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Class 11 Mathematics - Trigonometric Functions - Angles Medium Quiz

Level 68 • 50/50 questions • 35 seconds per question.

Level readiness 50/50 Questions
Time Left 29:10 35 sec/question
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Question 1 / 50 0 score
Answered 0/50 Correct 0 Time 29:10

\(37.5^\circ\) का रेडियन माप क्या है?

What is the radian measure of \(37.5^\circ\)?

Explanation opens after your attempt
Correct Answer

B. \( \frac{5\pi}{24} \) रेडियन\( \frac{5\pi}{24} \) radians

Step 1

Concept

\(37.5^\circ=\frac{37.5\pi}{180}=\frac{5\pi}{24}\). You can also treat \(37.5^\circ\) as \( \frac{75^\circ}{2} \).

Step 2

Why this answer is correct

The correct answer is B. \( \frac{5\pi}{24} \) रेडियन / \( \frac{5\pi}{24} \) radians. \(37.5^\circ=\frac{37.5\pi}{180}=\frac{5\pi}{24}\). You can also treat \(37.5^\circ\) as \( \frac{75^\circ}{2} \).

Step 3

Exam Tip

\(37.5^\circ=\frac{37.5\pi}{180}=\frac{5\pi}{24}\) होता है। \(37.5^\circ\) को \( \frac{75^\circ}{2} \) मानकर भी हल कर सकते हैं।

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\(-225^\circ\) को रेडियन में बदलें।

Convert \(-225^\circ\) into radians.

Explanation opens after your attempt
Correct Answer

C. \(-\frac{5\pi}{4}\) रेडियन\(-\frac{5\pi}{4}\) radians

Step 1

Concept

\(-225^\circ=\frac{-225\pi}{180}=-\frac{5\pi}{4}\). Keep the negative sign till the end.

Step 2

Why this answer is correct

The correct answer is C. \(-\frac{5\pi}{4}\) रेडियन / \(-\frac{5\pi}{4}\) radians. \(-225^\circ=\frac{-225\pi}{180}=-\frac{5\pi}{4}\). Keep the negative sign till the end.

Step 3

Exam Tip

\(-225^\circ=\frac{-225\pi}{180}=-\frac{5\pi}{4}\) है। ऋणात्मक कोण का चिह्न अंत तक बनाए रखें।

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\(405^\circ\) का रेडियन रूप कौन सा है?

Which is the radian form of \(405^\circ\)?

Explanation opens after your attempt
Correct Answer

D. \( \frac{9\pi}{4} \) रेडियन\( \frac{9\pi}{4} \) radians

Step 1

Concept

\(405^\circ=\frac{405\pi}{180}=\frac{9\pi}{4}\). Use the same rule even for angles greater than \(360^\circ\).

Step 2

Why this answer is correct

The correct answer is D. \( \frac{9\pi}{4} \) रेडियन / \( \frac{9\pi}{4} \) radians. \(405^\circ=\frac{405\pi}{180}=\frac{9\pi}{4}\). Use the same rule even for angles greater than \(360^\circ\).

Step 3

Exam Tip

\(405^\circ=\frac{405\pi}{180}=\frac{9\pi}{4}\) होता है। \(360^\circ\) से बड़े कोणों को भी उसी नियम से बदलें।

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\( \frac{3\pi}{8} \) रेडियन को डिग्री में बदलने पर क्या मिलेगा?

What do we get by converting \( \frac{3\pi}{8} \) radians into degrees?

Explanation opens after your attempt
Correct Answer

A. \(67.5^\circ\)

Step 1

Concept

\( \frac{3\pi}{8}\times \frac{180^\circ}{\pi}=67.5^\circ\). Divide \(180^\circ\) by (8) and then multiply.

Step 2

Why this answer is correct

The correct answer is A. \(67.5^\circ\). \( \frac{3\pi}{8}\times \frac{180^\circ}{\pi}=67.5^\circ\). Divide \(180^\circ\) by (8) and then multiply.

Step 3

Exam Tip

\( \frac{3\pi}{8}\times \frac{180^\circ}{\pi}=67.5^\circ\) है। \(180^\circ\div 8=22.5^\circ\) करके गुणा करें।

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\( \frac{5\pi}{24} \) रेडियन कितने डिग्री के बराबर है?

How many degrees are equal to \( \frac{5\pi}{24} \) radians?

Explanation opens after your attempt
Correct Answer

B. \(37.5^\circ\)

Step 1

Concept

\( \frac{5\pi}{24}\times \frac{180^\circ}{\pi}=37.5^\circ\). If the denominator is (24), calculate \(180^\circ\div 24\).

Step 2

Why this answer is correct

The correct answer is B. \(37.5^\circ\). \( \frac{5\pi}{24}\times \frac{180^\circ}{\pi}=37.5^\circ\). If the denominator is (24), calculate \(180^\circ\div 24\).

Step 3

Exam Tip

\( \frac{5\pi}{24}\times \frac{180^\circ}{\pi}=37.5^\circ\) है। हर (24) हो तो \(180^\circ\div 24\) करें।

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\( -\frac{7\pi}{6} \) रेडियन का डिग्री माप क्या है?

What is the degree measure of \( -\frac{7\pi}{6} \) radians?

Explanation opens after your attempt
Correct Answer

C. \(-210^\circ\)

Step 1

Concept

\( -\frac{7\pi}{6}\times \frac{180^\circ}{\pi}=-210^\circ\). The negative sign in radians remains in degrees.

Step 2

Why this answer is correct

The correct answer is C. \(-210^\circ\). \( -\frac{7\pi}{6}\times \frac{180^\circ}{\pi}=-210^\circ\). The negative sign in radians remains in degrees.

Step 3

Exam Tip

\( -\frac{7\pi}{6}\times \frac{180^\circ}{\pi}=-210^\circ\) होता है। रेडियन का ऋणात्मक चिह्न डिग्री में भी रहता है।

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\( \frac{13\pi}{8} \) रेडियन को डिग्री में बदलें।

Convert \( \frac{13\pi}{8} \) radians into degrees.

Explanation opens after your attempt
Correct Answer

D. \(292.5^\circ\)

Step 1

Concept

\( \frac{13\pi}{8}\times \frac{180^\circ}{\pi}=292.5^\circ\). Remember \( \frac{\pi}{8}=22.5^\circ \).

Step 2

Why this answer is correct

The correct answer is D. \(292.5^\circ\). \( \frac{13\pi}{8}\times \frac{180^\circ}{\pi}=292.5^\circ\). Remember \( \frac{\pi}{8}=22.5^\circ \).

Step 3

Exam Tip

\( \frac{13\pi}{8}\times \frac{180^\circ}{\pi}=292.5^\circ\) है। \( \frac{\pi}{8}=22.5^\circ \) को याद रखें।

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\(985^\circ\) का \(0^\circ\) से \(360^\circ\) के बीच सहसमापी कोण क्या है?

What is the coterminal angle of \(985^\circ\) between \(0^\circ\) and \(360^\circ\)?

Explanation opens after your attempt
Correct Answer

A. \(265^\circ\)

Step 1

Concept

\(985^\circ-720^\circ=265^\circ\). Subtract a suitable multiple of \(360^\circ\) from a large angle.

Step 2

Why this answer is correct

The correct answer is A. \(265^\circ\). \(985^\circ-720^\circ=265^\circ\). Subtract a suitable multiple of \(360^\circ\) from a large angle.

Step 3

Exam Tip

\(985^\circ-720^\circ=265^\circ\) है। बड़े कोण से \(360^\circ\) के उपयुक्त गुणज घटाएं।

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\( -1000^\circ \) का \(0^\circ\) से \(360^\circ\) के बीच सहसमापी कोण कौन सा है?

Which is the coterminal angle of \( -1000^\circ \) between \(0^\circ\) and \(360^\circ\)?

Explanation opens after your attempt
Correct Answer

B. \(80^\circ\)

Step 1

Concept

\( -1000^\circ+1080^\circ=80^\circ \). Add multiples of \(360^\circ\) for large negative angles.

Step 2

Why this answer is correct

The correct answer is B. \(80^\circ\). \( -1000^\circ+1080^\circ=80^\circ \). Add multiples of \(360^\circ\) for large negative angles.

Step 3

Exam Tip

\( -1000^\circ+1080^\circ=80^\circ \) है। ऋणात्मक बड़े कोणों में \(360^\circ\) के गुणज जोड़ें।

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\(1540^\circ\) का मुख्य कोण क्या होगा?

What will be the principal angle of \(1540^\circ\)?

Explanation opens after your attempt
Correct Answer

C. \(100^\circ\)

Step 1

Concept

\(1540^\circ-1440^\circ=100^\circ\). The principal angle is usually taken between \(0^\circ\) and \(360^\circ\).

Step 2

Why this answer is correct

The correct answer is C. \(100^\circ\). \(1540^\circ-1440^\circ=100^\circ\). The principal angle is usually taken between \(0^\circ\) and \(360^\circ\).

Step 3

Exam Tip

\(1540^\circ-1440^\circ=100^\circ\) है। मुख्य कोण सामान्यतः \(0^\circ\) से \(360^\circ\) के बीच लिया जाता है।

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\( -1430^\circ \) का मुख्य सहसमापी कोण क्या है?

What is the principal coterminal angle of \( -1430^\circ \)?

Explanation opens after your attempt
Correct Answer

D. \(10^\circ\)

Step 1

Concept

\( -1430^\circ+1440^\circ=10^\circ \). Adding the nearest larger multiple of \(360^\circ\) is easy.

Step 2

Why this answer is correct

The correct answer is D. \(10^\circ\). \( -1430^\circ+1440^\circ=10^\circ \). Adding the nearest larger multiple of \(360^\circ\) is easy.

Step 3

Exam Tip

\( -1430^\circ+1440^\circ=10^\circ \) है। निकटतम बड़े \(360^\circ\) के गुणज को जोड़ना आसान है।

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\( \frac{29\pi}{4} \) का (0) से \(2\pi\) के बीच सहसमापी कोण क्या है?

What is the coterminal angle of \( \frac{29\pi}{4} \) between (0) and \(2\pi\)?

Explanation opens after your attempt
Correct Answer

A. \( \frac{5\pi}{4} \)

Step 1

Concept

\( \frac{29\pi}{4}-\frac{24\pi}{4}=\frac{5\pi}{4} \). In radians subtract \(2\pi=\frac{8\pi}{4}\).

Step 2

Why this answer is correct

The correct answer is A. \( \frac{5\pi}{4} \). \( \frac{29\pi}{4}-\frac{24\pi}{4}=\frac{5\pi}{4} \). In radians subtract \(2\pi=\frac{8\pi}{4}\).

Step 3

Exam Tip

\( \frac{29\pi}{4}-\frac{24\pi}{4}=\frac{5\pi}{4} \) है। रेडियन में \(2\pi=\frac{8\pi}{4}\) घटाते हैं।

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\( -\frac{19\pi}{6} \) का (0) से \(2\pi\) के बीच सहसमापी कोण क्या है?

What is the coterminal angle of \( -\frac{19\pi}{6} \) between (0) and \(2\pi\)?

Explanation opens after your attempt
Correct Answer

B. \( \frac{5\pi}{6} \)

Step 1

Concept

\( -\frac{19\pi}{6}+\frac{24\pi}{6}=\frac{5\pi}{6} \). Add multiples of \(2\pi\) to a negative radian angle.

Step 2

Why this answer is correct

The correct answer is B. \( \frac{5\pi}{6} \). \( -\frac{19\pi}{6}+\frac{24\pi}{6}=\frac{5\pi}{6} \). Add multiples of \(2\pi\) to a negative radian angle.

Step 3

Exam Tip

\( -\frac{19\pi}{6}+\frac{24\pi}{6}=\frac{5\pi}{6} \) है। ऋणात्मक रेडियन कोण में \(2\pi\) के गुणज जोड़ें।

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\( \frac{31\pi}{3} \) का मुख्य सहसमापी कोण कौन सा है?

Which is the principal coterminal angle of \( \frac{31\pi}{3} \)?

Explanation opens after your attempt
Correct Answer

B. \( \frac{\pi}{3} \)

Step 1

Concept

\( \frac{31\pi}{3}-\frac{30\pi}{3}=\frac{\pi}{3} \). Subtract a multiple of \(2\pi=\frac{6\pi}{3}\).

Step 2

Why this answer is correct

The correct answer is B. \( \frac{\pi}{3} \). \( \frac{31\pi}{3}-\frac{30\pi}{3}=\frac{\pi}{3} \). Subtract a multiple of \(2\pi=\frac{6\pi}{3}\).

Step 3

Exam Tip

\( \frac{31\pi}{3}-\frac{30\pi}{3}=\frac{\pi}{3} \) है। \(2\pi=\frac{6\pi}{3}\) का गुणज घटाएं।

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\( -\frac{25\pi}{8} \) का (0) से \(2\pi\) के बीच कोण क्या है?

What is the angle between (0) and \(2\pi\) for \( -\frac{25\pi}{8} \)?

Explanation opens after your attempt
Correct Answer

C. \( \frac{7\pi}{8} \)

Step 1

Concept

\( -\frac{25\pi}{8}+\frac{32\pi}{8}=\frac{7\pi}{8} \). Keeping the same denominator is a safe method while adding \(2\pi\).

Step 2

Why this answer is correct

The correct answer is C. \( \frac{7\pi}{8} \). \( -\frac{25\pi}{8}+\frac{32\pi}{8}=\frac{7\pi}{8} \). Keeping the same denominator is a safe method while adding \(2\pi\).

Step 3

Exam Tip

\( -\frac{25\pi}{8}+\frac{32\pi}{8}=\frac{7\pi}{8} \) है। हर समान रखकर \(2\pi\) जोड़ना सुरक्षित तरीका है।

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\( -250^\circ \) की अंतिम भुजा किस चतुर्थांश में होगी?

In which quadrant will the terminal side of \( -250^\circ \) lie?

Explanation opens after your attempt
Correct Answer

B. द्वितीय चतुर्थांशSecond quadrant

Step 1

Concept

\( -250^\circ+360^\circ=110^\circ \) and \(110^\circ\) lies in the second quadrant. First find the positive coterminal angle.

Step 2

Why this answer is correct

The correct answer is B. द्वितीय चतुर्थांश / Second quadrant. \( -250^\circ+360^\circ=110^\circ \) and \(110^\circ\) lies in the second quadrant. First find the positive coterminal angle.

Step 3

Exam Tip

\( -250^\circ+360^\circ=110^\circ \) है और \(110^\circ\) द्वितीय चतुर्थांश में है। पहले धनात्मक सहसमापी कोण निकालें।

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\( -710^\circ \) किस चतुर्थांश में सहसमापी कोण देता है?

\( -710^\circ \) gives a coterminal angle in which quadrant?

Explanation opens after your attempt
Correct Answer

A. प्रथम चतुर्थांशFirst quadrant

Step 1

Concept

\( -710^\circ+720^\circ=10^\circ \), so the terminal side lies in the first quadrant. Add multiples of \(360^\circ\) to a large negative angle.

Step 2

Why this answer is correct

The correct answer is A. प्रथम चतुर्थांश / First quadrant. \( -710^\circ+720^\circ=10^\circ \), so the terminal side lies in the first quadrant. Add multiples of \(360^\circ\) to a large negative angle.

Step 3

Exam Tip

\( -710^\circ+720^\circ=10^\circ \) है इसलिए अंतिम भुजा प्रथम चतुर्थांश में है। बड़े ऋणात्मक कोण में \(360^\circ\) के गुणज जोड़ें।

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\( \frac{9\pi}{7} \) रेडियन किस चतुर्थांश में स्थित है?

In which quadrant does \( \frac{9\pi}{7} \) radians lie?

Explanation opens after your attempt
Correct Answer

C. तृतीय चतुर्थांशThird quadrant

Step 1

Concept

\( \pi<\frac{9\pi}{7}<\frac{3\pi}{2} \), so it lies in the third quadrant. Identify the quadrant directly from radian intervals.

Step 2

Why this answer is correct

The correct answer is C. तृतीय चतुर्थांश / Third quadrant. \( \pi<\frac{9\pi}{7}<\frac{3\pi}{2} \), so it lies in the third quadrant. Identify the quadrant directly from radian intervals.

Step 3

Exam Tip

\( \pi<\frac{9\pi}{7}<\frac{3\pi}{2} \) इसलिए यह तृतीय चतुर्थांश में है। रेडियन सीमा से सीधे चतुर्थांश पहचानें।

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\( \frac{13\pi}{9} \) रेडियन की अंतिम भुजा किस चतुर्थांश में है?

In which quadrant is the terminal side of \( \frac{13\pi}{9} \) radians?

Explanation opens after your attempt
Correct Answer

C. तृतीय चतुर्थांशThird quadrant

Step 1

Concept

\( \pi<\frac{13\pi}{9}<\frac{3\pi}{2} \), so it is in the third quadrant. The interval between \( \pi \) and \( \frac{3\pi}{2} \) is the third quadrant.

Step 2

Why this answer is correct

The correct answer is C. तृतीय चतुर्थांश / Third quadrant. \( \pi<\frac{13\pi}{9}<\frac{3\pi}{2} \), so it is in the third quadrant. The interval between \( \pi \) and \( \frac{3\pi}{2} \) is the third quadrant.

Step 3

Exam Tip

\( \pi<\frac{13\pi}{9}<\frac{3\pi}{2} \) है इसलिए यह तृतीय चतुर्थांश में है। \( \pi \) और \( \frac{3\pi}{2} \) के बीच तीसरा चतुर्थांश होता है।

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\( \frac{17\pi}{9} \) रेडियन किस चतुर्थांश में आता है?

In which quadrant does \( \frac{17\pi}{9} \) radians lie?

Explanation opens after your attempt
Correct Answer

D. चतुर्थ चतुर्थांशFourth quadrant

Step 1

Concept

\( \frac{3\pi}{2}<\frac{17\pi}{9}<2\pi \), so it lies in the fourth quadrant. Compare radians by using a common denominator.

Step 2

Why this answer is correct

The correct answer is D. चतुर्थ चतुर्थांश / Fourth quadrant. \( \frac{3\pi}{2}<\frac{17\pi}{9}<2\pi \), so it lies in the fourth quadrant. Compare radians by using a common denominator.

Step 3

Exam Tip

\( \frac{3\pi}{2}<\frac{17\pi}{9}<2\pi \) है इसलिए यह चतुर्थ चतुर्थांश में है। रेडियन की तुलना समान हर बनाकर करें।

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\( \frac{4\pi}{9} \) रेडियन की अंतिम भुजा किस चतुर्थांश में होगी?

In which quadrant will the terminal side of \( \frac{4\pi}{9} \) radians lie?

Explanation opens after your attempt
Correct Answer

A. प्रथम चतुर्थांशFirst quadrant

Step 1

Concept

\(0<\frac{4\pi}{9}<\frac{\pi}{2}\), so it lies in the first quadrant. Check the interval of small positive radian angles carefully.

Step 2

Why this answer is correct

The correct answer is A. प्रथम चतुर्थांश / First quadrant. \(0<\frac{4\pi}{9}<\frac{\pi}{2}\), so it lies in the first quadrant. Check the interval of small positive radian angles carefully.

Step 3

Exam Tip

\(0<\frac{4\pi}{9}<\frac{\pi}{2}\) है इसलिए यह प्रथम चतुर्थांश में है। छोटे धनात्मक रेडियन कोणों की सीमा ध्यान से देखें।

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\( \frac{5\pi}{9} \) रेडियन किस चतुर्थांश में है?

In which quadrant is \( \frac{5\pi}{9} \) radians?

Explanation opens after your attempt
Correct Answer

B. द्वितीय चतुर्थांशSecond quadrant

Step 1

Concept

\( \frac{\pi}{2}<\frac{5\pi}{9}<\pi \), so it lies in the second quadrant. Remember the interval between \( \frac{\pi}{2} \) and \( \pi \).

Step 2

Why this answer is correct

The correct answer is B. द्वितीय चतुर्थांश / Second quadrant. \( \frac{\pi}{2}<\frac{5\pi}{9}<\pi \), so it lies in the second quadrant. Remember the interval between \( \frac{\pi}{2} \) and \( \pi \).

Step 3

Exam Tip

\( \frac{\pi}{2}<\frac{5\pi}{9}<\pi \) है इसलिए यह द्वितीय चतुर्थांश में है। \( \frac{\pi}{2} \) और \( \pi \) की सीमा याद रखें।

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\(125^\circ 30'\) को दशमलव डिग्री में बदलने पर क्या मिलेगा?

What is \(125^\circ 30'\) in decimal degrees?

Explanation opens after your attempt
Correct Answer

C. \(125.5^\circ\)

Step 1

Concept

\(30'=\frac{30}{60}^\circ=0.5^\circ\), so the value is \(125.5^\circ\). Do not write minutes directly as decimals.

Step 2

Why this answer is correct

The correct answer is C. \(125.5^\circ\). \(30'=\frac{30}{60}^\circ=0.5^\circ\), so the value is \(125.5^\circ\). Do not write minutes directly as decimals.

Step 3

Exam Tip

\(30'=\frac{30}{60}^\circ=0.5^\circ\) इसलिए मान \(125.5^\circ\) है। मिनट को दशमलव में सीधे न लिखें।

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\(76^\circ 45'\) को दशमलव डिग्री में लिखें।

Write \(76^\circ 45'\) in decimal degrees.

Explanation opens after your attempt
Correct Answer

B. \(76.75^\circ\)

Step 1

Concept

\(45'=\frac{45}{60}^\circ=0.75^\circ\), so \(76^\circ 45'=76.75^\circ\). Divide minutes by (60).

Step 2

Why this answer is correct

The correct answer is B. \(76.75^\circ\). \(45'=\frac{45}{60}^\circ=0.75^\circ\), so \(76^\circ 45'=76.75^\circ\). Divide minutes by (60).

Step 3

Exam Tip

\(45'=\frac{45}{60}^\circ=0.75^\circ\) इसलिए \(76^\circ 45'=76.75^\circ\) है। मिनट को (60) से भाग दें।

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\(19.2^\circ\) को डिग्री और मिनट में बदलें।

Convert \(19.2^\circ\) into degrees and minutes.

Explanation opens after your attempt
Correct Answer

C. \(19^\circ 12'\)

Step 1

Concept

\(0.2^\circ\times 60'=12'\), so \(19.2^\circ=19^\circ 12'\). Multiply the decimal part by (60).

Step 2

Why this answer is correct

The correct answer is C. \(19^\circ 12'\). \(0.2^\circ\times 60'=12'\), so \(19.2^\circ=19^\circ 12'\). Multiply the decimal part by (60).

Step 3

Exam Tip

\(0.2^\circ\times 60'=12'\) इसलिए \(19.2^\circ=19^\circ 12'\) है। दशमलव भाग को (60) से गुणा करें।

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\(48.625^\circ\) को डिग्री मिनट सेकंड में बदलें।

Convert \(48.625^\circ\) into degrees minutes seconds.

Explanation opens after your attempt
Correct Answer

A. \(48^\circ 37' 30''\)

Step 1

Concept

\(0.625^\circ\times 60'=37.5'\) and \(0.5'\times 60''=30''\). Convert the decimal part step by step into minutes and seconds.

Step 2

Why this answer is correct

The correct answer is A. \(48^\circ 37' 30''\). \(0.625^\circ\times 60'=37.5'\) and \(0.5'\times 60''=30''\). Convert the decimal part step by step into minutes and seconds.

Step 3

Exam Tip

\(0.625^\circ\times 60'=37.5'\) और \(0.5'\times 60''=30''\) है। दशमलव को क्रम से मिनट और सेकंड में बदलें।

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\(33^\circ 20' 24''\) को कुल सेकंड में बदलें।

Convert \(33^\circ 20' 24''\) into total seconds.

Explanation opens after your attempt
Correct Answer

B. (120024'')

Step 1

Concept

\(33^\circ=118800''\) and (20'=1200''), so the total is (120024''). Remember \(1^\circ=3600''\) and (1'=60'').

Step 2

Why this answer is correct

The correct answer is B. (120024''). \(33^\circ=118800''\) and (20'=1200''), so the total is (120024''). Remember \(1^\circ=3600''\) and (1'=60'').

Step 3

Exam Tip

\(33^\circ=118800''\) और (20'=1200'') इसलिए कुल (120024'') है। \(1^\circ=3600''\) और (1'=60'') याद रखें।

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(4585'') को डिग्री मिनट सेकंड में बदलें।

Convert (4585'') into degrees minutes seconds.

Explanation opens after your attempt
Correct Answer

C. \(1^\circ 16' 25''\)

Step 1

Concept

(4585''=3600''+985'') and (985''=16'25''). First find degrees using (3600'').

Step 2

Why this answer is correct

The correct answer is C. \(1^\circ 16' 25''\). (4585''=3600''+985'') and (985''=16'25''). First find degrees using (3600'').

Step 3

Exam Tip

(4585''=3600''+985'') और (985''=16'25'') है। पहले (3600'') से डिग्री निकालें।

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(2) रेडियन को डिग्री में लगभग बदलने पर निकटतम मान कौन सा है?

When (2) radians is approximately converted into degrees, which value is nearest?

Explanation opens after your attempt
Correct Answer

D. \(114.6^\circ\)

Step 1

Concept

\(2\times \frac{180^\circ}{\pi}\approx 114.6^\circ\). For estimation take (1) radian as \(57.3^\circ\).

Step 2

Why this answer is correct

The correct answer is D. \(114.6^\circ\). \(2\times \frac{180^\circ}{\pi}\approx 114.6^\circ\). For estimation take (1) radian as \(57.3^\circ\).

Step 3

Exam Tip

\(2\times \frac{180^\circ}{\pi}\approx 114.6^\circ\) होता है। अनुमान में (1) रेडियन को \(57.3^\circ\) मानें।

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(3.2) रेडियन को डिग्री में लगभग बदलने पर मान किसके निकट है?

When (3.2) radians is approximately converted into degrees, the value is nearest to which option?

Explanation opens after your attempt
Correct Answer

A. \(183.4^\circ\)

Step 1

Concept

\(3.2\times 57.3^\circ\approx 183.4^\circ\). Multiply by \(57.3^\circ\) to convert radians approximately into degrees.

Step 2

Why this answer is correct

The correct answer is A. \(183.4^\circ\). \(3.2\times 57.3^\circ\approx 183.4^\circ\). Multiply by \(57.3^\circ\) to convert radians approximately into degrees.

Step 3

Exam Tip

\(3.2\times 57.3^\circ\approx 183.4^\circ\) है। रेडियन को डिग्री में बदलने के लिए \(57.3^\circ\) से गुणा करें।

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\(150^\circ\) को रेडियन में गलत रूप से \( \frac{2\pi}{3} \) लिखा गया। सही रेडियन रूप क्या है?

\(150^\circ\) was incorrectly written as \( \frac{2\pi}{3} \) radians. What is the correct radian form?

Explanation opens after your attempt
Correct Answer

B. \( \frac{5\pi}{6} \) रेडियन\( \frac{5\pi}{6} \) radians

Step 1

Concept

\(150^\circ=\frac{150\pi}{180}=\frac{5\pi}{6}\). \( \frac{2\pi}{3} \) means \(120^\circ\).

Step 2

Why this answer is correct

The correct answer is B. \( \frac{5\pi}{6} \) रेडियन / \( \frac{5\pi}{6} \) radians. \(150^\circ=\frac{150\pi}{180}=\frac{5\pi}{6}\). \( \frac{2\pi}{3} \) means \(120^\circ\).

Step 3

Exam Tip

\(150^\circ=\frac{150\pi}{180}=\frac{5\pi}{6}\) है। \( \frac{2\pi}{3} \) का अर्थ \(120^\circ\) होता है।

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\( \frac{7\pi}{5} \) रेडियन को डिग्री में बदलने पर सही मान क्या है?

What is the correct degree value of \( \frac{7\pi}{5} \) radians?

Explanation opens after your attempt
Correct Answer

C. \(252^\circ\)

Step 1

Concept

\( \frac{7\pi}{5}\times \frac{180^\circ}{\pi}=252^\circ\). If the denominator is (5), take \(180^\circ\div 5=36^\circ\).

Step 2

Why this answer is correct

The correct answer is C. \(252^\circ\). \( \frac{7\pi}{5}\times \frac{180^\circ}{\pi}=252^\circ\). If the denominator is (5), take \(180^\circ\div 5=36^\circ\).

Step 3

Exam Tip

\( \frac{7\pi}{5}\times \frac{180^\circ}{\pi}=252^\circ\) है। हर (5) हो तो \(180^\circ\div 5=36^\circ\) लें।

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यदि \( \theta=1.5 \) रेडियन है तो \( \theta \) का लगभग डिग्री माप क्या है?

If \( \theta=1.5 \) radians, what is the approximate degree measure of \( \theta \)?

Explanation opens after your attempt
Correct Answer

D. \(85.9^\circ\)

Step 1

Concept

\(1.5\times 57.3^\circ\approx 85.95^\circ\). Check the decimal carefully while choosing the nearest option.

Step 2

Why this answer is correct

The correct answer is D. \(85.9^\circ\). \(1.5\times 57.3^\circ\approx 85.95^\circ\). Check the decimal carefully while choosing the nearest option.

Step 3

Exam Tip

\(1.5\times 57.3^\circ\approx 85.95^\circ\) है। निकटतम विकल्प चुनते समय दशमलव को सावधानी से देखें।

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त्रिज्या (9) सेमी और चाप (6) सेमी होने पर केंद्र कोण रेडियन में क्या होगा?

If the radius is (9) cm and the arc is (6) cm, what is the central angle in radians?

Explanation opens after your attempt
Correct Answer

A. \( \frac{2}{3} \) रेडियन\( \frac{2}{3} \) radian

Step 1

Concept

\( \theta=\frac{s}{r}=\frac{6}{9}=\frac{2}{3} \) radian. Use \(s=r\theta\) in arc length questions.

Step 2

Why this answer is correct

The correct answer is A. \( \frac{2}{3} \) रेडियन / \( \frac{2}{3} \) radian. \( \theta=\frac{s}{r}=\frac{6}{9}=\frac{2}{3} \) radian. Use \(s=r\theta\) in arc length questions.

Step 3

Exam Tip

\( \theta=\frac{s}{r}=\frac{6}{9}=\frac{2}{3} \) रेडियन है। चाप लंबाई वाले प्रश्नों में \(s=r\theta\) प्रयोग करें।

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यदि (r=15) सेमी और \( \theta=\frac{2\pi}{5} \) रेडियन है तो चाप की लंबाई क्या होगी?

If (r=15) cm and \( \theta=\frac{2\pi}{5} \) radians, what will be the arc length?

Explanation opens after your attempt
Correct Answer

B. \(6\pi\) सेमी\(6\pi\) cm

Step 1

Concept

\(s=r\theta=15\times \frac{2\pi}{5}=6\pi\) cm. The formula applies directly when the angle is in radians.

Step 2

Why this answer is correct

The correct answer is B. \(6\pi\) सेमी / \(6\pi\) cm. \(s=r\theta=15\times \frac{2\pi}{5}=6\pi\) cm. The formula applies directly when the angle is in radians.

Step 3

Exam Tip

\(s=r\theta=15\times \frac{2\pi}{5}=6\pi\) सेमी है। कोण रेडियन में हो तो सूत्र सीधे लगता है।

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त्रिज्या (20) सेमी वाले वृत्त में \(72^\circ\) कोण से बने चाप की लंबाई क्या है?

What is the arc length made by an angle of \(72^\circ\) in a circle of radius (20) cm?

Explanation opens after your attempt
Correct Answer

C. \(8\pi\) सेमी\(8\pi\) cm

Step 1

Concept

\(72^\circ=\frac{2\pi}{5}\) and \(s=20\times \frac{2\pi}{5}=8\pi\) cm. Convert degrees to radians before finding the arc.

Step 2

Why this answer is correct

The correct answer is C. \(8\pi\) सेमी / \(8\pi\) cm. \(72^\circ=\frac{2\pi}{5}\) and \(s=20\times \frac{2\pi}{5}=8\pi\) cm. Convert degrees to radians before finding the arc.

Step 3

Exam Tip

\(72^\circ=\frac{2\pi}{5}\) और \(s=20\times \frac{2\pi}{5}=8\pi\) सेमी है। चाप निकालने से पहले डिग्री को रेडियन में बदलें।

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यदि चाप \(s=11\pi\) सेमी और कोण \( \theta=\frac{\pi}{2} \) रेडियन है तो त्रिज्या क्या है?

If arc \(s=11\pi\) cm and angle \( \theta=\frac{\pi}{2} \) radians, what is the radius?

Explanation opens after your attempt
Correct Answer

D. (22) सेमी(22) cm

Step 1

Concept

\(r=\frac{s}{\theta}=\frac{11\pi}{\pi/2}=22\) cm. Isolate (r) in \(s=r\theta\).

Step 2

Why this answer is correct

The correct answer is D. (22) सेमी / (22) cm. \(r=\frac{s}{\theta}=\frac{11\pi}{\pi/2}=22\) cm. Isolate (r) in \(s=r\theta\).

Step 3

Exam Tip

\(r=\frac{s}{\theta}=\frac{11\pi}{\pi/2}=22\) सेमी है। \(s=r\theta\) में (r) को अलग करें।

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त्रिज्या (10) सेमी और केंद्र कोण \( \frac{3\pi}{10} \) रेडियन हो तो त्रिज्यखंड का क्षेत्रफल क्या है?

If radius is (10) cm and central angle is \( \frac{3\pi}{10} \) radians, what is the area of the sector?

Explanation opens after your attempt
Correct Answer

A. \(15\pi\) वर्ग सेमी\(15\pi\) square cm

Step 1

Concept

Area is \( \frac{1}{2}r^2\theta=\frac{1}{2}\times100\times\frac{3\pi}{10}=15\pi \). Use this formula directly when the angle is in radians.

Step 2

Why this answer is correct

The correct answer is A. \(15\pi\) वर्ग सेमी / \(15\pi\) square cm. Area is \( \frac{1}{2}r^2\theta=\frac{1}{2}\times100\times\frac{3\pi}{10}=15\pi \). Use this formula directly when the angle is in radians.

Step 3

Exam Tip

क्षेत्रफल \( \frac{1}{2}r^2\theta=\frac{1}{2}\times100\times\frac{3\pi}{10}=15\pi \) है। कोण रेडियन में हो तो यह सूत्र सीधे लगाएं।

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त्रिज्या (12) सेमी और कोण \(45^\circ\) होने पर त्रिज्यखंड का क्षेत्रफल क्या होगा?

What will be the area of a sector with radius (12) cm and angle \(45^\circ\)?

Explanation opens after your attempt
Correct Answer

B. \(18\pi\) वर्ग सेमी\(18\pi\) square cm

Step 1

Concept

\(45^\circ=\frac{\pi}{4}\) and area is \( \frac{1}{2}\times144\times\frac{\pi}{4}=18\pi \). Convert the degree angle into radians first.

Step 2

Why this answer is correct

The correct answer is B. \(18\pi\) वर्ग सेमी / \(18\pi\) square cm. \(45^\circ=\frac{\pi}{4}\) and area is \( \frac{1}{2}\times144\times\frac{\pi}{4}=18\pi \). Convert the degree angle into radians first.

Step 3

Exam Tip

\(45^\circ=\frac{\pi}{4}\) और क्षेत्रफल \( \frac{1}{2}\times144\times\frac{\pi}{4}=18\pi \) है। डिग्री कोण को पहले रेडियन में बदलें।

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यदि त्रिज्यखंड का क्षेत्रफल (25) वर्ग सेमी और (r=5) सेमी है तो केंद्र कोण रेडियन में क्या होगा?

If the sector area is (25) square cm and (r=5) cm, what is the central angle in radians?

Explanation opens after your attempt
Correct Answer

B. (2) रेडियन(2) radians

Step 1

Concept

\(25=\frac{1}{2}\times25\times\theta\), so \( \theta=2 \) radians. Isolate the unknown angle in the area formula.

Step 2

Why this answer is correct

The correct answer is B. (2) रेडियन / (2) radians. \(25=\frac{1}{2}\times25\times\theta\), so \( \theta=2 \) radians. Isolate the unknown angle in the area formula.

Step 3

Exam Tip

\(25=\frac{1}{2}\times25\times\theta\) इसलिए \( \theta=2 \) रेडियन है। क्षेत्रफल सूत्र में अज्ञात कोण को अलग करें।

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यदि चाप की लंबाई (16) सेमी और त्रिज्यखंड क्षेत्रफल (64) वर्ग सेमी है तो त्रिज्या क्या है?

If arc length is (16) cm and sector area is (64) square cm, what is the radius?

Explanation opens after your attempt
Correct Answer

C. (8) सेमी(8) cm

Step 1

Concept

Sector area is \( \frac{1}{2}rs \), so \(64=\frac{1}{2}\times r\times16\) gives (r=8). When arc length is given, \( \frac{1}{2}rs \) is very useful.

Step 2

Why this answer is correct

The correct answer is C. (8) सेमी / (8) cm. Sector area is \( \frac{1}{2}rs \), so \(64=\frac{1}{2}\times r\times16\) gives (r=8). When arc length is given, \( \frac{1}{2}rs \) is very useful.

Step 3

Exam Tip

त्रिज्यखंड क्षेत्रफल \( \frac{1}{2}rs \) है इसलिए \(64=\frac{1}{2}\times r\times16\) से (r=8) है। चाप दिया हो तो \( \frac{1}{2}rs \) बहुत उपयोगी है।

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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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\( \theta=\frac{5\pi}{6} \) वाले कोण की संदर्भ कोण क्या है?

What is the reference angle of an angle \( \theta=\frac{5\pi}{6} \)?

Explanation opens after your attempt
Correct Answer

A. \( \frac{\pi}{6} \)

Step 1

Concept

\( \frac{5\pi}{6} \) lies in the second quadrant and the reference angle is \( \pi-\frac{5\pi}{6}=\frac{\pi}{6} \). In the second quadrant use \( \pi-\theta \).

Step 2

Why this answer is correct

The correct answer is A. \( \frac{\pi}{6} \). \( \frac{5\pi}{6} \) lies in the second quadrant and the reference angle is \( \pi-\frac{5\pi}{6}=\frac{\pi}{6} \). In the second quadrant use \( \pi-\theta \).

Step 3

Exam Tip

\( \frac{5\pi}{6} \) द्वितीय चतुर्थांश में है और संदर्भ कोण \( \pi-\frac{5\pi}{6}=\frac{\pi}{6} \) है। द्वितीय चतुर्थांश में \( \pi-\theta \) लें।

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\( \theta=\frac{7\pi}{6} \) का संदर्भ कोण क्या है?

What is the reference angle of \( \theta=\frac{7\pi}{6} \)?

Explanation opens after your attempt
Correct Answer

B. \( \frac{\pi}{6} \)

Step 1

Concept

\( \frac{7\pi}{6} \) lies in the third quadrant and \( \frac{7\pi}{6}-\pi=\frac{\pi}{6} \). In the third quadrant use \( \theta-\pi \).

Step 2

Why this answer is correct

The correct answer is B. \( \frac{\pi}{6} \). \( \frac{7\pi}{6} \) lies in the third quadrant and \( \frac{7\pi}{6}-\pi=\frac{\pi}{6} \). In the third quadrant use \( \theta-\pi \).

Step 3

Exam Tip

\( \frac{7\pi}{6} \) तृतीय चतुर्थांश में है और \( \frac{7\pi}{6}-\pi=\frac{\pi}{6} \) है। तृतीय चतुर्थांश में \( \theta-\pi \) प्रयोग करें।

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\( \theta=\frac{11\pi}{6} \) का संदर्भ कोण कौन सा है?

Which is the reference angle of \( \theta=\frac{11\pi}{6} \)?

Explanation opens after your attempt
Correct Answer

C. \( \frac{\pi}{6} \)

Step 1

Concept

\( \frac{11\pi}{6} \) lies in the fourth quadrant and \(2\pi-\frac{11\pi}{6}=\frac{\pi}{6}\). In the fourth quadrant use \(2\pi-\theta\).

Step 2

Why this answer is correct

The correct answer is C. \( \frac{\pi}{6} \). \( \frac{11\pi}{6} \) lies in the fourth quadrant and \(2\pi-\frac{11\pi}{6}=\frac{\pi}{6}\). In the fourth quadrant use \(2\pi-\theta\).

Step 3

Exam Tip

\( \frac{11\pi}{6} \) चतुर्थ चतुर्थांश में है और \(2\pi-\frac{11\pi}{6}=\frac{\pi}{6}\) है। चतुर्थ चतुर्थांश में \(2\pi-\theta\) लें।

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\(210^\circ\) का संदर्भ कोण क्या होगा?

What will be the reference angle of \(210^\circ\)?

Explanation opens after your attempt
Correct Answer

D. \(30^\circ\)

Step 1

Concept

\(210^\circ\) lies in the third quadrant and \(210^\circ-180^\circ=30^\circ\). In the third quadrant subtract \(180^\circ\).

Step 2

Why this answer is correct

The correct answer is D. \(30^\circ\). \(210^\circ\) lies in the third quadrant and \(210^\circ-180^\circ=30^\circ\). In the third quadrant subtract \(180^\circ\).

Step 3

Exam Tip

\(210^\circ\) तृतीय चतुर्थांश में है और \(210^\circ-180^\circ=30^\circ\) है। तृतीय चतुर्थांश में \(180^\circ\) घटाएं।

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\(330^\circ\) का संदर्भ कोण क्या है?

What is the reference angle of \(330^\circ\)?

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Correct Answer

A. \(30^\circ\)

Step 1

Concept

\(330^\circ\) lies in the fourth quadrant and \(360^\circ-330^\circ=30^\circ\). In the fourth quadrant use \(360^\circ-\theta\).

Step 2

Why this answer is correct

The correct answer is A. \(30^\circ\). \(330^\circ\) lies in the fourth quadrant and \(360^\circ-330^\circ=30^\circ\). In the fourth quadrant use \(360^\circ-\theta\).

Step 3

Exam Tip

\(330^\circ\) चतुर्थ चतुर्थांश में है और \(360^\circ-330^\circ=30^\circ\) है। चतुर्थ चतुर्थांश में \(360^\circ-\theta\) करें।

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\(135^\circ\) और \(-225^\circ\) के बारे में सही कथन कौन सा है?

Which statement about \(135^\circ\) and \(-225^\circ\) is correct?

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Correct Answer

B. वे सहसमापी कोण हैंThey are coterminal angles

Step 1

Concept

(135^\circ-\(-225^\circ\)=360^\circ), so they are coterminal angles. If the difference is a multiple of \(360^\circ\), the angles are coterminal.

Step 2

Why this answer is correct

The correct answer is B. वे सहसमापी कोण हैं / They are coterminal angles. (135^\circ-\(-225^\circ\)=360^\circ), so they are coterminal angles. If the difference is a multiple of \(360^\circ\), the angles are coterminal.

Step 3

Exam Tip

(135^\circ-\(-225^\circ\)=360^\circ) है इसलिए वे सहसमापी कोण हैं। अंतर \(360^\circ\) का गुणज हो तो कोण सहसमापी होते हैं।

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यदि \( \theta \) की अंतिम भुजा धनात्मक (y)-अक्ष पर है तो \(0^\circ\) से \(360^\circ\) के बीच \( \theta \) का मान क्या हो सकता है?

If the terminal side of \( \theta \) lies on the positive (y)-axis, what can be the value of \( \theta \) between \(0^\circ\) and \(360^\circ\)?

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Correct Answer

D. \(90^\circ\)

Step 1

Concept

The terminal side lies on the positive (y)-axis at \(90^\circ\). Axis angles are not placed in quadrants.

Step 2

Why this answer is correct

The correct answer is D. \(90^\circ\). The terminal side lies on the positive (y)-axis at \(90^\circ\). Axis angles are not placed in quadrants.

Step 3

Exam Tip

धनात्मक (y)-अक्ष पर अंतिम भुजा \(90^\circ\) पर होती है। अक्षीय कोणों को चतुर्थांश में नहीं रखा जाता।

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\(7^\circ 30'\) को रेडियन में बदलने पर सही मान क्या है?

What is the correct radian value of \(7^\circ 30'\)?

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Correct Answer

C. \( \frac{\pi}{24} \) रेडियन\( \frac{\pi}{24} \) radians

Step 1

Concept

\(30'=\frac{1}{2}^\circ\) so \(7^\circ 30'=7.5^\circ\) and \(7.5^\circ\times\frac{\pi}{180}=\frac{\pi}{24}\). Convert minutes into degrees first.

Step 2

Why this answer is correct

The correct answer is C. \( \frac{\pi}{24} \) रेडियन / \( \frac{\pi}{24} \) radians. \(30'=\frac{1}{2}^\circ\) so \(7^\circ 30'=7.5^\circ\) and \(7.5^\circ\times\frac{\pi}{180}=\frac{\pi}{24}\). Convert minutes into degrees first.

Step 3

Exam Tip

\(30'=\frac{1}{2}^\circ\) इसलिए \(7^\circ 30'=7.5^\circ\) और \(7.5^\circ\times\frac{\pi}{180}=\frac{\pi}{24}\) है। पहले मिनट को डिग्री में बदलें।

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FAQs

Class 11 Mathematics Quiz FAQs

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