k के पूर्णांक मानों की संख्या क्या है जिसके लिए समीकरण 2sinx = 2k + 1 का एक हल है?

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NDA (Held On: 18 Apr 2021) Maths Previous Year paper
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  1. शून्य
  2. एक
  3. दो
  4. चार

Answer (Detailed Solution Below)

Option 3 : दो
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Detailed Solution

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अवधारणा:

a sin x + b cos x का न्यूनतम और अधिकतम मान

- ≤ a sin x + b cos x ≤ 

गणना:

जैसा कि हम जानते हैं, - ≤ a sin x + b cos x ≤ 

⇒ - ≤  2sin x + 0 cos x ≤ 

⇒ -2 ≤ 2sin x ≤ 2

⇒ -2 ≤ 2k + 1 ≤ 2

⇒ -3 ≤ 2k ≤ 1

⇒ -1.5 ≤ k ≤ 0.5

k = 0, -1 

इसलिए, विकल्प 3 सही है।

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