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Question Hard Mathematics Trigonometric Functions Angles Class 11 Level 67

वृत्त की त्रिज्या (18) सेमी है और चाप \(15\pi\) सेमी है। केंद्र कोण डिग्री में क्या है?

The radius of a circle is (18) cm and the arc is \(15\pi\) cm. What is the central angle in degrees?

Explanation opens after your attempt

Correct Answer

C. \(150^\circ\)

Step 1

Concept

\( \theta=\frac{s}{r}=\frac{15\pi}{18}=\frac{5\pi}{6}=150^\circ \). First find the radian angle and then convert to degrees.

Step 2

Why this answer is correct

The correct answer is C. \(150^\circ\). \( \theta=\frac{s}{r}=\frac{15\pi}{18}=\frac{5\pi}{6}=150^\circ \). First find the radian angle and then convert to degrees.

Step 3

Exam Tip

\( \theta=\frac{s}{r}=\frac{15\pi}{18}=\frac{5\pi}{6}=150^\circ \) है। पहले रेडियन कोण निकालकर डिग्री में बदलें।

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MCQ Data:
Class: Class 11
Subject: Mathematics
Chapter: Trigonometric Functions
Topic: Angles
Difficulty: Hard
Level: 67

Question Hindi:
वृत्त की त्रिज्या (18) सेमी है और चाप (15\pi) सेमी है। केंद्र कोण डिग्री में क्या है?

Question English:
The radius of a circle is (18) cm and the arc is (15\pi) cm. What is the central angle in degrees?

Options:
A. (120^\circ)
B. (135^\circ)
C. (150^\circ)
D. (165^\circ)

Correct Answer:
C. (150^\circ)

Explanation Hindi:
( \theta=\frac{s}{r}=\frac{15\pi}{18}=\frac{5\pi}{6}=150^\circ ) है। पहले रेडियन कोण निकालकर डिग्री में बदलें।

Explanation English:
( \theta=\frac{s}{r}=\frac{15\pi}{18}=\frac{5\pi}{6}=150^\circ ). First find the radian angle and then convert to degrees.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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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.
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7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Medium Mathematics Trigonometric Functions Angles Class 11 Level 69

यदि वृत्त की त्रिज्या (21) सेमी और चाप \(14\pi\) सेमी है तो केंद्र कोण रेडियन में क्या है?

If the radius of a circle is (21) cm and the arc is \(14\pi\) cm, what is the central angle in radians?

Explanation opens after your attempt

Correct Answer

B. \( \frac{2\pi}{3} \) रेडियन\( \frac{2\pi}{3} \) radians

Step 1

Concept

\( \theta=\frac{s}{r}=\frac{14\pi}{21}=\frac{2\pi}{3} \). Use \( \theta=\frac{s}{r} \) to find the angle from arc length.

Step 2

Why this answer is correct

The correct answer is B. \( \frac{2\pi}{3} \) रेडियन / \( \frac{2\pi}{3} \) radians. \( \theta=\frac{s}{r}=\frac{14\pi}{21}=\frac{2\pi}{3} \). Use \( \theta=\frac{s}{r} \) to find the angle from arc length.

Step 3

Exam Tip

\( \theta=\frac{s}{r}=\frac{14\pi}{21}=\frac{2\pi}{3} \) है। चाप लंबाई से कोण निकालते समय \( \theta=\frac{s}{r} \) लगाएं।

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MCQ Data:
Class: Class 11
Subject: Mathematics
Chapter: Trigonometric Functions
Topic: Angles
Difficulty: Medium
Level: 69

Question Hindi:
यदि वृत्त की त्रिज्या (21) सेमी और चाप (14\pi) सेमी है तो केंद्र कोण रेडियन में क्या है?

Question English:
If the radius of a circle is (21) cm and the arc is (14\pi) cm, what is the central angle in radians?

Options:
A. ( \frac{\pi}{2} ) रेडियन / ( \frac{\pi}{2} ) radians
B. ( \frac{2\pi}{3} ) रेडियन / ( \frac{2\pi}{3} ) radians
C. ( \frac{3\pi}{2} ) रेडियन / ( \frac{3\pi}{2} ) radians
D. ( \frac{4\pi}{3} ) रेडियन / ( \frac{4\pi}{3} ) radians

Correct Answer:
B. ( \frac{2\pi}{3} ) रेडियन / ( \frac{2\pi}{3} ) radians

Explanation Hindi:
( \theta=\frac{s}{r}=\frac{14\pi}{21}=\frac{2\pi}{3} ) है। चाप लंबाई से कोण निकालते समय ( \theta=\frac{s}{r} ) लगाएं।

Explanation English:
( \theta=\frac{s}{r}=\frac{14\pi}{21}=\frac{2\pi}{3} ). Use ( \theta=\frac{s}{r} ) to find the angle from arc length.

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Question Medium Mathematics Trigonometric Functions Angles Class 11 Level 68

एक वृत्त में त्रिज्या (18) सेमी और चाप \(6\pi\) सेमी है। केंद्र कोण डिग्री में क्या होगा?

In a circle the radius is (18) cm and arc is \(6\pi\) cm. What is the central angle in degrees?

Explanation opens after your attempt

Correct Answer

B. \(60^\circ\)

Step 1

Concept

\( \theta=\frac{s}{r}=\frac{6\pi}{18}=\frac{\pi}{3}=60^\circ \). First find the radian angle and then convert it into degrees.

Step 2

Why this answer is correct

The correct answer is B. \(60^\circ\). \( \theta=\frac{s}{r}=\frac{6\pi}{18}=\frac{\pi}{3}=60^\circ \). First find the radian angle and then convert it into degrees.

Step 3

Exam Tip

\( \theta=\frac{s}{r}=\frac{6\pi}{18}=\frac{\pi}{3}=60^\circ \) है। पहले रेडियन कोण निकालकर डिग्री में बदलें।

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MCQ Data:
Class: Class 11
Subject: Mathematics
Chapter: Trigonometric Functions
Topic: Angles
Difficulty: Medium
Level: 68

Question Hindi:
एक वृत्त में त्रिज्या (18) सेमी और चाप (6\pi) सेमी है। केंद्र कोण डिग्री में क्या होगा?

Question English:
In a circle the radius is (18) cm and arc is (6\pi) cm. What is the central angle in degrees?

Options:
A. (45^\circ)
B. (60^\circ)
C. (90^\circ)
D. (120^\circ)

Correct Answer:
B. (60^\circ)

Explanation Hindi:
( \theta=\frac{s}{r}=\frac{6\pi}{18}=\frac{\pi}{3}=60^\circ ) है। पहले रेडियन कोण निकालकर डिग्री में बदलें।

Explanation English:
( \theta=\frac{s}{r}=\frac{6\pi}{18}=\frac{\pi}{3}=60^\circ ). First find the radian angle and then convert it into degrees.

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".

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Question Medium Mathematics Trigonometric Functions Angles Class 11 Level 67

यदि (r=12) सेमी और चाप \(s=6\pi\) सेमी है तो कोण \( \theta \) क्या होगा?

If (r=12) cm and arc \(s=6\pi\) cm then what is the angle \( \theta \)?

Explanation opens after your attempt

Correct Answer

D. \( \frac{\pi}{2} \) रेडियन\( \frac{\pi}{2} \) radians

Step 1

Concept

\( \theta=\frac{s}{r}=\frac{6\pi}{12}=\frac{\pi}{2} \) radians. Rearrange \(s=r\theta\) as \( \theta=\frac{s}{r} \).

Step 2

Why this answer is correct

The correct answer is D. \( \frac{\pi}{2} \) रेडियन / \( \frac{\pi}{2} \) radians. \( \theta=\frac{s}{r}=\frac{6\pi}{12}=\frac{\pi}{2} \) radians. Rearrange \(s=r\theta\) as \( \theta=\frac{s}{r} \).

Step 3

Exam Tip

\( \theta=\frac{s}{r}=\frac{6\pi}{12}=\frac{\pi}{2} \) रेडियन है। \(s=r\theta\) को \( \theta=\frac{s}{r} \) में बदलें।

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MCQ Data:
Class: Class 11
Subject: Mathematics
Chapter: Trigonometric Functions
Topic: Angles
Difficulty: Medium
Level: 67

Question Hindi:
यदि (r=12) सेमी और चाप (s=6\pi) सेमी है तो कोण ( \theta ) क्या होगा?

Question English:
If (r=12) cm and arc (s=6\pi) cm then what is the angle ( \theta )?

Options:
A. ( \frac{\pi}{4} ) रेडियन / ( \frac{\pi}{4} ) radians
B. ( \frac{\pi}{3} ) रेडियन / ( \frac{\pi}{3} ) radians
C. ( \pi ) रेडियन / ( \pi ) radians
D. ( \frac{\pi}{2} ) रेडियन / ( \frac{\pi}{2} ) radians

Correct Answer:
D. ( \frac{\pi}{2} ) रेडियन / ( \frac{\pi}{2} ) radians

Explanation Hindi:
( \theta=\frac{s}{r}=\frac{6\pi}{12}=\frac{\pi}{2} ) रेडियन है। (s=r\theta) को ( \theta=\frac{s}{r} ) में बदलें।

Explanation English:
( \theta=\frac{s}{r}=\frac{6\pi}{12}=\frac{\pi}{2} ) radians. Rearrange (s=r\theta) as ( \theta=\frac{s}{r} ).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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वृत्त की त्रिज्या (18) सेमी है और चाप \(15\pi\) सेमी है। केंद्र कोण डिग्री में क्या है?

Concept

Why this answer is correct

Exam Tip

यदि वृत्त की त्रिज्या (21) सेमी और चाप \(14\pi\) सेमी है तो केंद्र कोण रेडियन में क्या है?

Concept

Why this answer is correct

Exam Tip

एक वृत्त में त्रिज्या (18) सेमी और चाप \(6\pi\) सेमी है। केंद्र कोण डिग्री में क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (r=12) सेमी और चाप \(s=6\pi\) सेमी है तो कोण \( \theta \) क्या होगा?

Concept

Why this answer is correct

Exam Tip

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