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NDA 1 2025 Maths, question 98

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.

Q98

What is f(20)+f(−20)f(20) + f( - 20) equal to?

  1. (a) 0
  2. (b) 10
  3. (c) 20Correct answer
  4. (d) 40

Solution.

Answer: (c) 20

  1. Setting x=0x = 0 shows f(y)=f(0)f(y) = f(0) for every real yy.
  2. Since f(5)=10f(5) = 10, both f(20)f(20) and f(−20)f( - 20) equal 10.
  3. Their sum is 10+10=2010 + 10 = 20.