Home
Class 12
MATHS
Let X={a1, a2, ,a6}a n dY={b1, b2,b3}dot...

Let `X={a_1, a_2, ,a_6}a n dY={b_1, b_2,b_3}dot` The number of functions `f` from `xtoy` such that it is onto and there are exactly three elements `x inX` such that `f(x)=b_1` is

A

75

B

90

C

100

D

120

Text Solution

Verified by Experts

The correct Answer is:
D
Image `b_(1)` is assigned to any three of the six pre-images in `""^(6)C_(3)` ways.
Rest two images can be assigned to remaining three pre-images in `2^(3)-2` ways (as function is onto).
Hence, number of function are `""^(6)C_(3) xx (2^(3)-2)=20xx6=120.`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|32 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.15|8 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|31 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Let X={a_(1),a_(2),...,a_(6)} and Y={b_(1),b_(2),b_(3)} The number of functions f from x to y such that it is onto and there are exactly three elements x in X such that f(x)=b_(1) is 75 (b) 90( c) 100 (d) 120

Let A = {x_1, x_2, x_3, ,x_7},B={y_1, y_2, y_3} The total number of functions f: A->B that are onto and there are exactly three element x in A such that f(x)=y_2 is equal to a. 490 b. 510 c. 630 d. none of these

Let A={x_(1),x_(2),x_(3)....,x_(7)},B={y_(1)y_(2)y_(3)} . The total number of functions f:AtoB that are onto and ther are exactly three elements x in A such that f(x)=y_(2) , is equal to

Let 'A={1,2,3,.....n}' and 'B={a,b,c}' , the number of functions from A to B that are onto is

If f:A rarr B,A={1,2,3,4},B={1,2,3} and f(i)!=i then the number of onto functions from A to B is

Let A = {1, 2, 3, 4} and B = {a, b}. A function f : A to B is selected randomly. Probability that function is an onto function is

Consider set A = {x_(1), x_(2), x_(3), x_(4), x_(5)} and set B = {y_(1), y_(2), y_(3)} . Function f is defined from A to B. Number of function from A to B such that f(x_(1)) = y_(1) and f(x_(2)) != y_(2) is

CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Single)
  1. The function f:(-oo,-1)vec(0, e^5) defined by f(x)=e^x^(3-3x+2) is man...

    Text Solution

    |

  2. Let f:N->N be defined by f(x)=x^2+x+1,x in N. Then is f is

    Text Solution

    |

  3. Let X={a1, a2, ,a6}a n dY={b1, b2,b3}dot The number of functions f fro...

    Text Solution

    |

  4. Which of the following functions is an injective (one-one) function in...

    Text Solution

    |

  5. Given the function f(x)=(a^x+a^(-x))/2(w h e r ea >2)dotT h e nf(x+y)+...

    Text Solution

    |

  6. If f(x)=cos (logx), then f(x)f(y)-1/2[f(x/y)+f(xy)]=

    Text Solution

    |

  7. The domain of the function f(x)=(1)/(sqrt(""^(10)C(x-1)-3xx""^(10)C(x)...

    Text Solution

    |

  8. The domain of the function f(x)=(sin^(-1)(3-x))/("In"(|x|-2)) is

    Text Solution

    |

  9. The domain of f(x)=(log(2)(x+3))/(x^(2)+3x+2) is

    Text Solution

    |

  10. The domain of the function f(x)=sqrt(x^2-[x]^2) , where [x] is the gre...

    Text Solution

    |

  11. The domain of the function f(x)=log(3+x)(x^(2)-1) is

    Text Solution

    |

  12. Domain of the function, f(x)=[log10 ((5x-x^2)/4)]^(1/2) is

    Text Solution

    |

  13. The domain of f(x)=log|logx| is

    Text Solution

    |

  14. If x^3f(x)=sqrt(1+cos2x)+|f(x)|, (-3pi)/4ltxlt(-pi) /2 and f(x)=(alpha...

    Text Solution

    |

  15. The function f(x)=(sec^(-1)x)/(sqrt(x)-[x]), where [x] denotes the gre...

    Text Solution

    |

  16. The domain of definition of the function f(x) given by the equation 2^...

    Text Solution

    |

  17. The domain of f(x)=cos^(-1)((2-|x|)/4)+[l log(3-x)]^1 is [-2,6] (b...

    Text Solution

    |

  18. The domain of the function f(x)=sqrt(log((1)/(|sinx|)))

    Text Solution

    |

  19. Domain of definition of the function f(x) = log2 (-log(1/2) (1+x^(-4))...

    Text Solution

    |

  20. The number of real solutions of the (log)(0. 5)|x|=2|x| is

    Text Solution

    |