Suppose f(x) is differentiable x = 1 and  from Mathematics Rel

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 Multiple Choice QuestionsMultiple Choice Questions

161.

A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?

  • Interval Function
    (-∞, ∞) x3 – 3x2 + 3x + 3
  • Interval Function
    [2, ∞) 2x3 – 3x2 – 12x + 6
  • Interval Function
    (-∞, 1/3] 3x2 – 2x + 1
  • Interval Function
    (-∞, 1/3] 3x2 – 2x + 1
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162.

Suppose f(x) is differentiable x = 1 and limit as straight h rightwards arrow 0 of 1 over straight h space straight f left parenthesis 1 plus straight h right parenthesis space equals space 5 space comma then space straight f apostrophe left parenthesis 1 right parenthesis space equals

  • 3

  • 4

  • 5

  • 5


C.

5

straight f apostrophe left parenthesis 1 right parenthesis space equals space limit as straight h rightwards arrow 0 of space fraction numerator straight f left parenthesis 1 plus straight h right parenthesis minus straight f left parenthesis 1 right parenthesis over denominator straight h end fraction semicolon As the function is differentiable so it is continuous as it is given that limit as straight h rightwards arrow 0 of space fraction numerator straight f left parenthesis 1 plus straight h right parenthesis over denominator straight h end fraction space equals space 5 and hence f(1) = 0 Hence  limit as straight h rightwards arrow 0 of space fraction numerator straight f left parenthesis 1 plus straight h right parenthesis over denominator straight h end fraction space equals space 5
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163.

A real valued function f(x) satisfies the functional equation f(x – y) = f(x) f(y) – f(a – x) f(a + y) where a is a given constant and f(0) = 1, f(2a – x) is equal to

  • –f(x)

  • f(x)

  • f(a) + f(a – x)

  • f(a) + f(a – x)

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164.

Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is

  • a function

  • reflexive

  • not symmetric

  • not symmetric

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165.

The range of the function 7-xPx-3 is

  • {1, 2, 3}

  • {1, 2, 3, 4, 5}

  • {1, 2, 3, 4}

  • {1, 2, 3, 4}

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166.

Let f and g be differentiable functions satisfying g′(a) = 2, g(a) = b and fog = I (identity function). Then f ′(b) is equal to

  • 1/2

  • 2

  • 2/3

  • 2/3

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167.

Let S = {t ∈ R: f(x) = |x-π|.(e|x| - 1) sin |x| is not differentiable at t}. Then the set S is equal to

  • {0,π}

  • ϕ (an empty set)

  • {0}

  • {π}


168.

Let S = { x ∈ R : x ≥ 0 and 2|x-3| + x(x-6) + 6 = 0} Then S:

  • Contains exactly four elements

  • Is an empty set

  • Contains exactly one element

  • Contains exactly two elements


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169.

On the set R of real numbers we define xPy if and only if xy  0. Then, the relation P is

  • reflexive but not symmetric

  • symmetric but not reflexive

  • transitive but not reflexive

  • reflexive and symmetric but not transitive


170.

On R, the relation p be defined by 'xρy holds if and only if x- y is zero or irrational'. Then,

  • ρ s reflexive and transitive but not symmetric

  • ρ s reflexive and symmetric but not transitive 

  • ρ s symmetric and transitive but not reflexive

  • ρ is equivalence relation


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