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Mathematics Trigonometric functions and their properties MCQ Questions for Class 11

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Trigonometric functions and their properties Practice Questions

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Question 281/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\tan \theta=\frac{4}{3}\) और \(\theta\) प्रथम चतुर्थांश में है, तो \(\sin \theta\) का मान क्या है?

If \(\tan \theta=\frac{4}{3}\) and \(\theta\) is in the first quadrant, what is \(\sin \theta\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{4}{5}\)

Explanation

Simple Explanation

\(\tan \theta=\frac{4}{3}\) में opposite (4), adjacent (3), hypotenuse (5) होगा। परीक्षा में Pythagorean triplet पहचानें। / In \( \tan \theta=\frac{4}{3}\), opposite is (4), adjacent is (3), and hypotenuse is (5). In exams identify Pythagorean triplets.

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Question 282/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\cot \theta=\frac{12}{5}\) और \(\theta\) प्रथम चतुर्थांश में है, तो \(\cos \theta\) का मान क्या है?

If \(\cot \theta=\frac{12}{5}\) and \(\theta\) is in the first quadrant, what is \(\cos \theta\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{12}{13}\)

Explanation

Simple Explanation

\(\cot \theta=\frac{12}{5}\) में adjacent (12), opposite (5), hypotenuse (13) है। \(परीक्षा में (\cos \theta=\frac{\)adjacent}{hypotenuse}) लगाएं। \(/ In ( \cot \theta=\frac{12}{5}), adjacent is (12), opposite is (5), and hypotenuse is (13). In exams use ( \cos \theta=\frac{\)adjacent}{hypotenuse}).

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Question 283/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\sec \theta=2\) और \(\theta\) प्रथम चतुर्थांश में है, तो \(\cos \theta\) का मान क्या है?

If \(\sec \theta=2\) and \(\theta\) is in the first quadrant, what is \(\cos \theta\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{1}{2}\)

Explanation

Simple Explanation

\(\sec \theta=\frac{1}{\cos \theta}\), इसलिए \(\cos \theta=\frac{1}{2}\) है। परीक्षा में reciprocal relations याद रखें। / \( \sec \theta=\frac{1}{\cos \theta}\), so \( \cos \theta=\frac{1}{2}\). In exams remember reciprocal relations.

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Question 284/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\cosec \theta=\frac{5}{2}\) और \(\theta\) प्रथम चतुर्थांश में है, तो \(\sin \theta\) का मान क्या है?

If \(\cosec \theta=\frac{5}{2}\) and \(\theta\) is in the first quadrant, what is \(\sin \theta\)?

Explanation opens after your attempt
Correct Answer

C. \(\frac{2}{5}\)

Explanation

Simple Explanation

\(\cosec \theta=\frac{1}{\sin \theta}\), इसलिए \(\sin \theta=\frac{2}{5}\) है। परीक्षा में cosecant और sine reciprocal हैं। / \( \cosec \theta=\frac{1}{\sin \theta}\), so \( \sin \theta=\frac{2}{5}\). In exams remember cosecant and sine are reciprocals.

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Question 285/350 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 286/350 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 287/350 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 288/350 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 289/350 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 290/350 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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