Class 11 cosine-equation MCQ Questions

Question 1/2 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\cos \theta=\frac{1}{2}\) और \(0<\theta<2\pi\), तो \(\theta\) के मान कौन से हैं?

If \(\cos \theta=\frac{1}{2}\) and \(0<\theta<2\pi\), what are the values of \(\theta\)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{\pi}{3},\frac{5\pi}{3}\)

Step 1

Concept

For \( \cos \theta=\frac{1}{2}\), the reference angle is \( \frac{\pi}{3}\), and cosine is positive in the first and fourth quadrants. In exams write both solutions up to \(2\pi\).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{\pi}{3},\frac{5\pi}{3}\). For \( \cos \theta=\frac{1}{2}\), the reference angle is \( \frac{\pi}{3}\), and cosine is positive in the first and fourth quadrants. In exams write both solutions up to \(2\pi\).

Step 3

Exam Tip

\(\cos \theta=\frac{1}{2}\) के लिए reference angle \(\frac{\pi}{3}\) है और cosine प्रथम व चतुर्थ चतुर्थांश में धनात्मक है। परीक्षा में \(2\pi\) तक के दोनों हल लिखें।

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MCQ Data:
Class: Class 11
Subject: Mathematics
Chapter: Trigonometric Functions
Topic: Trigonometric functions and their properties
Difficulty: Medium
Level: 72

Question Hindi:
यदि (\cos \theta=\frac{1}{2}) और (0<\theta<2\pi), तो (\theta) के मान कौन से हैं?

Question English:
If (\cos \theta=\frac{1}{2}) and (0<\theta<2\pi), what are the values of (\theta)?

Options:
A. (\frac{\pi}{3},\frac{5\pi}{3})
B. (\frac{\pi}{6},\frac{11\pi}{6})
C. (\frac{2\pi}{3},\frac{4\pi}{3})
D. (\frac{\pi}{4},\frac{7\pi}{4})

Correct Answer:
A. (\frac{\pi}{3},\frac{5\pi}{3})

Explanation Hindi:
(\cos \theta=\frac{1}{2}) के लिए reference angle (\frac{\pi}{3}) है और cosine प्रथम व चतुर्थ चतुर्थांश में धनात्मक है। परीक्षा में (2\pi) तक के दोनों हल लिखें।

Explanation English:
For ( \cos \theta=\frac{1}{2}), the reference angle is ( \frac{\pi}{3}), and cosine is positive in the first and fourth quadrants. In exams write both solutions up to (2\pi).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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Question 2/2 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\cos \theta=\cos \alpha\), तो सामान्य हल कौन सा है?

If \(\cos \theta=\cos \alpha\), which is the general solution?

Explanation opens after your attempt

Correct Answer

B. \(\theta=2n\pi\pm\alpha\)

Step 1

Concept

For \( \cos \theta=\cos \alpha\), angles occur in both directions. In exams do not forget \( \pm\alpha\).

Step 2

Why this answer is correct

The correct answer is B. \(\theta=2n\pi\pm\alpha\). For \( \cos \theta=\cos \alpha\), angles occur in both directions. In exams do not forget \( \pm\alpha\).

Step 3

Exam Tip

\(\cos \theta=\cos \alpha\) के लिए दोनों दिशाओं में कोण मिलते हैं। परीक्षा में \(\pm\alpha\) लगाना न भूलें।

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AI Video Prompt 16:9 + 9:16

Is question ka premium MCQ video banane ke liye ready prompt. Copy karke Sora, Runway, Canva AI, CapCut AI, ChatGPT video workflow ya editor me use karein.

Create a premium AI MCQ quiz video for Muft Shiksha in BOTH formats: 16:9 landscape and 9:16 vertical short.

Brand:
- Name: Muft Shiksha
- Website: https://muftshiksha.com
- Style: dark navy futuristic learning game UI, neon cyan/blue glow, gold reward highlights, clean Devanagari text, premium educational look.
- Do not add wrong facts. Do not change the question, options or answer.

Question Page:
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MCQ Data:
Class: Class 11
Subject: Mathematics
Chapter: Trigonometric Functions
Topic: Trigonometric functions and their properties
Difficulty: Medium
Level: 72

Question Hindi:
यदि (\cos \theta=\cos \alpha), तो सामान्य हल कौन सा है?

Question English:
If (\cos \theta=\cos \alpha), which is the general solution?

Options:
A. (\theta=n\pi+(-1)^n\alpha)
B. (\theta=2n\pi\pm\alpha)
C. (\theta=n\pi+\alpha)
D. (\theta=2n\pi+\frac{\pi}{2})

Correct Answer:
B. (\theta=2n\pi\pm\alpha)

Explanation Hindi:
(\cos \theta=\cos \alpha) के लिए दोनों दिशाओं में कोण मिलते हैं। परीक्षा में (\pm\alpha) लगाना न भूलें।

Explanation English:
For ( \cos \theta=\cos \alpha), angles occur in both directions. In exams do not forget ( \pm\alpha).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

Custom Support:
- Make 16:9 version for YouTube/Facebook.
- Make 9:16 version for Shorts/Reels.
- Add Hindi-English natural voice-over.
- Add readable subtitles.
- Add light background music, low volume.
- Keep all text inside safe margins.
- Use smooth transitions, no clutter, no watermark except Muft Shiksha branding.
- Formula/Math/Chemistry text must stay exactly readable; use LaTeX-style clean rendering where needed.

Output Needed:
- Final narration script.
- Scene-by-scene visual direction.
- Text overlays for 16:9 and 9:16.
- Thumbnail idea.
- Hashtags: #MuftShiksha #FreeEducation #MCQ #Quiz #Class11 #Study

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cosine-equation MCQ Questions for Class 11

Practice Questions

यदि \(\cos \theta=\frac{1}{2}\) और \(0<\theta<2\pi\), तो \(\theta\) के मान कौन से हैं?

Concept

Why this answer is correct

Exam Tip

यदि \(\cos \theta=\cos \alpha\), तो सामान्य हल कौन सा है?

Concept

Why this answer is correct

Exam Tip

cosine-equation Revision Links

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cosine-equation MCQ Questions for Class 11

Practice Questions

यदि \(\cos \theta=\frac{1}{2}\) और \(0<\theta<2\pi\), तो \(\theta\) के मान कौन से हैं?

Concept

Why this answer is correct

Exam Tip

यदि \(\cos \theta=\cos \alpha\), तो सामान्य हल कौन सा है?

Concept

Why this answer is correct

Exam Tip

cosine-equation Revision Links

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All Subjects

Search cosine-equation

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