Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Consider a binary operation star on N defined as a star b equals a to the power 3 plus b to the power 3 . Choose the correct answer.(A) Is star both associative and commutative? (B) Is star commutative but not associative? (C) Is star associative but not

Q. 13 Consider a binary operation ∗ on N defined as a * b = a^3 + b^3 . Choose the
correct answer.

(A) Is ∗ both associative and commutative?
(B) Is ∗ commutative but not associative?
(C) Is ∗ associative but not commutative?
(D) Is ∗ neither commutative nor associative?

Answers (2)

best_answer

A binary operation ∗ on N defined as a * b = a^3 + b^3 .

For a,b \in N

       a * b = a^3 + b^3 = b^{3}+a^{3}=b*a

Thus , it is commutative.

(1*2)*3 = (1^{3}+2^{3})*3=9*3 =9^{3}+3^{3}=729+27=756

1*(2*3) = 1*(2^{3}+3^{3})=1*35 =1^{3}+35^{3}=1+42875=42876

\therefore \, \, \, \, \, (1*2)*3 \neq 1*(2*3)     where  1,2,3 \in N

Hence, it is not associative.

Hence, B is correct option.

 

Posted by

seema garhwal

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

14953/

Posted by

Safeer PP

View full answer

Similar Questions

Trending Articles/News

anam-khan

No changes in exam, IA system: CBSE rebuts claims of syllabus reduction, open book exams in 2025
anam-khan

Fact-check: CBSE hasn't reduced syllabus by 15%, internal assessments will not be 40% of score in 2025
anam-khan

CBSE date sheet 2025 for Classes 10, 12 likely in November last week: Reports

Latest Question