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Mathematics Trigonometric functions and their properties MCQ Questions for Class 11 General

Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.

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Trigonometric functions and their properties Practice Questions

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Question 261/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

(\tan\(\pi+\theta\)) का मान क्या है?

What is the value of (\tan\(\pi+\theta\))?

Explanation opens after your attempt
Correct Answer

B. \(\tan \theta\)

Explanation

Simple Explanation

\(\tan \theta\) का period \(\pi\) है इसलिए (\tan\(\pi+\theta\)=\tan \theta)। परीक्षा में tangent की periodicity याद रखें। / The period of \( \tan \theta\) is \( \pi\), so ( \tan\(\pi+\theta\)=\tan \theta). In exams remember the periodicity of tangent.

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Question 262/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

(\tan\(2\pi-\theta\)) का मान क्या होगा?

What is the value of (\tan\(2\pi-\theta\))?

Explanation opens after your attempt
Correct Answer

B. \(-\tan \theta\)

Explanation

Simple Explanation

\(2\pi-\theta\) चतुर्थ चतुर्थांश में है जहां tangent ऋणात्मक होता है। परीक्षा में sine और cosine के sign से tangent निकालें। / \(2\pi-\theta\) is in the fourth quadrant where tangent is negative. In exams derive tangent from sine and cosine signs.

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Question 263/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\sin \theta=0\), तो \(\theta\) का सामान्य हल क्या है?

If \(\sin \theta=0\), what is the general solution for \(\theta\)?

Explanation opens after your attempt
Correct Answer

A. \(\theta=n\pi\)

Explanation

Simple Explanation

\(\sin \theta\) शून्य (0), \(\pi\), \(2\pi\) जैसे बिंदुओं पर होता है। परीक्षा में \(n\in\mathbb{Z}\) मानकर सामान्य हल लिखें। / \( \sin \theta\) is zero at points like (0), \(\pi\), and \(2\pi\). In exams write the general solution with \(n\in\mathbb{Z}\).

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Question 264/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\cos \theta=0\), तो \(\theta\) का सामान्य हल क्या है?

If \(\cos \theta=0\), what is the general solution for \(\theta\)?

Explanation opens after your attempt
Correct Answer

B. (\theta=\frac{(2n+1)\pi}{2})

Explanation

Simple Explanation

\(\cos \theta\) शून्य odd multiples of \(\frac{\pi}{2}\) पर होता है। परीक्षा में (\frac{(2n+1)\pi}{2}) पैटर्न याद रखें। / \( \cos \theta\) is zero at odd multiples of \( \frac{\pi}{2}\). In exams remember the pattern ( \frac{(2n+1)\pi}{2}).

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Question 265/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

\(\tan \theta=0\) का सामान्य हल क्या है?

What is the general solution of \(\tan \theta=0\)?

Explanation opens after your attempt
Correct Answer

A. \(\theta=n\pi\)

Explanation

Simple Explanation

\(\tan \theta=0\) तब होता है जब \(\sin \theta=0\) और \(\cos \theta\neq0\)। परीक्षा में tangent का period \(\pi\) रखें। / \( \tan \theta=0\) occurs when \( \sin \theta=0\) and \( \cos \theta\neq0\). In exams use period \( \pi\) for tangent.

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Question 266/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\sin \theta=\sin \alpha\), तो सामान्य हल कौन सा है?

If \(\sin \theta=\sin \alpha\), which is the general solution?

Explanation opens after your attempt
Correct Answer

A. (\theta=n\pi+(-1)^n\alpha)

Explanation

Simple Explanation

\(\sin \theta=\sin \alpha\) का संयुक्त हल (\theta=n\pi+(-1)^n\alpha) होता है। परीक्षा में दो अलग हलों को एक सूत्र में लिखना सीखें। / The combined solution of \( \sin \theta=\sin \alpha\) is ( \theta=n\pi+(-1)^n\alpha). In exams learn to write two cases in one formula.

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Question 267/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\cos \theta=\cos \alpha\), तो सामान्य हल कौन सा है?

If \(\cos \theta=\cos \alpha\), which is the general solution?

Explanation opens after your attempt
Correct Answer

B. \(\theta=2n\pi\pm\alpha\)

Explanation

Simple Explanation

\(\cos \theta=\cos \alpha\) के लिए दोनों दिशाओं में कोण मिलते हैं। परीक्षा में \(\pm\alpha\) लगाना न भूलें। / For \( \cos \theta=\cos \alpha\), angles occur in both directions. In exams do not forget \( \pm\alpha\).

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Question 268/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\tan \theta=\tan \alpha\), तो सामान्य हल क्या है?

If \(\tan \theta=\tan \alpha\), what is the general solution?

Explanation opens after your attempt
Correct Answer

B. \(\theta=n\pi+\alpha\)

Explanation

Simple Explanation

\(\tan \theta\) का period \(\pi\) है इसलिए हल \(\theta=n\pi+\alpha\) होगा। परीक्षा में tangent equations में \(\pi\) period लगाएं। / The period of \( \tan \theta\) is \( \pi\), so the solution is \( \theta=n\pi+\alpha\). In exams use period \( \pi\) for tangent equations.

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Question 269/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

(\tan\left\(\frac{\pi}{2}-\theta\right\)) का मान क्या है?

What is the value of (\tan\left\(\frac{\pi}{2}-\theta\right\))?

Explanation opens after your attempt
Correct Answer

C. \(\cot \theta\)

Explanation

Simple Explanation

\(\frac{\pi}{2}-\theta\) पर tangent का co-function cotangent होता है। परीक्षा में complementary angle property याद रखें। / At \( \frac{\pi}{2}-\theta\), tangent changes to its co-function cotangent. In exams remember complementary angle property.

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Question 270/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

(\cot\left\(\frac{\pi}{2}-\theta\right\)) किसके बराबर है?

What is (\cot\left\(\frac{\pi}{2}-\theta\right\)) equal to?

Explanation opens after your attempt
Correct Answer

D. \(\tan \theta\)

Explanation

Simple Explanation

\(\frac{\pi}{2}-\theta\) पर cotangent का co-function tangent होता है। परीक्षा में reciprocal function pair याद रखें। / At \( \frac{\pi}{2}-\theta\), cotangent changes to the co-function tangent. In exams remember reciprocal function pairs.

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