Concept-wise Practice

coterminal-angle MCQ Questions for Class 11

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Practice Questions

24 questions tagged with coterminal-angle.

किसी कोण का \(-2\pi\) और (0) के बीच ऋणात्मक सहप्रारंभी कोण \(-\frac{7\pi}{18}\) है। उसका मुख्य धनात्मक कोण क्या है?

The negative coterminal angle of an angle between \(-2\pi\) and (0) is \(-\frac{7\pi}{18}\). What is its principal positive angle?

Explanation opens after your attempt
Correct Answer

D. \(\frac{29\pi}{18}\)

Step 1

Concept

Add \(2\pi\) to the negative angle. \(-\frac{7\pi}{18}+2\pi=\frac{29\pi}{18}\).

Step 2

Why this answer is correct

The correct answer is D. \(\frac{29\pi}{18}\). Add \(2\pi\) to the negative angle. \(-\frac{7\pi}{18}+2\pi=\frac{29\pi}{18}\).

Step 3

Exam Tip

ऋणात्मक कोण में \(2\pi\) जोड़ें। \(-\frac{7\pi}{18}+2\pi=\frac{29\pi}{18}\) मिलता है।

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यदि \(\theta\) और \(\frac{5\pi}{2}-\theta\) सहप्रारंभी हैं और \(0<\theta<2\pi\) है तो \(\theta\) क्या है?

If \(\theta\) and \(\frac{5\pi}{2}-\theta\) are coterminal and \(0<\theta<2\pi\) then what is \(\theta\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

The difference \(\frac{5\pi}{2}-2\theta\) must be a multiple of \(2\pi\). In the given interval \(\theta=\frac{\pi}{4}\) is suitable.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{\pi}{4}\). The difference \(\frac{5\pi}{2}-2\theta\) must be a multiple of \(2\pi\). In the given interval \(\theta=\frac{\pi}{4}\) is suitable.

Step 3

Exam Tip

अंतर \(\frac{5\pi}{2}-2\theta\) को \(2\pi\) का गुणज होना चाहिए। दिए अंतराल में \(\theta=\frac{\pi}{4}\) उपयुक्त है।

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यदि दो कोणों का अंतर \(1980^\circ\) है तो क्या वे सहप्रारंभी हो सकते हैं?

If the difference between two angles is \(1980^\circ\) can they be coterminal?

Explanation opens after your attempt
Correct Answer

D. नहीं क्योंकि \(\frac{1980}{360}\) पूर्णांक नहीं हैNo because \(\frac{1980}{360}\) is not an integer

Step 1

Concept

The difference of coterminal angles is an integer multiple of \(360^\circ\). \(\frac{1980}{360}=\frac{11}{2}\) is not an integer.

Step 2

Why this answer is correct

The correct answer is D. नहीं क्योंकि \(\frac{1980}{360}\) पूर्णांक नहीं है / No because \(\frac{1980}{360}\) is not an integer. The difference of coterminal angles is an integer multiple of \(360^\circ\). \(\frac{1980}{360}=\frac{11}{2}\) is not an integer.

Step 3

Exam Tip

सहप्रारंभी कोणों का अंतर \(360^\circ\) का पूर्णांक गुणज होता है। \(\frac{1980}{360}=\frac{11}{2}\) पूर्णांक नहीं है।

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सबसे छोटा धनात्मक पूर्णांक (n) क्या है ताकि \(\frac{5\pi}{12}+\frac{n\pi}{6}\) और \(\frac{17\pi}{12}\) सहप्रारंभी हों?

What is the least positive integer (n) such that \(\frac{5\pi}{12}+\frac{n\pi}{6}\) and \(\frac{17\pi}{12}\) are coterminal?

Explanation opens after your attempt
Correct Answer

C. (6)

Step 1

Concept

Equating them gives \(\frac{n\pi}{6}=\pi\). Hence (n=6).

Step 2

Why this answer is correct

The correct answer is C. (6). Equating them gives \(\frac{n\pi}{6}=\pi\). Hence (n=6).

Step 3

Exam Tip

दोनों को बराबर करने पर \(\frac{n\pi}{6}=\pi\) मिलता है। इसलिए (n=6) है।

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यदि \(7x+10^\circ\) और \(2x-50^\circ\) सहप्रारंभी हैं तो (x) का सबसे छोटा धनात्मक मान क्या है?

If \(7x+10^\circ\) and \(2x-50^\circ\) are coterminal then what is the least positive value of (x)?

Explanation opens after your attempt
Correct Answer

C. \(60^\circ\)

Step 1

Concept

The difference is \(5x+60^\circ\) and it must be a multiple of \(360^\circ\). For the least positive value \(x=60^\circ\).

Step 2

Why this answer is correct

The correct answer is C. \(60^\circ\). The difference is \(5x+60^\circ\) and it must be a multiple of \(360^\circ\). For the least positive value \(x=60^\circ\).

Step 3

Exam Tip

अंतर \(5x+60^\circ\) है और यह \(360^\circ\) का गुणज होना चाहिए। सबसे छोटे धनात्मक मान के लिए \(x=60^\circ\) है।

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\(\frac{5\pi}{8}\) के साथ सहप्रारंभी और \(-4\pi\) तथा \(-2\pi\) के बीच कौन सा कोण है?

Which angle is coterminal with \(\frac{5\pi}{8}\) and lies between \(-4\pi\) and \(-2\pi\)?

Explanation opens after your attempt
Correct Answer

D. \(-\frac{27\pi}{8}\)

Step 1

Concept

\(\frac{5\pi}{8}-4\pi=-\frac{27\pi}{8}\). This satisfies the given interval.

Step 2

Why this answer is correct

The correct answer is D. \(-\frac{27\pi}{8}\). \(\frac{5\pi}{8}-4\pi=-\frac{27\pi}{8}\). This satisfies the given interval.

Step 3

Exam Tip

\(\frac{5\pi}{8}-4\pi=-\frac{27\pi}{8}\) है। यह दिया गया अंतराल पूरा करता है।

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कोण \(-1025^\circ\) का सबसे छोटा धनात्मक सहप्रारंभी कोण क्या है?

What is the least positive coterminal angle of \(-1025^\circ\)?

Explanation opens after your attempt
Correct Answer

C. \(55^\circ\)

Step 1

Concept

\(-1025^\circ+1080^\circ=55^\circ\). Add multiples of \(360^\circ\) to a large negative angle.

Step 2

Why this answer is correct

The correct answer is C. \(55^\circ\). \(-1025^\circ+1080^\circ=55^\circ\). Add multiples of \(360^\circ\) to a large negative angle.

Step 3

Exam Tip

\(-1025^\circ+1080^\circ=55^\circ\) है। नकारात्मक बड़े कोण में \(360^\circ\) के गुणज जोड़ें।

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कोण \(-1460^\circ\) की अंतिम भुजा किस चतुर्थांश में होगी?

In which quadrant will the terminal side of \(-1460^\circ\) lie?

Explanation opens after your attempt
Correct Answer

D. चतुर्थFourth

Step 1

Concept

\(-1460^\circ+1800^\circ=340^\circ\). \(340^\circ\) lies in the fourth quadrant.

Step 2

Why this answer is correct

The correct answer is D. चतुर्थ / Fourth. \(-1460^\circ+1800^\circ=340^\circ\). \(340^\circ\) lies in the fourth quadrant.

Step 3

Exam Tip

\(-1460^\circ+1800^\circ=340^\circ\) है। \(340^\circ\) चतुर्थ चतुर्थांश में आता है।

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यदि \(5\theta+20^\circ\) और \(\theta+140^\circ\) सहप्रारंभी कोण हैं तो \(\theta\) का सबसे छोटा धनात्मक मान क्या है?

If \(5\theta+20^\circ\) and \(\theta+140^\circ\) are coterminal angles then what is the least positive value of \(\theta\)?

Explanation opens after your attempt
Correct Answer

C. \(120^\circ\)

Step 1

Concept

The difference \(4\theta-120^\circ\) must be a multiple of \(360^\circ\). For the least positive value \(\theta=120^\circ\).

Step 2

Why this answer is correct

The correct answer is C. \(120^\circ\). The difference \(4\theta-120^\circ\) must be a multiple of \(360^\circ\). For the least positive value \(\theta=120^\circ\).

Step 3

Exam Tip

अंतर \(4\theta-120^\circ\) को \(360^\circ\) का गुणज होना चाहिए। सबसे छोटे धनात्मक मान के लिए \(\theta=120^\circ\) है।

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कौन सा कोण \(35^\circ\) के साथ सहप्रारंभी है और \(360^\circ\) से बड़ा है लेकिन \(720^\circ\) से छोटा है?

Which angle is coterminal with \(35^\circ\) and greater than \(360^\circ\) but less than \(720^\circ\)?

Explanation opens after your attempt
Correct Answer

B. \(395^\circ\)

Step 1

Concept

\(35^\circ+360^\circ=395^\circ\) lies in the given interval. Add or subtract \(360^\circ\) for coterminal angles.

Step 2

Why this answer is correct

The correct answer is B. \(395^\circ\). \(35^\circ+360^\circ=395^\circ\) lies in the given interval. Add or subtract \(360^\circ\) for coterminal angles.

Step 3

Exam Tip

\(35^\circ+360^\circ=395^\circ\) दिए अंतराल में आता है। सहप्रारंभी कोण के लिए \(360^\circ\) जोड़ें या घटाएं।

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कोण \(-\frac{41\pi}{9}\) का (0) और \(2\pi\) के बीच सहप्रारंभी कोण क्या है?

What is the coterminal angle of \(-\frac{41\pi}{9}\) between (0) and \(2\pi\)?

Explanation opens after your attempt
Correct Answer

D. \(\frac{13\pi}{9}\)

Step 1

Concept

\(-\frac{41\pi}{9}+6\pi=\frac{13\pi}{9}\). Add multiples of \(2\pi\) to a negative angle.

Step 2

Why this answer is correct

The correct answer is D. \(\frac{13\pi}{9}\). \(-\frac{41\pi}{9}+6\pi=\frac{13\pi}{9}\). Add multiples of \(2\pi\) to a negative angle.

Step 3

Exam Tip

\(-\frac{41\pi}{9}+6\pi=\frac{13\pi}{9}\) है। नकारात्मक कोण में \(2\pi\) के गुणज जोड़ें।

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निम्न में से कौन सी जोड़ी सहप्रारंभी कोणों की है?

Which of the following pairs consists of coterminal angles?

Explanation opens after your attempt
Correct Answer

A. \(45^\circ\) और \(405^\circ\)\(45^\circ\) and \(405^\circ\)

Step 1

Concept

\(405^\circ-45^\circ=360^\circ\) so they are coterminal. The difference must be a multiple of \(360^\circ\).

Step 2

Why this answer is correct

The correct answer is A. \(45^\circ\) और \(405^\circ\) / \(45^\circ\) and \(405^\circ\). \(405^\circ-45^\circ=360^\circ\) so they are coterminal. The difference must be a multiple of \(360^\circ\).

Step 3

Exam Tip

\(405^\circ-45^\circ=360^\circ\) है इसलिए दोनों सहप्रारंभी हैं। अंतर \(360^\circ\) का गुणज होना चाहिए।

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कोण \(1490^\circ\) का सबसे छोटा धनात्मक सहप्रारंभी कोण क्या है?

What is the least positive coterminal angle of \(1490^\circ\)?

Explanation opens after your attempt
Correct Answer

B. \(50^\circ\)

Step 1

Concept

\(1490^\circ-1440^\circ=50^\circ\). Subtract the largest possible multiple of \(360^\circ\).

Step 2

Why this answer is correct

The correct answer is B. \(50^\circ\). \(1490^\circ-1440^\circ=50^\circ\). Subtract the largest possible multiple of \(360^\circ\).

Step 3

Exam Tip

\(1490^\circ-1440^\circ=50^\circ\) है। \(360^\circ\) के अधिकतम संभव गुणज को घटाएं।

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यदि \(\theta=-315^\circ\) है तो \(0^\circ\le\theta<360^\circ\) में इसका सहप्रारंभी कोण क्या होगा?

If \(\theta=-315^\circ\) then what is its coterminal angle in \(0^\circ\le\theta<360^\circ\)?

Explanation opens after your attempt
Correct Answer

B. \(45^\circ\)

Step 1

Concept

\(-315^\circ+360^\circ=45^\circ\). Add \(360^\circ\) to bring it into the given interval.

Step 2

Why this answer is correct

The correct answer is B. \(45^\circ\). \(-315^\circ+360^\circ=45^\circ\). Add \(360^\circ\) to bring it into the given interval.

Step 3

Exam Tip

\(-315^\circ+360^\circ=45^\circ\) है। दिए गए अंतराल में लाने के लिए \(360^\circ\) जोड़ें।

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कोण \(-\frac{23\pi}{6}\) का (0) और \(2\pi\) के बीच सहप्रारंभी कोण क्या है?

What is the coterminal angle of \(-\frac{23\pi}{6}\) between (0) and \(2\pi\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

\(-\frac{23\pi}{6}+4\pi=\frac{\pi}{6}\). Add multiples of \(2\pi\) to a negative radian angle.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{\pi}{6}\). \(-\frac{23\pi}{6}+4\pi=\frac{\pi}{6}\). Add multiples of \(2\pi\) to a negative radian angle.

Step 3

Exam Tip

\(-\frac{23\pi}{6}+4\pi=\frac{\pi}{6}\) है। नकारात्मक रेडियन कोण में \(2\pi\) के गुणज जोड़ें।

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\(\frac{13\pi}{6}\) किस छोटे धनात्मक कोण के साथ सहप्रारंभी है?

\(\frac{13\pi}{6}\) is coterminal with which smaller positive angle?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

\(\frac{13\pi}{6}-2\pi=\frac{\pi}{6}\). Subtract \(2\pi\) to obtain the principal angle.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{\pi}{6}\). \(\frac{13\pi}{6}-2\pi=\frac{\pi}{6}\). Subtract \(2\pi\) to obtain the principal angle.

Step 3

Exam Tip

\(\frac{13\pi}{6}-2\pi=\frac{\pi}{6}\) है। \(2\pi\) घटाकर मुख्य कोण प्राप्त करें।

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\(\frac{19\pi}{4}\) का (0) और \(2\pi\) के बीच सहप्रारंभी कोण क्या है?

What is the coterminal angle of \(\frac{19\pi}{4}\) between (0) and \(2\pi\)?

Explanation opens after your attempt
Correct Answer

C. \(\frac{3\pi}{4}\)

Step 1

Concept

\(\frac{19\pi}{4}-4\pi=\frac{3\pi}{4}\). Subtract multiples of \(2\pi\) to get the principal angle.

Step 2

Why this answer is correct

The correct answer is C. \(\frac{3\pi}{4}\). \(\frac{19\pi}{4}-4\pi=\frac{3\pi}{4}\). Subtract multiples of \(2\pi\) to get the principal angle.

Step 3

Exam Tip

\(\frac{19\pi}{4}-4\pi=\frac{3\pi}{4}\) है। \(2\pi\) के गुणज घटाकर मुख्य कोण पाएं।

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कोण \(-850^\circ\) की अंतिम भुजा किस चतुर्थांश में होगी?

In which quadrant will the terminal side of \(-850^\circ\) lie?

Explanation opens after your attempt
Correct Answer

C. तृतीयThird

Step 1

Concept

\(-850^\circ+1080^\circ=230^\circ\). \(230^\circ\) lies in the third quadrant.

Step 2

Why this answer is correct

The correct answer is C. तृतीय / Third. \(-850^\circ+1080^\circ=230^\circ\). \(230^\circ\) lies in the third quadrant.

Step 3

Exam Tip

\(-850^\circ+1080^\circ=230^\circ\) है। \(230^\circ\) तृतीय चतुर्थांश में आता है।

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कोण \(920^\circ\) का सबसे छोटा धनात्मक सहप्रारंभी कोण क्या है?

What is the least positive coterminal angle of \(920^\circ\)?

Explanation opens after your attempt
Correct Answer

C. \(200^\circ\)

Step 1

Concept

Since \(920^\circ-720^\circ=200^\circ\). Subtract multiples of \(360^\circ\) from large angles.

Step 2

Why this answer is correct

The correct answer is C. \(200^\circ\). Since \(920^\circ-720^\circ=200^\circ\). Subtract multiples of \(360^\circ\) from large angles.

Step 3

Exam Tip

\(920^\circ-720^\circ=200^\circ\) होता है। बड़े कोण में \(360^\circ\) के गुणज घटाएं।

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कोण \(-\frac{7\pi}{6}\) का \(0^\circ\) से \(360^\circ\) के बीच सहप्रारंभी कोण क्या होगा?

What is the coterminal angle of \(-\frac{7\pi}{6}\) between \(0^\circ\) and \(360^\circ\)?

Explanation opens after your attempt
Correct Answer

B. \(150^\circ\)

Step 1

Concept

\(-\frac{7\pi}{6}=-210^\circ\) and adding \(360^\circ\) gives \(150^\circ\). For a negative angle add \(360^\circ\) to get the principal angle.

Step 2

Why this answer is correct

The correct answer is B. \(150^\circ\). \(-\frac{7\pi}{6}=-210^\circ\) and adding \(360^\circ\) gives \(150^\circ\). For a negative angle add \(360^\circ\) to get the principal angle.

Step 3

Exam Tip

\(-\frac{7\pi}{6}=-210^\circ\) और \(360^\circ\) जोड़ने पर \(150^\circ\) मिलता है। नकारात्मक कोण में \(360^\circ\) जोड़कर मुख्य कोण खोजें।

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\( -780^\circ \) का धनात्मक सहसमापी कोण कौन सा है?

Which is the positive coterminal angle of \( -780^\circ \)?

Explanation opens after your attempt
Correct Answer

B. \(300^\circ\)

Step 1

Concept

\( -780^\circ+1080^\circ=300^\circ \). Add \(360^\circ\) repeatedly to get a positive value.

Step 2

Why this answer is correct

The correct answer is B. \(300^\circ\). \( -780^\circ+1080^\circ=300^\circ \). Add \(360^\circ\) repeatedly to get a positive value.

Step 3

Exam Tip

\( -780^\circ+1080^\circ=300^\circ \) होता है। \(360^\circ\) बार-बार जोड़कर धनात्मक मान पाएं।

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\(420^\circ\) का \(0^\circ\) से \(360^\circ\) के बीच सहसमापी कोण क्या है?

What is the coterminal angle of \(420^\circ\) between \(0^\circ\) and \(360^\circ\)?

Explanation opens after your attempt
Correct Answer

C. \(60^\circ\)

Step 1

Concept

\(420^\circ-360^\circ=60^\circ\). Subtract \(360^\circ\) to get a coterminal angle.

Step 2

Why this answer is correct

The correct answer is C. \(60^\circ\). \(420^\circ-360^\circ=60^\circ\). Subtract \(360^\circ\) to get a coterminal angle.

Step 3

Exam Tip

\(420^\circ-360^\circ=60^\circ\) है। सहसमापी कोण पाने के लिए \(360^\circ\) घटाएं।

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\(45^\circ\) का एक धनात्मक सहसमापी कोण कौन सा है?

Which is a positive coterminal angle of \(45^\circ\)?

Explanation opens after your attempt
Correct Answer

C. \(405^\circ\)

Step 1

Concept

\(45^\circ+360^\circ=405^\circ\) so it is coterminal. Add or subtract \(360^\circ\) for coterminal angles.

Step 2

Why this answer is correct

The correct answer is C. \(405^\circ\). \(45^\circ+360^\circ=405^\circ\) so it is coterminal. Add or subtract \(360^\circ\) for coterminal angles.

Step 3

Exam Tip

\(45^\circ+360^\circ=405^\circ\) इसलिए यह सहसमापी कोण है। सहसमापी कोण के लिए \(360^\circ\) जोड़ें या घटाएं।

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\(30^\circ\) का एक धनात्मक सह-अंतिम कोण कौन सा है?

Which is a positive coterminal angle of \(30^\circ\)?

Explanation opens after your attempt
Correct Answer

A. \(390^\circ\)

Step 1

Concept

\(30^\circ+360^\circ=390^\circ\). Add or subtract \(360^\circ\) to get a coterminal angle.

Step 2

Why this answer is correct

The correct answer is A. \(390^\circ\). \(30^\circ+360^\circ=390^\circ\). Add or subtract \(360^\circ\) to get a coterminal angle.

Step 3

Exam Tip

\(30^\circ+360^\circ=390^\circ\) होता है। सह-अंतिम कोण के लिए \(360^\circ\) जोड़ें या घटाएं।

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AI Video Prompt 16:9 + 9:16

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