If f is defined in [1, 3] by f(x) = x3 + bx2 + ax,such that f(1)

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 Multiple Choice QuestionsMultiple Choice Questions

111.

Let Q be the set of all rational numbers in [0, 1]and f: [0, 1]  [0,1] be defined by

f(x) = x, for x  Q1 - x for x QThen, the set S = x  0, 21 : fofx = ?

  • [0, 1]

  • - Q

  • [0, 1] - Q

  • (0, 1)


112.

If f : R  R, g : R  R are defined by fx = 5x - 3, gx = x2 + 3, then gof - 13 = ?

  • 253

  • 11125

  • 925

  • 25111


113.

If A = x  Rlπ4  x π3 and fx = sinx - x, then fA =?

  • 32 - π3, 12 - π4

  • - 12 - π4, 32 - π3

  • - π3, - π4

  • π4, π3


114.

In a ABC, atanA + btanB + ctanC = ?

  • 2r

  • r +2R

  • 2r +R

  • 2(r + R)


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115.

If f is defined in [1, 3] by f(x) = x3 + bx2 + ax,such that f(1) - f(3) = 0 and f'(c) = 0, where c = 2 + 13, then (a, b) is equal to

  • ( - 6, 11)

  • 2 - 13, 2 + 13

  • (11, - 6)

  • (6, 11)


C.

(11, - 6)

Since, f1 - f3 = 0 f1 = f3 1 + b + a = 27 +9b +3a 8b + 2a = - 26      iFrom options, a = 11and b = - 6satisfies the eq. i a, b = 11, - 6


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116.

The domain of the function f(x) = log0.5x! is

  • 0, 1, 2, 3, ...

  • 0, 1, 2, 3, ...

  • 0, 

  • 0, 1


117.

If f(x) = x - 1 + x - 2 + x - 3, 2 < x < 3, then f is

  • an onto function but not one-one

  • one-one function but not onto

  • a bijection

  • neither one-one nor onto


118.

If x = a is a root of multiplicity two of a polynomial equation f(x) = 0, then

  • f'(a) = f''(a) = 0

  • f''(a) = f(a) = 0

  • f'a  0  f''(a)

  • fa = f'a = 0, f''a  0


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119.

Suppose f(x) = x(x + 3)(x - 2), x  [- 1, 4]. Then, a value of c in (- 1, 4) satisfying f'(c) = 10 is

  • 2

  • 52

  • 3

  • 72


120.

Let A = {- 4, - 2, - 1, 0, 3, 5} and f : A  IR be defined by

fx = 3x - 1 for x > 3x2 + 1 for - 3  x  32x - 3 for x < - 3Then the range of f is

  • - 11, 5, 2, 1, 10, 14

  • - 11, - 7, 2, 1, 8, 14

  • - 11, 5, 2, 1, 8, 14

  • - 11, - 7, - 5, 1, 10, 14


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