The range of the functionfx = tanπ29 - x2&

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 Multiple Choice QuestionsMultiple Choice Questions

191.

If the magnitude of the coefficient of x7 in the expansion of ax2 + 1bx8, where a, b are positive numbers, is equal to the magnitude of the coefficient of x-7 in the expansion of ax2 - 1bx8, then a and b are connected by the relation

  • ab = 1

  • ab = 2

  • a2b = 1

  • ab2 = 2


192.

The mapping f: N N given by f(n) = 1 + n2, n  N where N is the set of natural numbers, is

  • one - to - one and onto

  • onto but not one - to - one

  • one - to - one but not onto

  • neither one - to - one nor onto


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193.

The range of the function

fx = tanπ29 - x2 is

  • [0, 3]

  • (0, 3)

  • [0, 3)

  • (0, 3]


A.

[0, 3]

Clearly, f(x) is defined for

x  - π3, π3

Since, tan(x) is an increasing function in [0, π2] and 0  π29 - x2  π29 for x  - π3, π3

 0  π29 - x2  π3 for x  - π3, π3Also, f- x = fx for all x  - π3, π3

Therefore, Range (f) = [f(- π/3), f(0)]

                              = [tan(0), tan(π/3)] = [0, 3]


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194.

If N is a set of natural numbers, then under binary operation a · b = a + b, (N, ·) is

  • quasi-group

  • semi-group

  • monoid

  • group


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195.

If f : R  R be such that f(1) = 3 and f'(1) = 6. Then limx0f1 + xf11x equals to

  • 1

  • e1/2

  • e2

  • e3


196.

The domain of the function f(x) = 1log101 - x + x +2 is

  • - 3, - 2.5  - 2.5, - 2

  • - 2, 0  0, 1

  • [0, 1]

  • None of the above


197.

The relation R defined on set A = x : x < 3, x  I by R = x, y : y = x is

  • {(- 2, 2), (- 1, 1), (0, 0), (1, 1), (2, 2)}

  • {(- 2, - 2), (- 2, 2), (-1, 1), (0, 0), (1, - 2), (1, 2), (2, - 1), (2, - 2)}

  • {(0, 0), (1, 1), (2, 2)}

  • None of the above


198.

The domain of the function f(x) = 4 - x2sin-12 - x is

  • [0, 2]

  • [0, 2)

  • [1, 2)

  • [1, 2]


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199.

The roots of (x - a)(x - a - 1) + (x - a - 1)(x - a - 2) + (x - a)(x - a - 2) = 0, a  R are always

  • equal

  • imaginary

  • real and distinct

  • rational and equal


200.

Let f(x) = x2 + ax + b, where a, b  R. If f(x) = 0 has all its roots imaginary, then the roots of f(x) + f'(x) + f''(x) = 0 are

  • real and distinct

  • imaginary

  • real and distinct

  • rational and equal


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