Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | Point of minima of \(f(x) = |x+1|\) | (I) | 1 |
| (B) | Minimum value of \(f(x) = |x|\) | (II) | −1 |
| (C) | Maximum value of \(f(x) = 1-x^2\) | (III) | 2 |
| (D) | Minimum value of \(f(x) = 2+ \sin^2x\) | (IV) | 0 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
Each function is built from a term that is never negative (\(|\,\cdot\,|\), \(x^2\), \(\sin^2 x\)), so its extreme value occurs where that term is 0.
(A) Point of minima of \(f(x) = |x+1|\)
This matches (II) −1:
\(|x + 1| \ge 0\), and \(|x + 1| = 0\) only when \(x = -1\)
(B) Minimum value of \(f(x) = |x|\)
This matches (IV) 0:
\(|x| \ge 0\), and \(f(0) = 0\)
(C) Maximum value of \(f(x) = 1-x^2\)
This matches (I) 1:
\(x^2 \ge 0\), so \(1 - x^2 \le 1\), and \(f(0) = 1\)
(D) Minimum value of \(f(x) = 2+ \sin^2x\)
This matches (III) 2:
\(\sin^2 x \ge 0\), so \(2 + \sin^2 x \ge 2\), and \(f(0) = 2\)
So the matching is (A)-(II), (B)-(IV), (C)-(I), (D)-(III).
Tip: Note whether an item asks for the point (the value of x) or the value (the value of f). For \(|x + 1|\) the point of minima is −1, while the minimum value is 0.