Home
Class 12
MATHS
The binary operation ** defined on NN by...

The binary operation `**` defined on `NN` by `a**b=a+b+ab` for all `a,binNN` is--

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE 1 (e) (Long Answer Type Questions (I))|8 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise Objective Type Questions (A. Multiple Choice Questions)|30 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE 1 (d) (Long Answer Type Questions (I))|9 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise MOCK TEST SECTION D|6 Videos

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHAPTER TEST 11|11 Videos

Similar Questions

Explore conceptually related problems

The binary operation * defined on N by a*b=a+b+ab for all a,b in N is (a) commutative only (b) associative only (c) commutative and associative both (d) none of these

For the binary operation * defined on R-{-1} by the rule a*b=a+b+ab for all a,b in R-{1}, the inverse of a is a (b) -(a)/(a+1)(c)(1)/(a) (d) a^(2)

Discuss the commutativity and associativity of binary operation* defined on Q by the rule a*b=a-b+ab for all a,b in Q

Discuss the commutativity and associativity of the binary operation * on R defined by a*b=(ab)/(4) for all a,b in R

If the binary operation * defined on Q, is defined as a*b=2a+b-ab, for all a*bQ, find the value of 3*4

Let * be a binary operation on N defined by a*b = a^(b) for all a,b in N show that * is neither commutative nor associative

Q^(+) is the set of all positive rational numbers with the binary operation * defined by a*b=(ab)/(2) for all a,b in Q^(+). The inverse of an element a in Q^(+) is a (b) (1)/(a)( c) (2)/(a) (d) (4)/(a)

Show that the binary operation * on A=R-{-1} defined as a^(*)b=a+b+ab for all a,b in A is commutative and associative on A. Also find the identity element of * in A and prove that every element of A is invertible.

Let * be a binary operation on Q-{-1} defined by a*b=a+b+ab for all a,b in Q-{-1}. Then,Show that * is both commutative and associative on Q-{-1} (ii) Find the identity element in Q-{-1}

Let ^(*) be a binary operation on Q-{-1} defined by a*b=a+b+ab for all a,b in Q-{-1}. Then,Show that every element of Q-{-1} is invertible.Also,find the inverse of an arbitrary element.

MODERN PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE 1 (e) (Short Answer Type Questions)
  1. Determine whether or not each of the definition of '**' given below gi...

    Text Solution

    |

  2. Show that the binary operation '**' defined from NxxNrarrN and given ...

    Text Solution

    |

  3. For each binary operation * defined below, determine whether * is com...

    Text Solution

    |

  4. For each binary operation '**' defined below, determine whether '**' i...

    Text Solution

    |

  5. For each binary operation '**' defined below, determine whether '**' i...

    Text Solution

    |

  6. For each binary operation '**' defined below, determine whether '**' i...

    Text Solution

    |

  7. For each binary operation '**' defined below, determine whether '**' i...

    Text Solution

    |

  8. For each binary operation '**' defined below, determine whether '**' i...

    Text Solution

    |

  9. For each binary operation '**' defined below, determine whether '**' i...

    Text Solution

    |

  10. Is *defined on the set {1, 2, 3, 4, 5} b y a * b = LdotCdotMdotof a a...

    Text Solution

    |

  11. Let *be the binary operation on N given by a*b = LdotCdotMdotof a and...

    Text Solution

    |

  12. Let * be a binary operation on N defined by a ** b = HCF of a and b. S...

    Text Solution

    |

  13. If n(A) = p and n(B) = q, then the number of relations from set A to s...

    Text Solution

    |

  14. (a) Let '**' be a binary operation defined on Q, the set of rational n...

    Text Solution

    |

  15. If A = { 1, 2, 3}, then the relation R = {(1, 2), (2, 3), (1, 3)} in A...

    Text Solution

    |

  16. In the binary operation **: QxxQrarrQ is defined as : (i) a**b=a+b-a...

    Text Solution

    |

  17. The binary operation ** defined on NN by a**b=a+b+ab for all a,binNN i...

    Text Solution

    |

  18. Discuss the commutativity and associativity of the binary operation * ...

    Text Solution

    |

  19. Find the domain and range of the real function f(x) = x/(1-x^2)

    Text Solution

    |

  20. Show that the operation '**' on Q - {1} defined by a**b=a+b-ab for...

    Text Solution

    |