Home
Class 12
MATHS
Let A={1,2,3}dot Write all one-one fr...

Let `A={1,2,3}dot` Write all one-one from `A` to itself.

Text Solution

Verified by Experts

`A={1,2,3}`

Number of elements in `A=3`

Number of one-one functions = number of ways of arranging 3 elements `=3 =6`

(i) `{(1,1),(2,2),(3,3)}`

(ii) `{(1,1),(2,3),(3,2)}`

(iii) `{(1,2),(2,2),(3,3)}`

(iv) `{(1,2),(2,1),(3,3)}`

(v) `{(1,3),(2,2),(3,1)}`

...
Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos
  • HIGHER ORDER DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|176 Videos

Similar Questions

Explore conceptually related problems

Let A={1,2,3}. Write all one-one from A to itself.

Let A={1,2,3}. Write all one-one from A to itself.

Let A={1,2}. Find all one-to-one function from A to A.

Let A={1,2}&B={3.4}. Write all subsets of A xx B.

Find the number of all one-one functions from set A={1,2,3} to itself.

Write the number of all one-one functions from the set A{a,b,c} to itself.

Let A={1,2,3} and B={1,2,3,4,5,6,7} Among all the functions from A to B, the number of such that

Let A={1,2,3,4,5,6}dot Let R be a relation on A defined by R={(a , b): a , b in A , b is exactly divisible by a} Write R is roster form Find the domain of R Find the range of Rdot

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. f: R->R is defined by f(x)=(e^x^2-e^-x^2)/(e^x^2+e^-x^2) is (a) one-on...

    Text Solution

    |

  2. The inverse of the function f: Rvec{x in R : x<1} given by f(x)=(e^x-...

    Text Solution

    |

  3. Let A={1,2,3}dot Write all one-one from A to itself.

    Text Solution

    |

  4. If f: RvecR be the function defined by f(x)=4x^3+7, show that f is a b...

    Text Solution

    |

  5. If the function f:[1,oo)->[1,oo) is defined by f(x)=2^(x(x-1)), then ...

    Text Solution

    |

  6. The value of parameter alpha, for which the function f(x) = 1+alpha x,...

    Text Solution

    |

  7. Let R^+ be the set of all non-negative real numbers. if f: R^+ rar...

    Text Solution

    |

  8. Show that the function f: R ->R is given by f(x)=1+x^2 is not invertib...

    Text Solution

    |

  9. If f: Rvec(-1,1) defined by f(x)=(10^x-10^(-x))/(10^x+10^(-x)) is inve...

    Text Solution

    |

  10. Let f:[-1,oo]vec[-1,) is given by f(x)=(x+1)^2-1,xgeq-1. Show that f i...

    Text Solution

    |

  11. Let f: NvecS be a function defined as f(x)=4x^2+12 x+15. Show that f: ...

    Text Solution

    |

  12. Let A=R-{3} and B=R-[1]dot Consider the function f: AvecB defined by f...

    Text Solution

    |

  13. Let f,g:vec R be defined by f(x)=2x+1 and g(x)=x^2-2 for all x in R, r...

    Text Solution

    |

  14. Let A and B be any two sets such that n(B)=P, n(A)=q then the total nu...

    Text Solution

    |

  15. If f: ArightarrowA ,g: ArightarrowA are two bijections, then prove tha...

    Text Solution

    |

  16. Let f: Z->Z be defined by f(x)=x+2. Find g: Z->Z such that gof=IZ .

    Text Solution

    |

  17. Which one the following relations on A={1,2,3} is function? f={(1,3),(...

    Text Solution

    |

  18. Write the domain of the real function f defined by f(x)=sqrt(25-x^2) .

    Text Solution

    |

  19. Let A}x :-1lt=xlt=1}a n df: Avec such that f(x)=x|x|, then f is a bije...

    Text Solution

    |

  20. If the function f:(1,oo)rarr(1,oo) is defined by f(x)=2^(x(x-1)),t h e...

    Text Solution

    |