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Mathematics Principal value branch MCQ Questions for Class 12 General

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01 Practice Topic Domain and range 24 MCQs 02 Practice Topic Graphs of inverse trigonometric functions 3 MCQs 03 Practice Topic Introduction to inverse trigonometric functions 106 MCQs 04 Practice Topic Properties of inverse trigonometric functions 48 MCQs

Principal value branch Practice Questions

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Question 51/69 Medium Mathematics Inverse Trigonometric Functions Principal value branch Class 12 Level 31

\(cosec^{-1}\left(\frac{2}{\sqrt{3}}\right)\) का मुख्य मान क्या है?

What is the principal value of \(cosec^{-1}\left(\frac{2}{\sqrt{3}}\right)\)?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

\(\csc y=\frac{2}{\sqrt{3}}\) से \(\sin y=\frac{\sqrt{3}}{2}\), इसलिए \(y=\frac{\pi}{3}\) है। \(\csc^{-1}\) को \(\sin^{-1}\) से जोड़कर हल करें। / From \(\csc y=\frac{2}{\sqrt{3}}\), \(\sin y=\frac{\sqrt{3}}{2}\), so \(y=\frac{\pi}{3}\). Solve \(\csc^{-1}\) by relating it to \(\sin^{-1}\).

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Question 52/69 Medium Mathematics Inverse Trigonometric Functions Principal value branch Class 12 Level 32

\(\sin^{-1}\left(\frac{1}{2}\right)\) का मुख्य मान क्या है?

What is the principal value of \(\sin^{-1}\left(\frac{1}{2}\right)\)?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

\(\sin\frac{\pi}{6}=\frac{1}{2}\) और \(\frac{\pi}{6}\) मुख्य परिसर में है। मुख्य मान हमेशा range में चुनें। / \(\sin\frac{\pi}{6}=\frac{1}{2}\) and \(\frac{\pi}{6}\) lies in the principal range. Always choose the value inside the principal range.

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Question 53/69 Medium Mathematics Inverse Trigonometric Functions Principal value branch Class 12 Level 32

\(\sin^{-1}(\sin\theta)=\theta\) कब निश्चित रूप से सत्य है?

When is \(\sin^{-1}(\sin\theta)=\theta\) definitely true?

Explanation opens after your attempt
Correct Answer

B. \(\theta\in[-\frac{\pi}{2},\frac{\pi}{2}]\)

Explanation

Simple Explanation

\(\sin^{-1}x\) का आउटपुट \([-\frac{\pi}{2},\frac{\pi}{2}]\) में होता है। इसलिए \(\theta\) इसी range में होना चाहिए। / The output of \(\sin^{-1}x\) lies in \([-\frac{\pi}{2},\frac{\pi}{2}]\). Therefore \(\theta\) must lie in this range.

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Question 54/69 Medium Mathematics Inverse Trigonometric Functions Principal value branch Class 12 Level 32

\(\cos^{-1}(\cos\theta)=\theta\) कब निश्चित रूप से सत्य है?

When is \(\cos^{-1}(\cos\theta)=\theta\) definitely true?

Explanation opens after your attempt
Correct Answer

A. \(\theta\in[0,\pi]\)

Explanation

Simple Explanation

\(\cos^{-1}x\) का principal output \([0,\pi]\) में होता है। equality के लिए \(\theta\) को उसी interval में लें। / The principal output of \(\cos^{-1}x\) lies in \([0,\pi]\). For equality, take \(\theta\) in that interval.

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Question 55/69 Medium Mathematics Inverse Trigonometric Functions Principal value branch Class 12 Level 32

\(\tan^{-1}(\tan\theta)=\theta\) कब निश्चित रूप से सत्य है?

When is \(\tan^{-1}(\tan\theta)=\theta\) definitely true?

Explanation opens after your attempt
Correct Answer

B. \(\theta\in(-\frac{\pi}{2},\frac{\pi}{2})\)

Explanation

Simple Explanation

\(\tan^{-1}x\) का principal range \((-\frac{\pi}{2},\frac{\pi}{2})\) है। \(\tan\) period वाला है, इसलिए principal interval जरूरी है। / The principal range of \(\tan^{-1}x\) is (\(-\frac{\pi}{2},\frac{\pi}{2}\)). Since \(\tan\) is periodic, the principal interval is necessary.

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Question 56/69 Medium Mathematics Inverse Trigonometric Functions Principal value branch Class 12 Level 32

\(cosec^{-1}2\) का मुख्य मान क्या है?

What is the principal value of \(cosec^{-1}2\)?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

\(cosec\frac{\pi}{6}=2\), इसलिए मुख्य मान \(\frac{\pi}{6}\) है। \(cosec^{-1}x\) को \(\sin^{-1}\frac{1}{x}\) से जोड़कर सोचें। / \(cosec\frac{\pi}{6}=2\), so the principal value is \(\frac{\pi}{6}\). Think of \(cosec^{-1}x\) through \(\sin^{-1}\frac{1}{x}\).

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Question 57/69 Medium Mathematics Inverse Trigonometric Functions Principal value branch Class 12 Level 32

\(\cos^{-1}\left(\cos\frac{4\pi}{3}\right)\) का मुख्य मान क्या है?

What is the principal value of \(\cos^{-1}\left(\cos\frac{4\pi}{3}\right)\)?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

\(\cos\frac{4\pi}{3}=-\frac{1}{2}\), इसलिए \(\cos^{-1}\left(-\frac{1}{2}\right)=\frac{2\pi}{3})। (\cos^{-1}x\) का उत्तर \([0,\pi]\) में दें। / \(\cos\frac{4\pi}{3}=-\frac{1}{2}\), so \(\cos^{-1}\left(-\frac{1}{2}\right)=\frac{2\pi}{3}\). Give the answer of \(\cos^{-1}x) in ([0,\pi]\).

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Question 58/69 Medium Mathematics Inverse Trigonometric Functions Principal value branch Class 12 Level 32

यदि \(\tan^{-1}x=-\frac{\pi}{3}\), तो \(x\) का मान क्या है?

If \(\tan^{-1}x=-\frac{\pi}{3}\), what is the value of \(x\)?

Explanation opens after your attempt
Correct Answer

A. -\(\sqrt{3}\)

Explanation

Simple Explanation

\(\tan^{-1}x=-\frac{\pi}{3}\) का अर्थ है \(x=\tan\left(-\frac{\pi}{3}\right)\)। इसलिए \(x=-\sqrt{3}\)। / \(\tan^{-1}x=-\frac{\pi}{3}\) means \(x=\tan\left(-\frac{\pi}{3}\right)\). Hence \(x=-\sqrt{3}\).

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Question 59/69 Medium Mathematics Inverse Trigonometric Functions Principal value branch Class 12 Level 32

\(\sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)\) का मुख्य मान क्या है?

What is the principal value of \(\sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)\)?

Explanation opens after your attempt
Correct Answer

A. -\(\frac{\pi}{3}\)

Explanation

Simple Explanation

\(\sin\left(-\frac{\pi}{3}\right)=-\frac{\sqrt{3}}{2}\) और यह principal range में है। \(\sin^{-1}x\) के लिए answer \([-\frac{\pi}{2},\frac{\pi}{2}]\) में रखें। / \(\sin\left(-\frac{\pi}{3}\right)=-\frac{\sqrt{3}}{2}\) and it lies in the principal range. Keep the answer of \(\sin^{-1}x) in ([-\frac{\pi}{2},\frac{\pi}{2}]\).

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Question 60/69 Medium Mathematics Inverse Trigonometric Functions Principal value branch Class 12 Level 32

\(\cos^{-1}(0)\) का मुख्य मान क्या है?

What is the principal value of \(\cos^{-1}(0)\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{\pi}{2}\)

Explanation

Simple Explanation

\(\cos\frac{\pi}{2}=0\) और \(\frac{\pi}{2}\in[0,\pi]\)। special values को principal range के साथ याद करें। / \(\cos\frac{\pi}{2}=0\) and \(\frac{\pi}{2}\in[0,\pi]\). Remember special values along with the principal range.

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