Instructions

Directions for the next 3 questions: For three distinct real positive numbers x, y and z, let

f(x, y, z) = min (max(x, y), max (y, z), max (z, x))

g(x, y, z) = max (min(x, y), min (y, z), min (z, x))

h(x, y, z) = max (max(x, y), max(y, z), max (z, x))

j(x, y, z) = min (min (x, y), min(y, z), min (z, x))

m(x, y, z) = max (x, y, z)

n(x, y, z) = min (x, y, z)

Question 117

# Which of the following expressions is indeterminate?

Solution

From the given functions we can make out that function h and m give max value ,Â function n and j give min value ,Â function f and g give middle Â value.So in option B , j cancels out n and h cancels out m . So the denominator becomes 0 and value is indeterminable.Â

Suppose x>y>z

f(x,y,z) = y

g(x,y,z) = y

h(x,y,z) = x

j(x,y,z) = z

m(x,y,z) = x

n(x,y,z) = z

The denominator of the second option becomes 0, hence making it indeterminate.

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