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

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Trigonometric functions and their properties Practice Questions

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Question 281/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

\(\sin \theta \cdot \cosec \theta\) का मान क्या है, जब दोनों परिभाषित हों?

What is the value of \(\sin \theta \cdot \cosec \theta\), when both are defined?

Explanation opens after your attempt
Correct Answer

B. (1)

Explanation

Simple Explanation

\(\cosec \theta=\frac{1}{\sin \theta}\) इसलिए गुणनफल (1) है। परीक्षा में defined condition को नजरअंदाज न करें। / \( \cosec \theta=\frac{1}{\sin \theta}\), so the product is (1). In exams do not ignore the defined condition.

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Question 282/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

\(\cos \theta \cdot \sec \theta\) का मान क्या है, जब दोनों परिभाषित हों?

What is the value of \(\cos \theta \cdot \sec \theta\), when both are defined?

Explanation opens after your attempt
Correct Answer

B. (1)

Explanation

Simple Explanation

\(\sec \theta=\frac{1}{\cos \theta}\) होने से गुणनफल (1) बनता है। परीक्षा में reciprocal pair तुरंत पहचानें। / Since \( \sec \theta=\frac{1}{\cos \theta}\), the product becomes (1). In exams identify reciprocal pairs quickly.

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Question 283/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

\(\tan \theta \cdot \cot \theta\) का मान क्या है, जब दोनों परिभाषित हों?

What is the value of \(\tan \theta \cdot \cot \theta\), when both are defined?

Explanation opens after your attempt
Correct Answer

C. (1)

Explanation

Simple Explanation

\(\cot \theta=\frac{1}{\tan \theta}\), इसलिए गुणनफल (1) है। परीक्षा में reciprocal formulas से समय बचता है। / \( \cot \theta=\frac{1}{\tan \theta}\), so the product is (1). In exams reciprocal formulas save time.

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Question 284/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि (\sin \theta+\sin\(-\theta\)=p), तो (p) का मान क्या है?

If (\sin \theta+\sin\(-\theta\)=p), what is the value of (p)?

Explanation opens after your attempt
Correct Answer

B. (0)

Explanation

Simple Explanation

(\sin\(-\theta\)=-\sin \theta), इसलिए दोनों पद कट जाते हैं। परीक्षा में odd function property से ऐसे प्रश्न जल्दी हल होते हैं। / ( \sin\(-\theta\)=-\sin \theta), so both terms cancel. In exams odd function property solves such questions quickly.

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Question 285/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि (\cos \theta-\cos\(-\theta\)=q), तो (q) का मान क्या है?

If (\cos \theta-\cos\(-\theta\)=q), what is the value of (q)?

Explanation opens after your attempt
Correct Answer

A. (0)

Explanation

Simple Explanation

(\cos\(-\theta\)=\cos \theta), इसलिए अंतर (0) है। परीक्षा में even function property ध्यान रखें। / ( \cos\(-\theta\)=\cos \theta), so the difference is (0). In exams keep the even function property in mind.

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Question 286/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि (\tan \theta+\tan\(\pi-\theta\)=r), तो (r) का मान क्या है?

If (\tan \theta+\tan\(\pi-\theta\)=r), what is the value of (r)?

Explanation opens after your attempt
Correct Answer

C. (0)

Explanation

Simple Explanation

(\tan\(\pi-\theta\)=-\tan \theta), इसलिए योग (0) होता है। परीक्षा में allied angle sign से उत्तर तुरंत मिलता है। / ( \tan\(\pi-\theta\)=-\tan \theta), so the sum is (0). In exams allied angle sign gives the answer quickly.

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Question 287/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

\(\sin^2 \theta-\cos^2 \theta\) किसके बराबर है?

What is \(\sin^2 \theta-\cos^2 \theta\) equal to?

Explanation opens after your attempt
Correct Answer

B. \(-\cos 2\theta\)

Explanation

Simple Explanation

क्योंकि \(\cos 2\theta=\cos^2 \theta-\sin^2 \theta\), इसलिए दिया गया रूप \(-\cos 2\theta\) है। परीक्षा में double angle identities को उल्टा भी पढ़ें। / Because \( \cos 2\theta=\cos^2 \theta-\sin^2 \theta\), the given form is \(-\cos 2\theta\). In exams read double angle identities in reverse too.

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Question 288/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\sin \theta+\cos \theta=\sqrt{2}\) और \(0<\theta<\frac{\pi}{2}\), तो \(\theta\) का मान क्या है?

If \(\sin \theta+\cos \theta=\sqrt{2}\) and \(0<\theta<\frac{\pi}{2}\), what is the value of \(\theta\)?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

प्रथम चतुर्थांश में \(\sin \theta+\cos \theta\) का अधिकतम \(\sqrt{2}\) \(\theta=\frac{\pi}{4}\) पर होता है। परीक्षा में symmetry का उपयोग करें। / In the first quadrant, the maximum of \( \sin \theta+\cos \theta\) is \( \sqrt{2}\) at \( \theta=\frac{\pi}{4}\). In exams use symmetry.

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Question 289/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

\(\sin \theta+\cos \theta\) का अधिकतम मान क्या है?

What is the maximum value of \(\sin \theta+\cos \theta\)?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{2}\)

Explanation

Simple Explanation

(\sin \theta+\cos \theta=\sqrt{2}\sin\left\(\theta+\frac{\pi}{4}\right\)), इसलिए अधिकतम \(\sqrt{2}\) है। परीक्षा में \(a\sin x+b\cos x\) का maximum \(\sqrt{a^2+b^2}\) लें। / ( \sin \theta+\cos \theta=\sqrt{2}\sin\left\(\theta+\frac{\pi}{4}\right\)), so the maximum is \( \sqrt{2}\). In exams use maximum of \(a\sin x+b\cos x\) as \( \sqrt{a^2+b^2}\).

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Question 290/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

\(\sin \theta-\cos \theta\) का न्यूनतम मान क्या है?

What is the minimum value of \(\sin \theta-\cos \theta\)?

Explanation opens after your attempt
Correct Answer

A. \(-\sqrt{2}\)

Explanation

Simple Explanation

\(\sin \theta-\cos \theta\) का amplitude (\sqrt{12+(-1)2}=\sqrt{2}) है। परीक्षा में minimum हमेशा negative amplitude होगा। / The amplitude of \( \sin \theta-\cos \theta\) is ( \sqrt{12+(-1)2}=\sqrt{2}). In exams the minimum is the negative amplitude.

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