question:2(v) Check the injectivity and surjectivity of the following functions:

(v) f : Z \rightarrow Z given by f(x) = x^3

Answer:

f : Z \rightarrow Z

f(x) = x^3

One- one:

For (x,y) \in Z then f(x) = f(y)

x^{3}=y^{3}

x=y

\therefore f is one- one i.e. injective.

For 3 \in Z there is no x in Z such that f(x)=x^{3}= 3

\therefore f is not onto i.e. not surjective.

Hence, f is injective but not surjective.

Question:3 Prove that the Greatest Integer Function f : R\longrightarrow R , given by f (x) = [x] , is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x .

Answer:

f : R\longrightarrow R

f (x) = [x]

One- one:

For 1.5,1.7 \in R then f(1.5)=\left [ 1.5 \right ] = 1 and f(1.7)=\left [ 1.7 \right ] = 1

but 1.5\neq 1.7

\therefore f is not one- one i.e. not injective.

For 0.6 \in R there is no x in R such that f(x)=\left [ 0.6 \right ]

\therefore f is not onto i.e. not surjective.

Hence, f is not injective but not surjective.

Question:4 Show that the Modulus Function f : R → R, given by f (x) = | x | , is neither one-one nor onto, where | x | is x, if x is positive or 0 and | x | is - x , if x is negative.

Answer:

f : R \rightarrow R

f (x) = | x |

f (x) = | x | = x \, if\, x\geq 0 \,\, and \, \, -x\, if\, x< 0

One- one:

For -1,1 \in R then f (-1) = | -1 |= 1

f (1) = | 1 |= 1

-1\neq 1

\therefore f is not one- one i.e. not injective.

For -2 \in R ,

We know f (x) = | x | is always positive there is no x in R such that f (x) = | x |=-2

\therefore f is not onto i.e. not surjective.

Hence, f (x) = | x | , is neither one-one nor onto.

Question:5 Show that the Signum Function f : R \rightarrow R , given by

f (x) = \left\{\begin{matrix} 1 & if\;x>0 \\ 0& if\;x=0 \\ -1& if\;x<0 \end{matrix}\right. is neither one-one nor onto.

Answer:

f : R \rightarrow R is given by

f (x) = \left\{\begin{matrix} 1 & if\;x>0 \\ 0& if\;x=0 \\ -1& if\;x<0 \end{matrix}\right.

As we can see f(1)=f(2)=1 , but 1\neq 2

So it is not one-one.

Now, f(x) takes only 3 values (1,0,-1) for the element -3 in codomain R ,there does not exists x in domain R such that f(x)= -3 .

So it is not onto.

Hence, signum function is neither one-one nor onto.

Question:6 Let A = \{1, 2, 3\} , B = \{4, 5, 6, 7\} and let f = \{(1, 4), (2, 5), (3, 6)\} be a function from A to B. Show that f is one-one.

Answer:

A = \{1, 2, 3\}

B = \{4, 5, 6, 7\}

f = \{(1, 4), (2, 5), (3, 6)\}

f : A \rightarrow B

\therefore f(1)=4,f(2)=5,f(3)=6

Every element of A has a distant value in f.

Hence, it is one-one.

Question:7(i) In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.

(i) f: R\rightarrow R defined by f(x) = 3 -4x

Answer:

f: R\rightarrow R

f(x) = 3 -4x

Let there be (a,b) \in R such that f(a)=f(b)

3-4a = 3 -4b

-4a = -4b

a = b

\therefore f is one-one.

Let there be y \in R , y = 3 -4x

x = \frac{(3-y)}{4}

f(x) = 3 -4x

Puting value of x, f(\frac{3-y}{4}) = 3 - 4(\frac{3-y}{4})

f(\frac{3-y}{4}) = y

\therefore f is onto.

f is both one-one and onto hence, f is bijective.

Question:7(ii) In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.

(ii) f : R\rightarrow R defined by f(x) = 1 + x^2

Answer:

f : R\rightarrow R

f(x) = 1 + x^2

Let there be (a,b) \in R such that f(a)=f(b)

1+a^{2} = 1 +b^{2}

a^{2}=b^{2}

a = \pm b

For f(1)=f(-1)=2 and 1\neq -1

\therefore f is not one-one.

Let there be -2 \in R (-2 in codomain of R)

f(x) = 1 + x^2 = -2

There does not exists any x in domain R such that f(x) = -2

\therefore f is not onto.

Hence, f is neither one-one nor onto.

Question:8 Let A and B be sets. Show that f : A \times B \rightarrow B \times A such that f (a, b) = (b, a) is
bijective function.

Answer:

f : A \times B \rightarrow B \times A

f (a, b) = (b, a)

Let (a_1,b_1),(a_2,b_2) \in A\times B

such that f (a_1, b_1) = f(a_2, b_2)

(b_1,a_1)=(b_2,a_2)

\Rightarrow b_1= b_2 and a_1= a_2

\Rightarrow (a_1,b_1) = (a_2,b_2)

\therefore f is one- one

Let, (b,a) \in B\times A

then there exists (a,b) \in A\times B such that f (a, b) = (b, a)

\therefore f is onto.

Hence, it is bijective.

Question:9 Let f : N \rightarrow N be defined by f(n) = \left\{\begin{matrix} \frac{n+1}{2} & if\;n\;is\;odd \\ \frac{n}{2} & if\;n\;is\;even \end{matrix}\right. for all n\in N . State whether the function f is bijective. Justify your answer.

Answer:

f : N \rightarrow N , n\in N

f(n) = \left\{\begin{matrix} \frac{n+1}{2} & if\;n\;is\;odd \\ \frac{n}{2} & if\;n\;is\;evem \end{matrix}\right.

Here we can observe,

f(2)=\frac{2}{2}=1 and f(1)=\frac{1+1}{2}=1

As we can see f(1)=f(2)=1 but 1\neq 2

\therefore f is not one-one.

Let, n\in N (N=co-domain)

case1 n be even

For r \in N , n=2r

then there is 4r \in N such that f(4r)=\frac{4r}{2}=2r

case2 n be odd

For r \in N , n=2r+1

then there is 4r+1 \in N such that f(4r+1)=\frac{4r+1+1}{2}=2r +1

\therefore f is onto.

f is not one-one but onto

hence, the function f is not bijective.

Question:10 Let A = R - \{3\} and B = R - \{1\} . Consider the function f : A\rightarrow B defined by f(x) = \left (\frac{x-2}{x-3} \right ) . Is f one-one and onto? Justify your answer.

Answer:

A = R - \{3\}

B = R - \{1\}

f : A\rightarrow B

f(x) = \left (\frac{x-2}{x-3} \right )

Let a,b \in A such that f(a)=f(b)

\left (\frac{a-2}{a-3} \right ) = \left ( \frac{b-2}{b-3} \right )

(a-2)(b-3)=(b-2)(a-3)

ab-3a-2b+6=ab-2a-3b+6

-3a-2b=-2a-3b

3a+2b= 2a+3b

3a-2a= 3b-2b

a=b

\therefore f is one-one.

Let, b \in B = R - \{1\} then b\neq 1

a \in A such that f(a)=b

\left (\frac{a-2}{a-3} \right ) =b

(a-2)=(a-3)b

a-2 = ab -3b

a-ab = 2 -3b

a(1-b) = 2 -3b

a= \frac{2-3b}{1-b}\, \, \, \, \in A

For any b \in B there exists a= \frac{2-3b}{1-b}\, \, \, \, \in A such that

f(\frac{2-3b}{1-b}) = \frac{\frac{2-3b}{1-b}-2}{\frac{2-3b}{1-b}-3}

=\frac{2-3b-2+2b}{2-3b-3+3b}

=\frac{-3b+2b}{2-3}

= b

\therefore f is onto

Hence, the function is one-one and onto.

Question:11 Let f : R \rightarrow R be defined as f(x) = x^4 . Choose the correct answer.

(A) f is one-one onto

(B) f is many-one onto

(C) f is one-one but not onto

(D) f is neither one-one nor onto.

Answer:

f : R \rightarrow R

f(x) = x^4

One- one:

For a,b \in R then f(a) = f(b)

a^{4}=b^{4}

a=\pm b

\therefore f(a)=f(b) does not imply that a=b

example: and 2\neq -2

\therefore f is not one- one

For 2\in R there is no x in R such that f(x)=x^{4}= 2

\therefore f is not onto.

Hence, f is neither one-one nor onto.

Option D is correct.

Question:12 Let f : R\rightarrow R be defined as f(x) = 3x . Choose the correct answer.

(A) f is one-one onto

(B) f is many-one onto

(C) f is one-one but not onto

(D) f is neither one-one nor onto.

Answer:

f : R\rightarrow R

f(x) = 3x

One - One :

Let \left ( x,y \right ) \in R

f(x)=f(y)

3x=3y

x=y

\therefore f is one-one.

Onto:

We have y \in R , then there exists x=\frac{y}{3} \in R such that

f(\frac{y}{3})= 3\times \frac{y}{3} = y

\therefore f is \, \, onto .

Hence, the function is one-one and onto.

The correct answer is A .

More About NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.2

The NCERT Class 12 Maths chapter Relations and Functions has a total of 5 exercises including miscellaneous. Exercise 1.2 Class 12 Maths covers solutions to 12 main questions and their sub-questions. Most of the questions are related to proving a function one to one. Hence NCERT Solutions for Class 12 Maths chapter 1 exercise 1.2 can be referred for learning the concepts related to proof etc.

Also Read| NCERT Notes For Class 12 Mathematics Chapter 1

Benefits of NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.2

  • The Class 12th Maths chapter 1 exercise provided here is solved by subject matter experts having rich experience in the domain of competitive exam preparation.
  • Students can practice Exercise 1.2 Class 12 Maths to prepare various concepts like signus functions, one to one functions etc, many direct questions are asked in Board exams from this chapter.
  • These Class 12 Maths chapter 1 exercise 1.2 solutions can be referred by students to revise before the exam and clarify any doubt regarding solution of exercise questions.
  • NCERT Solutions for Class 12 Maths chapter 1 exercise 1.2 provided here are most recommended solutions for students aspiring to score well in examinations.
JEE Main Highest Scoring Chapters & Topics
Just Study 40% Syllabus and Score upto 100%
Download EBook

Key Features Of NCERT Solutions for Exercise 1.2 Class 12 Maths Chapter 1

  • Comprehensive Coverage: The solutions encompass all the topics covered in ex 1.2 class 12, ensuring a thorough understanding of the concepts.
  • Step-by-Step Solutions: In this class 12 maths ex 1.2, each problem is solved systematically, providing a stepwise approach to aid in better comprehension for students.
  • Accuracy and Clarity: Solutions for class 12 ex 1.2 are presented accurately and concisely, using simple language to help students grasp the concepts easily.
  • Conceptual Clarity: In this 12th class maths exercise 1.2 answers, emphasis is placed on conceptual clarity, providing explanations that assist students in understanding the underlying principles behind each problem.
  • Inclusive Approach: Solutions for ex 1.2 class 12 cater to different learning styles and abilities, ensuring that students of various levels can grasp the concepts effectively.
  • Relevance to Curriculum: The solutions for class 12 maths ex 1.2 align closely with the NCERT curriculum, ensuring that students are prepared in line with the prescribed syllabus.

Also see-

NCERT Solutions Subject Wise

Subject wise NCERT Exemplar solutions

Happy learning!!!

Frequently Asked Question (FAQs)

1. Which concepts are covered in Exercise 1.2 Class 12 Maths?

Concepts related to one to one functions, reflexive functions etc, are discussed in the Exercise 1.2 Class 12 Maths

2. What is a set?

In Mathematics, A set is a collection of distinct or well-defined numbers or elements

3. How much weightage is given to chapter NCERT book chapter Relations and Functions for the CBSE board exam ?

Weightage of the chapters 'relation and function' is around 5 % weightage in the CBSE final board exam.

4. What are the various ways of representing a set?

There are 3 ways to represent a set:

a. Statement form.

b. Roaster form .

c. Set Builder form.

5. What is the meaning of the empty set in Class 12 Maths?

 A set with no elements is called an empty set. Also known by Null set or void set.

6. What is the meaning of Relation discussed in Exercise 1.2 Class 12 Maths

A relation is the set of ordered pair numbers.

7. How many questions are covered in Exercise 1.2 Class 12 Maths ?

12 questions  are there  in Exercise 1.2 Class 12 Maths

8. What is the total number of exercises there are in the NCERT Class 12 Maths chapter 1 Relations and Functions ?

5 exercises are there including a miscellaneous exercise in the NCERT class 12 maths chapter 1.

Also Read

Articles

Upcoming School Exams

National Means Cum-Merit Scholarship

Application Date:22 July,2024 - 31 August,2024

International General Knowledge Olympiad

Exam Date:19 September,2024 - 19 September,2024

Unified Cyber Olympiad

Exam Date:20 September,2024 - 20 September,2024

International English Olympiad

Exam Date:26 September,2024 - 26 September,2024

International Olympiad of Mathematics

Application Date:30 September,2024 - 30 September,2024

View All School Exams

Certifications By Top Providers

Edx
 1113 courses
Coursera
 804 courses
Udemy
 394 courses
Futurelearn
 222 courses
Harvard University, Cambridge
 98 courses
IBM
 85 courses

Explore Top Universities Across Globe

University of Essex, Colchester
  Wivenhoe Park Colchester CO4 3SQ
University College London, London
  Gower Street, London, WC1E 6BT
The University of Edinburgh, Edinburgh
  Old College, South Bridge, Edinburgh, Post Code EH8 9YL
University of Bristol, Bristol
  Beacon House, Queens Road, Bristol, BS8 1QU
University of Delaware, Newark
  Newark, DE 19716
University of Nottingham, Nottingham
  University Park, Nottingham NG7 2RD

Related E-books & Sample Papers

CBSE 12th Sociology Question Paper 2024

12+ Downloads

Questions related to CBSE Class 12th

Have a question related to CBSE Class 12th ?
i have taken admission in clg after my campartment exam in chemistry along with the neet 2025 preperation but unfortunately i again got campartment after doing all this preparation i got 15 marks only now I can't able to think what should I do next.

You can use them people also used problem

Read Complete Answer
Divyan 06 August,2024
i upload 12th board result screenshot in ncweb form from the cbse site so it is valid

hello mahima,

If you have uploaded screenshot of your 12th board result taken from CBSE official website,there won,t be a problem with that.If the screenshot that you have uploaded is clear and legible. It should display your name, roll number, marks obtained, and any other relevant details in a readable forma.ALSO, the screenshot clearly show it is from the official CBSE results portal.

hope this helps.

Read Complete Answer
Ashvadha 12 July,2024
Kya mujhe class 12 ka important question milega jo exam mai per year puche jate hai

Hello Akash,

If you are looking for important questions of class 12th then I would like to suggest you to go with previous year questions of that particular board. You can go with last 5-10 years of PYQs so and after going through all the questions you will have a clear idea about the type and level of questions that are being asked and it will help you to boost your class 12th board preparation.

You can get the Previous Year Questions (PYQs) on the official website of the respective board.

I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.

Thank you and wishing you all the best for your bright future.

Read Complete Answer
kumardurgesh1802 10 July,2024
I have completed my 12th with arts cbse. I want to repeat my 12th with pcmb. How to become a private candidate and what are deadline to be able to appear in 2025 exam?

Hello student,

If you are planning to appear again for class 12th board exam with PCMB as a private candidate here is the right information you need:

  • No school admission needed! Register directly with CBSE. (But if you want to attend the school then you can take admission in any private school of your choice but it will be waste of money)
  • You have to appear for the 2025 12th board exams.
  • Registration for class 12th board exam starts around September 2024 (check CBSE website for exact dates).
  • Aim to register before late October to avoid extra fees.
  • Schools might not offer classes for private students, so focus on self-study or coaching.

Remember , these are tentative dates based on last year. Keep an eye on the CBSE website ( https://www.cbse.gov.in/ ) for the accurate and official announcement.

I hope this answer helps you. If you have more queries then feel free to share your questions with us, we will be happy to help you.

Good luck with your studies!

Read Complete Answer
kumardurgesh1802 10 July,2024
I passed my 12th cbse boards in 2023 , and first time appear for jee mains and advance in 2024 so , am i eligible for 2025 jee mains and advance ?

Hello Aspirant , Hope your doing great . As per your query , your eligible for JEE mains in the year of 2025 , Every candidate can appear for the JEE Main exam 6 times over three consecutive years . The JEE Main exam is held two times every year, in January and April.

Read Complete Answer
satyamercedes0626 23 July,2024
View All

Popular CBSE Class 12th Questions

A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

 Option 2)

0.16\; J
Option 3)

1.00\; J

 Option 4)

0.67\; J
Read More

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

 Option 2)

 6.45×10−3 kg
Option 3)

 9.89×10−3 kg

 Option 4)

12.89×10−3 kg

 
Read More

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

 Option 2)

200 \, \, J - 500 \, \, J
Option 3)

2\times 10^{5}J-3\times 10^{5}J

 Option 4)

20,000 \, \, J - 50,000 \, \, J
Read More

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

 Option 2)

\; K\;
Option 3)

zero\;

 Option 4)

K/4
Read More

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

 Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced
Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

 Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .
Read More

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

 Option 2)

3.125 × 10-2
Option 3)

1.25 × 10-2

 Option 4)

2.5 × 10-2
Read More

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

 Option 2)

increase two fold
Option 3)

remain unchanged

 Option 4)

be a function of the molecular mass of the substance.
Read More

With increase of temperature, which of these changes?

Option 1)

Molality

 Option 2)

Weight fraction of solute
Option 3)

Fraction of solute present in water

 Option 4)

Mole fraction.
Read More

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

 Option 2)

6.023 × 1022
Option 3)

half that in 8 g He

 Option 4)

558.5 × 6.023 × 1023
Read More

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

 Option 2)

more than 3 but less than 6
Option 3)

more than 6 but less than 9

 Option 4)

more than 9
Read More

Colleges After 12th

Applications for Admissions are open.

Tallentex 2025 - ALLEN's Talent Encouragement Exam
Tallentex 2025 - ALLEN's Talent Encouragement Exam
Apply

Register for Tallentex '25 - One of The Biggest Talent Encouragement Exam

JEE Main Important Physics formulas
JEE Main Important Physics formulas
Apply

As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters

JEE Main Important Chemistry formulas
JEE Main Important Chemistry formulas
Apply

As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters

TOEFL ® Registrations 2024
TOEFL ® Registrations 2024
Apply

Accepted by more than 11,000 universities in over 150 countries worldwide

PTE Registrations 2024
PTE Registrations 2024
Apply

Register now for PTE & Unlock 10% OFF : Use promo code: 'C360SPL10'. Limited Period Offer!

JEE Main high scoring chapters and topics
JEE Main high scoring chapters and topics
Apply

As per latest 2024 syllabus. Study 40% syllabus and score upto 100% marks in JEE

View All Application Forms
News and Notifications
‘Marks inflation’: CBSE to overhaul internal assessment system, develop framework with British Council
August 28, 2024 - 04:58 PM IST
65 lakh students didn't clear Class 10, 12 board exams last year: Education ministry
August 21, 2024 - 10:24 PM IST
CBSE Compartment Result 2024: Marks verification, answer book photocopy, revaluation dates out
August 06, 2024 - 12:37 PM IST
CBSE Class 12 compartment results 2024 declared at cbseresults.nic.in; 29.78% pass
August 02, 2024 - 04:46 PM IST
CBSE best, Kerala board worst in curriculum, infrastructure: NCERT PARAKH report
July 30, 2024 - 04:48 PM IST
Assign 40% weightage to Class 12 exam in final result; have ‘on-demand exams’: NCERT PARAKH report
July 29, 2024 - 07:54 PM IST
CBSE Class 10, 12 compartment 2024 exams today for 2.5 lakh students; exam timings, guidelines
July 15, 2024 - 07:42 AM IST

Stay up-to date with CBSE Class 12th News

Back to top