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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 141/346 Easy Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\cos x=\frac{12}{13}\) और (x) प्रथम चतुर्थांश में है, तो \(\sin x\) का मान क्या है?

If \(\cos x=\frac{12}{13}\) and (x) is in the first quadrant, what is the value of \(\sin x\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{5}{13}\)

Explanation

Simple Explanation

\(\sin^2 x=1-\cos^2 x\) से \(\sin x=\frac{5}{13}\) मिलता है। प्रथम चतुर्थांश में मान धनात्मक लिया जाता है। / From \(\sin^2 x=1-\cos^2 x\), \(\sin x=\frac{5}{13}\). In the first quadrant, the positive value is taken.

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Question 142/346 Easy Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\tan x=\frac{7}{24}\) और (x) प्रथम चतुर्थांश में है, तो \(\sec x\) का मान क्या है?

If \(\tan x=\frac{7}{24}\) and (x) is in the first quadrant, what is the value of \(\sec x\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{25}{24}\)

Explanation

Simple Explanation

\(\sec^2 x=1+\tan^2 x\) लगाने पर \(\sec x=\frac{25}{24}\) मिलता है। प्रथम चतुर्थांश में \(\sec x\) धनात्मक होता है। / Using \(\sec^2 x=1+\tan^2 x\), \(\sec x=\frac{25}{24}\). In the first quadrant, \(\sec x\) is positive.

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Question 143/346 Easy Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\cot x=\frac{8}{15}\) और (x) प्रथम चतुर्थांश में है, तो \(\cosec x\) का मान क्या है?

If \(\cot x=\frac{8}{15}\) and (x) is in the first quadrant, what is the value of \(\cosec x\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{17}{15}\)

Explanation

Simple Explanation

\(\cosec^2 x=1+\cot^2 x\) से \(\cosec x=\frac{17}{15}\) मिलता है। प्रथम चतुर्थांश में धनात्मक मान लें। / From \(\cosec^2 x=1+\cot^2 x\), \(\cosec x=\frac{17}{15}\). Take the positive value in the first quadrant.

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Question 144/346 Easy Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

(\sin\(\pi+x\)) किसके बराबर है?

What is (\sin\(\pi+x\)) equal to?

Explanation opens after your attempt
Correct Answer

C. \(-\sin x\)

Explanation

Simple Explanation

\(\pi+x\) तीसरे चतुर्थांश में आता है और वहाँ \(\sin x\) ऋणात्मक होता है। इसलिए (\sin\(\pi+x\)=-\sin x)। / \(\pi+x\) lies in the third quadrant and \(\sin x\) is negative there. Hence (\sin\(\pi+x\)=-\sin x).

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Question 145/346 Easy Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

(\cos\(\pi+x\)) किसके बराबर है?

What is (\cos\(\pi+x\)) equal to?

Explanation opens after your attempt
Correct Answer

B. \(-\cos x\)

Explanation

Simple Explanation

\(\pi+x\) तीसरे चतुर्थांश में है और वहाँ \(\cos x\) ऋणात्मक होता है। इसलिए (\cos\(\pi+x\)=-\cos x)। / \(\pi+x\) is in the third quadrant and \(\cos x\) is negative there. Therefore, (\cos\(\pi+x\)=-\cos x).

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Question 146/346 Easy Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

निम्न में से कौन-सी पहचान सही है?

Which of the following identities is correct?

Explanation opens after your attempt
Correct Answer

D. \(1+\tan^2 x=\sec^2 x\)

Explanation

Simple Explanation

सही पहचान \(1+\tan^2 x=\sec^2 x\) है। पहचान आधारित प्रश्नों में चिन्ह और भिन्न को सावधानी से देखें। / The correct identity is \(1+\tan^2 x=\sec^2 x\). In identity-based questions, check signs and fractions carefully.

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Question 147/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\sin x+\cos x=\sqrt{2}\), तो \(\sin x\cos x\) का मान क्या होगा?

If \(\sin x+\cos x=\sqrt{2}\), what is the value of \(\sin x\cos x\)?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

दोनों पक्षों का वर्ग करने पर \(1+2\sin x\cos x=2\) मिलता है। इसलिए \(\sin x\cos x=\frac{1}{2}\); ऐसे प्रश्नों में वर्ग करना उपयोगी है। / Squaring both sides gives \(1+2\sin x\cos x=2\). Hence \(\sin x\cos x=\frac{1}{2}\); squaring is useful in such questions.

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Question 148/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\tan x=2\), तो \(\frac{\sin x}{\cos x}\) का मान क्या है?

If \(\tan x=2\), what is the value of \(\frac{\sin x}{\cos x}\)?

Explanation opens after your attempt
Correct Answer

A. (2)

Explanation

Simple Explanation

\(\tan x=\frac{\sin x}{\cos x}\) होता है। इसलिए दिया गया मान सीधे (2) है। / \(\tan x=\frac{\sin x}{\cos x}\). Therefore, the required value is directly (2).

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Question 149/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\sec x=5\), तो \(\cos x\) का मान क्या है?

If \(\sec x=5\), what is the value of \(\cos x\)?

Explanation opens after your attempt
Correct Answer

C. \(\frac{1}{5}\)

Explanation

Simple Explanation

\(\sec x=\frac{1}{\cos x}\) होता है। इसलिए \(\cos x=\frac{1}{5}\); व्युत्क्रम संबंध याद रखें। / \(\sec x=\frac{1}{\cos x}\). Hence \(\cos x=\frac{1}{5}\); remember reciprocal relations.

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Question 150/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\cosec x=4\), तो \(\sin x\) का मान क्या है?

If \(\cosec x=4\), what is the value of \(\sin x\)?

Explanation opens after your attempt
Correct Answer

D. \(\frac{1}{4}\)

Explanation

Simple Explanation

\(\cosec x=\frac{1}{\sin x}\) होता है। इसलिए \(\sin x=\frac{1}{4}\); हर व्युत्क्रम फलन को जोड़ी में याद करें। / \(\cosec x=\frac{1}{\sin x}\). Hence \(\sin x=\frac{1}{4}\); learn each reciprocal function as a pair.

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