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CAT 2000 — QA Question 52

Basics (Functions)Easy

For all non-negative integers x and y, f(x, y) is defined as below

f(0, y) = y + 1

f(x + 1, 0) = f(x, 1)

f(x + 1,y + 1) = f(x, f(x + 1, y))

Then, what is the value of f(1, 2)?

Answer & solution

Correct answer: Four

  • A

    Two

  • Four

  • C

    Three

  • D

    Cannot be determined

Solution

f (1, 2) = f(0 + 1, 1 + 1) = f(0, f(0 + 1, 1)) = f(0, f (1, 1))

f (1, 1) = f(0, f(1, 0))

f(1, 0) = f(0, 1) = 2

∴ f(1, 1) = f(0, 2) = 2 + 1 = 3

f (1, 2) = f(0 + 1, 1 + 1) = f(0, f(0 + 1, 1)) = f(0, f (1, 1)) = f(0, 3)

f(0, 3) = 3 + 1 = 4

Hence, option (b).

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CAT 2000 QA Q52: For all non-negative integers x and y, f(x, y) is defined as below f(0, y) = y + 1 f(x + 1, 0) = f(x, 1) f(x + — Solution | TheCATExam