Home
Class 12
MATHS
Let * be a binary operations on Z and is...

Let * be a binary operations on Z and is defined by , a * b = a + b + 1, `a, bin Z`. Find the identity element.

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Let * be a binary operation on Zdefined by a*b=a+b- 15 for a,binZ . Find the identity element in (Z,*)

On the set Q^+ of all positive rational numbers if the binary operation * is defined by a * b = 1/4ab for all a,b in Q^+ find the identity element in Q^+ .

Let A={0,1,2,3,4,5} be a given set, a binary operation @ is defined on A by a@b=ab(mod6) for all a,bin A. Find the identity element for @ in A . Show that 1 and 5 are the only invetible elements in A.

Let * be a binary operation on Zdefined by a*b=a+b- 15 for a,binZ Find the inverse of an element in (Z ,*).

Let ** be a binary operation on set QQ-{1} defined by a**b=a+b-abinQQ-{1}. e is the identity element with respect to ** on QQ . Every element of QQ-{1} is invertible, then value of e and inverse of an element a are---

An operation @ on QQ-{-1} is defined by a@b=a+b+ab for a,binQQ-{-1}. Find the identity element einQQ-{-1} .

On the set QQ^(+) of all positive rational numbers if the binary operation ** is defined by a**b=(1)/(4)ab for all a,binQQ^(+) , find the identity element in QQ^(+) . Also prove that any element in QQ^(+) is invertible.

Let * be a binary operation on Zdefined by a*b=a+b- 15 for a,binZ . Show that *is commutative

Let A= Q xxQ . Let * be a binary operation Defined by: (a,b)*(c,d)= (ac,ad +b). Then (i) find the identity element of (A,*)

Let * be a binary operation on Zdefined by a*b=a+b- 15 for a,binZ .Show that *is associative

UNITED BOOK HOUSE-SET 19-EXERCISE
  1. If sin^-1 x - cos^-1 x = pi/6 then x is

    Text Solution

    |

  2. The I.F. of the differential equation x log x (dy)/(dx) + 2y = log x i...

    Text Solution

    |

  3. Let * be a binary operations on Z and is defined by , a * b = a + b + ...

    Text Solution

    |

  4. Evaluate: 4(2tan^(-1)(1/3)+tan^(-1)(1/7))

    Text Solution

    |

  5. Prove that (a+b+c+x) is a factor of |(x+a, b,c),(b,x+c,a),(c,a,x+b)|

    Text Solution

    |

  6. If P = ((1,2,1),(1,3,1)) and Q = PP^T , then find Q

    Text Solution

    |

  7. Verify Rolle's theorem for the function f(x) = sin x + cosx in the int...

    Text Solution

    |

  8. Evaluate : underset(x rarr0) Lt (logecosx)/(sin^2 x)

    Text Solution

    |

  9. Evaluate: int((cosx+xsinx)/(x(x+cosx)))dx.

    Text Solution

    |

  10. If x>1/2, show that the function f(x) = x(4x^2 - 3) is steadily increa...

    Text Solution

    |

  11. If |veca| = sqrt3,|vecb| = 2 and veca.vecb = sqrt6, then find the angl...

    Text Solution

    |

  12. If the line (x-2)/(6) = (y-1)/(lambda) = (z+5)/(-4) is perpendicular t...

    Text Solution

    |

  13. The probability that A hits a target is 1/3 and the probability that B...

    Text Solution

    |

  14. An unbiased coin is toosed 7 times. Find the probability of getting an...

    Text Solution

    |

  15. answer any one question : (ii) prove that , tan(pi/4 +1/2 (cos ^(-1) (...

    Text Solution

    |

  16. Solve : |(x+4, 2x,2x),(2x , x+4, 2x),(2x, 2x, x+4)| = 0

    Text Solution

    |

  17. By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: ...

    Text Solution

    |

  18. If y^(1/3) + y^(-1/3) = 2x, prove that (x^2 - 1)y2 + xy1 = 9y.

    Text Solution

    |

  19. Evaluate : int(loge(x+1))/((x+1)^2) dx

    Text Solution

    |

  20. Evaluate :int(5^(5^(5^x)cdot 5^(5^(x))cdot 5^x))dx

    Text Solution

    |