2023 · Q21
Consider the following statements:
- 1If (a + b) is directly proportional to (a − b), then (a² + b²) is directly proportional to ab.
- 2If a is directly proportional to b, then (a² − b²) is directly proportional to ab.
Which of the statements given above is/are correct?
Elementary MathematicsRatio and Proportion
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
St.1: (a+b)=k(a-b) gives a/b=(k+1)/(k-1)=m constant; then (a^2+b^2)/ab=(m^2+1)/m constant, so (a^2+b^2) proportional to ab: true. St.2: a=kb gives (a^2-b^2)/ab=(k^2-1)/k constant: true. Both correct. Option (c). Key disputed: verify against the official UPSC key.