Home
Class 12
MATHS
If functions f:{1,2,…,n} rarr {1995,1996...

If functions `f:{1,2,…,n} rarr {1995,1996}` satisfying f(1)+f(2)+…+f(1996)=odd integer are formed, the number of such functions can be

A

`2^(n)`

B

`2^(n//2)`

C

`n^(2)`

D

`2^(n-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|25 Videos
  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos
  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 12|4 Videos
  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos
  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

Consider the function f: A -> A where A:{1,2,3,4,5} which satisfy the condition f(f(x))=x, If the number of such functions are lambda, then

The number of functions f: {1,2, 3,... n}-> {2016, 2017} , where ne N, which satisfy thecondition f1)+f(2)+ ...+ f(n) is an odd number are a. 2^n b. n*2^(n-1) c. 2^(n-1) d. n!

Let A={1,2,3,4,5} and f:A rarr A be an into function such that f(x) nex forall x in A . Then number of such functions f is:

A function f : R rarr R satisfies the equation f(x + y) = f(x) . f(y) for all, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2. Then,

A function f : R rarr R satisfies the equation f(x+y) = f(x). f(y) for all x y in R, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2 , then prove that f' = 2f(x) .

Show that f: [ -1, 1] rarr R , given by f(x)= (x)/(x+2) is one-one. Find the inverse of the function f: [-1,1] rarr Range f.

Let f be real valued function from N to N satisfying. The relation f(m+n)=f(m)+f(n) for all m,n in N . The range of f contains all the even numbers, the value of f(1) is

If f(x) is a real-valued function discontinuous at all integral points lying in [0,n] and if (f(x))^(2)=1, forall x in [0,n], then number of functions f(x) are

If the function f:[1,∞)→[1,∞) is defined by f(x)=2 ^(x(x-1)) then f^-1(x) is

The function f: N rarr N , given by f(x) = 2x is

ARIHANT MATHS-FUNCTIONS-Exercise (Single Option Correct Type Questions)
  1. Let f(x) be a polynominal with real coefficients such that xf(x)=f'(x)...

    Text Solution

    |

  2. Let A={1,2,3,4,5} and f:A rarr A be an into function such that f(x) ne...

    Text Solution

    |

  3. If functions f:{1,2,…,n} rarr {1995,1996} satisfying f(1)+f(2)+…+f(199...

    Text Solution

    |

  4. Find the range of y=sin^3x-6sin^2x+11sinx-6.

    Text Solution

    |

  5. Let f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-(x))dot Show that g(...

    Text Solution

    |

  6. If f(x) and g(x) are non-periodic functions, then h(x)=f(g(x)) is

    Text Solution

    |

  7. If f(x) is a real-valued function discontinuous at all integral points...

    Text Solution

    |

  8. A function f from integers to integers is defined as f(x)={{:(n+3, n ...

    Text Solution

    |

  9. If f:R->R and f(x)=sin(pi{x})/(x^4+3x^2+7), where {} is a fractional p...

    Text Solution

    |

  10. Show that f: R→ R defined as f(a) = 3a – 4 is one to one function.

    Text Solution

    |

  11. Find dy/dx if y= 3^x

    Text Solution

    |

  12. Let y be element of the set A={1,2,3,,5,6,10,15,30} and x(1),x(2),x(3)...

    Text Solution

    |

  13. If A gt 0, c,d,u.v are non-zero constants and the graph of f(x)=abs(Ax...

    Text Solution

    |

  14. f(x)=x^(3)+3x^(2)+4x+bsinx+c cosx,forall x in R is a one-one function,...

    Text Solution

    |

  15. If two roots of the equation (p-1)(x^2 +x +1)^2 -(p+1)(x^4+x^2+1)=0 ar...

    Text Solution

    |

  16. If f(x)=x^11+x^9−x^7+x^3+1 and f(sin^(−1)(sin8))=α,α is constant, then...

    Text Solution

    |

  17. Let f(x)=sin^(-1)2x + cos^(-1)2x + sec^(-1)2x. Then the sum of the max...

    Text Solution

    |

  18. The complete set of values of a for which the function f(x)=tan^(-1)(x...

    Text Solution

    |

  19. The domain of the function f(x)=sin^(-1)""(1)/abs(x^(2)-1)+1/sqrt(si...

    Text Solution

    |

  20. The domain of f(x)=(log(sin^(-1)sqrt(x^(2)+x+1)))/(log(x^(2)-x+1)) is ...

    Text Solution

    |