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The number of one-one functions f : {a, ...

The number of one-one functions f : {a, b, c, d} to {0, 1, 2, ..., 10} such that 2f(a) - f(b) + 3f (c) + f(d)=0 is ______

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Knowledge Check

  • If a twice differentiable function f(x) on (a,b) and continuous on [a, b] is such that f''(x)lt0 for all x in (a,b) then for any c in (a,b),(f(c)-f(a))/(f(b)-f(c))gt

    A
    `(b-c)/(c-a)`
    B
    `(c-a)/(b-c)`
    C
    `(b-c)(c-a)`
    D
    `(1)/((b-c)(c-a))`

  • If f(x) is twice differentiable and continuous function in x in [a,b] also f'(x) gt 0 and f ''(x) lt 0 and c in (a,b) then (f(c) - f(a))/(f(b) - f(a)) is greater than

    A
    `(b - c)/(c-a)`
    B
    1
    C
    `(a + b)/(b - c)`
    D
    `(c-a)/(b - c)`

  • Let f:[a,b] to R be a function such that , for c in (a,b), f.(c ) = f..( c) = f...( c) = f.... (c ) = f.....( c) = 0 . Then :

    A
    f has local extremum at x = c
    B
    f has neither local maximum nor local minimum at x = c
    C
    f is necessarily a constant function
    D
    It is difficult to say whether (A) or (B)

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