Class 11 trigonometry angles arc length hard class11 MCQ...

Question 1/5 Hard Mathematics Trigonometric Functions Angles Class 11 Level 68

यदि एक वृत्त की त्रिज्या (21) सेमी है और केंद्र कोण \(40^\circ\) है, तो चाप की लंबाई क्या है?

If a circle has radius (21) cm and central angle \(40^\circ\), what is the arc length?

Explanation opens after your attempt

Correct Answer

B. \(\frac{14\pi}{3}\) सेमी\(\frac{14\pi}{3}\) cm

Step 1

Concept

\(40^\circ=\frac{2\pi}{9}\) and \(s=21\times\frac{2\pi}{9}=\frac{14\pi}{3}\). In exams, convert degrees into radians and apply \(s=r\theta\).

Step 2

Why this answer is correct

The correct answer is B. \(\frac{14\pi}{3}\) सेमी / \(\frac{14\pi}{3}\) cm. \(40^\circ=\frac{2\pi}{9}\) and \(s=21\times\frac{2\pi}{9}=\frac{14\pi}{3}\). In exams, convert degrees into radians and apply \(s=r\theta\).

Step 3

Exam Tip

\(40^\circ=\frac{2\pi}{9}\) और \(s=21\times\frac{2\pi}{9}=\frac{14\pi}{3}\)। परीक्षा में डिग्री को रेडियन में बदलकर \(s=r\theta\) लगाएं।

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

Question Hindi:
यदि एक वृत्त की त्रिज्या (21) सेमी है और केंद्र कोण (40^\circ) है, तो चाप की लंबाई क्या है?

Question English:
If a circle has radius (21) cm and central angle (40^\circ), what is the arc length?

Options:
A. (\frac{7\pi}{3}) सेमी / (\frac{7\pi}{3}) cm
B. (\frac{14\pi}{3}) सेमी / (\frac{14\pi}{3}) cm
C. (\frac{21\pi}{4}) सेमी / (\frac{21\pi}{4}) cm
D. (\frac{28\pi}{3}) सेमी / (\frac{28\pi}{3}) cm

Correct Answer:
B. (\frac{14\pi}{3}) सेमी / (\frac{14\pi}{3}) cm

Explanation Hindi:
(40^\circ=\frac{2\pi}{9}) और (s=21\times\frac{2\pi}{9}=\frac{14\pi}{3})। परीक्षा में डिग्री को रेडियन में बदलकर (s=r\theta) लगाएं।

Explanation English:
(40^\circ=\frac{2\pi}{9}) and (s=21\times\frac{2\pi}{9}=\frac{14\pi}{3}). In exams, convert degrees into radians and apply (s=r\theta).

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Question 2/5 Hard Mathematics Trigonometric Functions Angles Class 11 Level 68

एक वृत्त में केंद्र कोण \(\frac{2\pi}{3}\) है और चाप \(10\pi\) सेमी है। त्रिज्या क्या होगी?

In a circle, the central angle is \(\frac{2\pi}{3}\) and the arc length is \(10\pi\) cm. What is the radius?

Explanation opens after your attempt

Correct Answer

C. (15) सेमी(15) cm

Step 1

Concept

\(s=r\theta\), so \(r=\frac{10\pi}{\frac{2\pi}{3}}=15\). In exams, multiply by the reciprocal while dividing by a fraction.

Step 2

Why this answer is correct

The correct answer is C. (15) सेमी / (15) cm. \(s=r\theta\), so \(r=\frac{10\pi}{\frac{2\pi}{3}}=15\). In exams, multiply by the reciprocal while dividing by a fraction.

Step 3

Exam Tip

\(s=r\theta\), इसलिए \(r=\frac{10\pi}{\frac{2\pi}{3}}=15\)। परीक्षा में भिन्न से भाग देते समय उल्टा गुणा करें।

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

Question Hindi:
एक वृत्त में केंद्र कोण (\frac{2\pi}{3}) है और चाप (10\pi) सेमी है। त्रिज्या क्या होगी?

Question English:
In a circle, the central angle is (\frac{2\pi}{3}) and the arc length is (10\pi) cm. What is the radius?

Options:
A. (10) सेमी / (10) cm
B. (12) सेमी / (12) cm
C. (15) सेमी / (15) cm
D. (18) सेमी / (18) cm

Correct Answer:
C. (15) सेमी / (15) cm

Explanation Hindi:
(s=r\theta), इसलिए (r=\frac{10\pi}{\frac{2\pi}{3}}=15)। परीक्षा में भिन्न से भाग देते समय उल्टा गुणा करें।

Explanation English:
(s=r\theta), so (r=\frac{10\pi}{\frac{2\pi}{3}}=15). In exams, multiply by the reciprocal while dividing by a fraction.

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1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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Question 3/5 Hard Mathematics Trigonometric Functions Angles Class 11 Level 68

यदि सेक्टर की त्रिज्या (9) सेमी और कोण \(80^\circ\) है, तो चाप की लंबाई क्या होगी?

If a sector has radius (9) cm and angle \(80^\circ\), what is the arc length?

Explanation opens after your attempt

Correct Answer

C. \(4\pi\) सेमी\(4\pi\) cm

Step 1

Concept

\(80^\circ=\frac{4\pi}{9}\) radians and \(s=9\times\frac{4\pi}{9}=4\pi\). In exams, convert degrees into radians first.

Step 2

Why this answer is correct

The correct answer is C. \(4\pi\) सेमी / \(4\pi\) cm. \(80^\circ=\frac{4\pi}{9}\) radians and \(s=9\times\frac{4\pi}{9}=4\pi\). In exams, convert degrees into radians first.

Step 3

Exam Tip

\(80^\circ=\frac{4\pi}{9}\) रेडियन और \(s=9\times\frac{4\pi}{9}=4\pi\)। परीक्षा में डिग्री को पहले रेडियन में बदलें।

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

Question Hindi:
यदि सेक्टर की त्रिज्या (9) सेमी और कोण (80^\circ) है, तो चाप की लंबाई क्या होगी?

Question English:
If a sector has radius (9) cm and angle (80^\circ), what is the arc length?

Options:
A. (2\pi) सेमी / (2\pi) cm
B. (3\pi) सेमी / (3\pi) cm
C. (4\pi) सेमी / (4\pi) cm
D. (5\pi) सेमी / (5\pi) cm

Correct Answer:
C. (4\pi) सेमी / (4\pi) cm

Explanation Hindi:
(80^\circ=\frac{4\pi}{9}) रेडियन और (s=9\times\frac{4\pi}{9}=4\pi)। परीक्षा में डिग्री को पहले रेडियन में बदलें।

Explanation English:
(80^\circ=\frac{4\pi}{9}) radians and (s=9\times\frac{4\pi}{9}=4\pi). In exams, convert degrees into radians first.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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Question 4/5 Hard Mathematics Trigonometric Functions Angles Class 11 Level 68

यदि (5) सेमी त्रिज्या वाले वृत्त में केंद्र कोण \(\frac{7\pi}{10}\) है, तो चाप की लंबाई क्या होगी?

If a circle of radius (5) cm has central angle \(\frac{7\pi}{10}\), what is the arc length?

Explanation opens after your attempt

Correct Answer

B. \(\frac{7\pi}{2}\) सेमी\(\frac{7\pi}{2}\) cm

Step 1

Concept

\(s=r\theta=5\times\frac{7\pi}{10}=\frac{7\pi}{2}\) cm. In exams, put the radian angle directly in the formula.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{7\pi}{2}\) सेमी / \(\frac{7\pi}{2}\) cm. \(s=r\theta=5\times\frac{7\pi}{10}=\frac{7\pi}{2}\) cm. In exams, put the radian angle directly in the formula.

Step 3

Exam Tip

\(s=r\theta=5\times\frac{7\pi}{10}=\frac{7\pi}{2}\) सेमी। परीक्षा में रेडियन कोण को सीधे सूत्र में रखें।

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

Question Hindi:
यदि (5) सेमी त्रिज्या वाले वृत्त में केंद्र कोण (\frac{7\pi}{10}) है, तो चाप की लंबाई क्या होगी?

Question English:
If a circle of radius (5) cm has central angle (\frac{7\pi}{10}), what is the arc length?

Options:
A. (\frac{5\pi}{2}) सेमी / (\frac{5\pi}{2}) cm
B. (\frac{7\pi}{2}) सेमी / (\frac{7\pi}{2}) cm
C. (\frac{3\pi}{2}) सेमी / (\frac{3\pi}{2}) cm
D. (\frac{9\pi}{2}) सेमी / (\frac{9\pi}{2}) cm

Correct Answer:
B. (\frac{7\pi}{2}) सेमी / (\frac{7\pi}{2}) cm

Explanation Hindi:
(s=r\theta=5\times\frac{7\pi}{10}=\frac{7\pi}{2}) सेमी। परीक्षा में रेडियन कोण को सीधे सूत्र में रखें।

Explanation English:
(s=r\theta=5\times\frac{7\pi}{10}=\frac{7\pi}{2}) cm. In exams, put the radian angle directly in the formula.

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Question 5/5 Hard Mathematics Trigonometric Functions Angles Class 11 Level 68

एक वृत्त की त्रिज्या (14) सेमी है और चाप की लंबाई (11) सेमी है। केंद्र पर बना कोण रेडियन में कितना होगा?

A circle has radius (14) cm and arc length (11) cm. What is the angle subtended at the centre in radians?

Explanation opens after your attempt

Correct Answer

A. \(\frac{11}{14}\)

Step 1

Concept

For arc length, \(s=r\theta\), so \(\theta=\frac{s}{r}\). In exams, the angle in this formula is always in radians.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{11}{14}\). For arc length, \(s=r\theta\), so \(\theta=\frac{s}{r}\). In exams, the angle in this formula is always in radians.

Step 3

Exam Tip

चाप लंबाई के लिए \(s=r\theta\), इसलिए \(\theta=\frac{s}{r}\)। परीक्षा में इस सूत्र में कोण हमेशा रेडियन में होता है।

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

Question Hindi:
एक वृत्त की त्रिज्या (14) सेमी है और चाप की लंबाई (11) सेमी है। केंद्र पर बना कोण रेडियन में कितना होगा?

Question English:
A circle has radius (14) cm and arc length (11) cm. What is the angle subtended at the centre in radians?

Options:
A. (\frac{11}{14})
B. (\frac{14}{11})
C. (\frac{25}{14})
D. (\frac{3}{4})

Correct Answer:
A. (\frac{11}{14})

Explanation Hindi:
चाप लंबाई के लिए (s=r\theta), इसलिए (\theta=\frac{s}{r})। परीक्षा में इस सूत्र में कोण हमेशा रेडियन में होता है।

Explanation English:
For arc length, (s=r\theta), so (\theta=\frac{s}{r}). In exams, the angle in this formula is always in radians.

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trigonometry angles arc length hard class11 MCQ Questions for Class 11

Practice Questions

यदि एक वृत्त की त्रिज्या (21) सेमी है और केंद्र कोण \(40^\circ\) है, तो चाप की लंबाई क्या है?

Concept

Why this answer is correct

Exam Tip

एक वृत्त में केंद्र कोण \(\frac{2\pi}{3}\) है और चाप \(10\pi\) सेमी है। त्रिज्या क्या होगी?

Concept

Why this answer is correct

Exam Tip

यदि सेक्टर की त्रिज्या (9) सेमी और कोण \(80^\circ\) है, तो चाप की लंबाई क्या होगी?

Concept

Why this answer is correct

Exam Tip

यदि (5) सेमी त्रिज्या वाले वृत्त में केंद्र कोण \(\frac{7\pi}{10}\) है, तो चाप की लंबाई क्या होगी?

Concept

Why this answer is correct

Exam Tip

एक वृत्त की त्रिज्या (14) सेमी है और चाप की लंबाई (11) सेमी है। केंद्र पर बना कोण रेडियन में कितना होगा?

Concept

Why this answer is correct

Exam Tip

trigonometry angles arc length hard class11 Revision Links

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trigonometry angles arc length hard class11 MCQ Questions for Class 11

Practice Questions

यदि एक वृत्त की त्रिज्या (21) सेमी है और केंद्र कोण \(40^\circ\) है, तो चाप की लंबाई क्या है?

Concept

Why this answer is correct

Exam Tip

एक वृत्त में केंद्र कोण \(\frac{2\pi}{3}\) है और चाप \(10\pi\) सेमी है। त्रिज्या क्या होगी?

Concept

Why this answer is correct

Exam Tip

यदि सेक्टर की त्रिज्या (9) सेमी और कोण \(80^\circ\) है, तो चाप की लंबाई क्या होगी?

Concept

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Exam Tip

यदि (5) सेमी त्रिज्या वाले वृत्त में केंद्र कोण \(\frac{7\pi}{10}\) है, तो चाप की लंबाई क्या होगी?

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एक वृत्त की त्रिज्या (14) सेमी है और चाप की लंबाई (11) सेमी है। केंद्र पर बना कोण रेडियन में कितना होगा?

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