\( {1 \over x - 2} < 0\) का हल  _________ है।

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  1. x  ∈ (−∞ ,2)
  2. x  ∈ (∞,2)
  3. x  ∈ (2,∞)
  4. x  ∈ (2,∞)

Answer (Detailed Solution Below)

Option 1 : x  ∈ (−∞ ,2)
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Detailed Solution

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अवधारणा:

हल समुच्चय: x के सभी संभावित मानों का समुच्चय।

जब (a > 0 और b < 0) या (a < 0 और b > 0) तो \(\rm \frac a b <0\)

जब (a > 0 और b > 0) या (a < 0 और b < 0) तो \(\rm \frac a b >0\)

गणना:

यहां, \( {1 \over x - 2} < 0\)

इसलिए, x - 2 < 0

⇒ x < 2

∴ x ∈ (-∞ , 2)

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