Home
Class 12
MATHS
If a ** b = 4a^(2) + 6b^(2) be a binary ...

If `a ** b = 4a^(2) + 6b^(2)` be a binary operations on Q, then verify that `**` is not commutative.

Text Solution

Verified by Experts

`a ** b = 4a^(2) + 6b^(2)`
`b ** a = 4b^(2) + 6a^(2)`
`a ** b = b ** a` (for commutative)
`4a^(2) + 6b^(2) = 4b^(2) + 6a^(2)`
`2b^(2) = 2a^(2)`
`b = +- a`
So it is not commutative
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment (Section - A) Objective Type Questions (one option is correct)|102 Videos

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment (Section - B) Objective Type Questions (one option is correct)|87 Videos

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment (Section - J) Aakash Challengers Questions|8 Videos

  • PROBABILITY

    AAKASH INSTITUTE|Exercise ASSIGNMENT SECTION-J (aakash challengers questions)|13 Videos

  • SEQUENCES AND SERIES

    AAKASH INSTITUTE|Exercise Assignment (SECTION - J) Aakash Challengers|12 Videos

Similar Questions

Explore conceptually related problems

Show that the binary operation * on Z defined by a*b=3a+7b is not commutative.

Is * defined by a^(*)b=(a+b)/(2) is binary operation on Z.

Let * be a binary operation on Z defined by a*b=a+b-4 for all a,b in Z. show that * is both commutative and associative.

Let '**' be a binary operation on Q defined by : a**b=(2ab)/(3) . Show that '**' is commutative as well as associative.

Let Q^(+) be the set of all positive rational numbers (i) show theat the operation * on Q^(+) defined by a* b = 1/2 (a+b) is binary operation (ii) show that * is commutative (iii) show that * is not associative

Which of the following is true? * defined by a*b=(a+b)/2 is a binary operation on Z (b) * defined by a*b=(a+b)/2 is a binary operation on Q (c) all binary commutative operations are associative (d) subtraction is a binary operation on N

If an operation * on the set of integers Z is defined by a*b=2a^(2)+b then find (i) whether is is binary or not,and (ii) if binary, then is it commutative or not

Commutativity of binary operations

AAKASH INSTITUTE-RELATIONS AND FUNCTIONS -Try Yourself
  1. Find the domain and range of |x-3|.

    Text Solution

    |

  2. Find the domain and range of -|x-5|.

    Text Solution

    |

  3. Consider that [] represents greatest integer function. Find the valu...

    Text Solution

    |

  4. Consider that [] represents greatest integer function. [(3)/(5)] + [...

    Text Solution

    |

  5. Let f(x) = x^(3) + 5 and g(x) = 5x + 3 be two real functions. Find (f+...

    Text Solution

    |

  6. Let f(x) = 3x + 8 and g(x) = x^(2) be two real functions. Find (f+g) (...

    Text Solution

    |

  7. If f, g : R rarr R be defined respectively by f(x) = 3x + 2 and g(x) =...

    Text Solution

    |

  8. If f, g : R rarr R be defined respectively by f(x) = 8x + 7 and g(x) =...

    Text Solution

    |

  9. Let f(x) = x^(3) + 6x + 9 and g(x) = x+5 be two functions. Find (f+g) ...

    Text Solution

    |

  10. Let f(x) = x^(2) + 2x +5 and g(x) = x^(3) - 1 be two real functions. F...

    Text Solution

    |

  11. Show that the function f : R rarr R defined by f(x) = cos (5x+3) is ne...

    Text Solution

    |

  12. Let A be the set of all 50 students of class X I I in a central sch...

    Text Solution

    |

  13. If f: R->R be given by f(x)=s in^2x+s in^2(x+pi//3)+cosx\ cos(x+pi//3)...

    Text Solution

    |

  14. Let f : R rarr R and g : R rarr R be two functions such that fog (x) =...

    Text Solution

    |

  15. If f : [0, oo) rarr [2, oo) be defined by f(x) = x^(2) + 2, AA xx in R...

    Text Solution

    |

  16. Let f : N ->Rbe a function defined as f(x)=4x^2+12 x+15. Show that f ...

    Text Solution

    |

  17. If ** be a binary operation on N (the setof natural numbers) defined b...

    Text Solution

    |

  18. Let A = {1, 2, 3}. Find the number of binary operations on A.

    Text Solution

    |

  19. If a ** b = 4a^(2) + 6b^(2) be a binary operations on Q, then verify t...

    Text Solution

    |

  20. Let A = N xx N and ** be the binary opertation on A defined by (a, b) ...

    Text Solution

    |