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NDA 1 2025 Maths, question 97

Topic: Algebra

Passage · Q97 to Q98

A function ff is such that f(xy)=f(x+y)f(xy) = f(x + y) for all real values of xx and yy, and f(5)=10f(5) = 10.

Q97

What is f(0)f(0) equal to?

  1. (a) 0
  2. (b) 1
  3. (c) 5
  4. (d) 10Correct answer

Solution.

Answer: (d) 10

  1. Put x=0x = 0.
  2. The functional equation becomes f(0)=f(y)f(0) = f(y) for every real yy, so ff is constant.
  3. In particular, f(0)=f(5)=10f(0) = f(5) = 10.