Match the LIST–I with LIST–II: LIST–I (Question) LIST–II (Answer) A. If (x +…
2025
Match the LIST–I with LIST–II:
LIST–I (Question) | LIST–II (Answer) |
|---|---|
A. | III. 0 |
B. | IV. ±9 |
C. | II. 2 |
D. | I. 11 |
- A.
A–I, B–III, C–IV, D–II
- B.
A–I, B–II, C–III, D–IV
- C.
A–II, B–III, C–I, D–IV
- D.
A–III, B–IV, C–II, D–I
Attempted by 4 students.
Show answer & explanation
Correct answer: D
To solve this matching problem, we evaluate each expression in List-I independently.
For A, squaring (x + 1/x = 2) gives x² + 2 + 1/x² = 4, so x² - 2 + 1/x² = 0, meaning (x - 1/x)² = 0; thus x - 1/x = 0 (Match III).
For B, squaring (x - y = 1) yields x² + y² - 2xy = 1. Substituting x² + y² = 41 gives 41 - 2xy = 1, so xy = 20.
Then (x + y)² = x² + y² + 2xy = 41 + 40 = 81, so x + y = ±9 (Match IV).
For C, from (1 - 1/x) = 2, we get 1/x = -1. Squaring gives 1/x² = 1, so 1 + 1/x² = 2 (Match II).
For D, squaring (x - 1/x) = 3 gives x² + 1/x² - 2 = 9, so x² + 1/x² = 11 (Match I).
Therefore, the correct matching is A–III, B–IV, C–II, D–I.
Options A and B are incorrect because they mismatch the calculated values for at least one item.