Home
Class 14
MATHS
The function f1 and f2 are defined as fo...

The function `f_1` and `f_2` are defined as follows : `f_1 = a! + b! and f_2 = a^a + b^b` for a, b > 1 and a, b in N` then the correct relation is :

A

`f_1 lt f_2`

B

`f_1 = f_2`

C

`f_1 gt f_2`

D

can't say

Text Solution

Verified by Experts

The correct Answer is:
A
Check for any value of `(a, b) gt 1` and a, b `epsilon` N
Since a! = a.(a-1)(a-2)…1 but `a^a` = a.a.a…a times
Therefore, `f_1 lt f_2`
Promotional Banner

Topper's Solved these Questions

  • MENSURATION

    QUANTUM CAT|Exercise QUESTION BANK|449 Videos

  • PERCENTAGES

    QUANTUM CAT|Exercise QUESTION BANK|271 Videos

Similar Questions

Explore conceptually related problems

The function f(x) is defined for all real x. If f(a+b)=f(ab) AA a " and " b " and " f(-(1)/(2))=-(1)/(2) then find the value of f(1005).

Let f: R to R be defined by f(x) =x/(x+1), x ne -1 If a,b in R and ab ne 0, f (a/b) + f(b/a) and a+b ne 0 is equal to

If the functions f(x) and g(x) are continuous on [a,b] and differentiable on (a,b) then in the interval (a,b) the equation |{:(f'(x),f(a)),(g'(x),g(a)):}|=(1)/(a-b)=|{:(f(a),f(b)),(g(a),g(b)):}|

Let f be a differentiable real function defined on (a;b) and if f'(x)>0 for all x in(a;b) then f is increasing on (a;b) and if f'(x)<0 for all x in(a;b) then f(x) is decreasing on (a;b)

Let the function f;R-{-b}rarr R-{1} be defined by f(x)=(x+a)/(x+b),a!=b, then

If the function f(x):A to B and g(x):B to C are defined such that (g(f(x)))^-1 exist then f(x) and g(x) are

QUANTUM CAT-NUMBER SYSTEM-QUESTION BANK
  1. If x # y = (x + y)/(xy), then the value of P # (q # r) for every p, q,...

    Text Solution

    |

  2. If f(x , y) = ((x + y)^2)/(xy) for every x, y > 0 then f(x,y) must be ...

    Text Solution

    |

  3. The function f1 and f2 are defined as follows : f1 = a! + b! and f2 = ...

    Text Solution

    |

  4. For any natural number p and q (i) p # q = p^3 + q^3 + 3 and p ** q ...

    Text Solution

    |

  5. For any natural number p and q (i) p # q = p 3 + q 3 + 3 and p ∗ q = ...

    Text Solution

    |

  6. The value of [Max (2,4)$ "Min" (6,8)] # [ "Min" (10,12) $ Max (14,16)]

    Text Solution

    |

  7. (1-1/3)(1-1/4)(1-1/5)…(1-1/n) equals:

    Text Solution

    |

  8. If the sum of three consecutive integers is 21, then the sum of the tw...

    Text Solution

    |

  9. The sum of squares of first ten natural numbers is :

    Text Solution

    |

  10. The sum of first 50 odd natural numbers is

    Text Solution

    |

  11. A boy draws n squares with sides 1,2,3,4,5,…. In inches. The average a...

    Text Solution

    |

  12. The 3rd and 6th term of an arithmetic progression are 4 and 9, respect...

    Text Solution

    |

  13. If the 9th and 19th terms of a G.P. are 12 and 18, what is the G.M. of...

    Text Solution

    |

  14. If the arithmetic mean of the numbers x1 , x2, x3,……., xn is barx, the...

    Text Solution

    |

  15. Which one of the following numbers belongs to the given series 18, 26,...

    Text Solution

    |

  16. When the natural numbers 1,2,3,……., 500 are written, then the digit 3 ...

    Text Solution

    |

  17. In how many ways can 1146600 be written as the product of two factors?

    Text Solution

    |

  18. How many natural numbers upto 990 are divisible by 5 & 9 both, but not...

    Text Solution

    |

  19. The number of solution of |x| + |y| le 0, for (x , y) in R, is :

    Text Solution

    |

  20. The remiander when 2^39 is divided by 39 is:

    Text Solution

    |