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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 201/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

यदि \(\cosec x+\cot x=6\), तो \(\cosec x-\cot x\) का मान क्या है?

If \(\cosec x+\cot x=6\), what is the value of \(\cosec x-\cot x\)?

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Correct Answer

A. \(\frac{1}{6}\)

Explanation

Simple Explanation

(\(\cosec x+\cot x\)\(\cosec x-\cot x\)=1) होता है। इसलिए आवश्यक मान \(\frac{1}{6}\) है। / The identity is (\(\cosec x+\cot x\)\(\cosec x-\cot x\)=1). Therefore, the required value is \(\frac{1}{6}\).

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Question 202/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

\(\frac{\sin x}{1-\cos x}\) किसके बराबर है?

What is \(\frac{\sin x}{1-\cos x}\) equal to?

Explanation opens after your attempt
Correct Answer

B. \(\cot \frac{x}{2}\)

Explanation

Simple Explanation

अर्ध-कोण पहचान से \(\frac{\sin x}{1-\cos x}=\cot \frac{x}{2}\) होता है। ऐसे रूपों में हर देखकर पहचान करें। / By the half-angle identity, \(\frac{\sin x}{1-\cos x}=\cot \frac{x}{2}\). In such forms, identify the denominator carefully.

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Question 203/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

\(\frac{1+\cos x}{\sin x}\) किसके बराबर है?

What is \(\frac{1+\cos x}{\sin x}\) equal to?

Explanation opens after your attempt
Correct Answer

C. \(\cot \frac{x}{2}\)

Explanation

Simple Explanation

मानक अर्ध-कोण रूप \(\cot \frac{x}{2}=\frac{1+\cos x}{\sin x}\) है। \(\tan \frac{x}{2}\) और \(\cot \frac{x}{2}\) के रूप अलग रखें। / The standard half-angle form is \(\cot \frac{x}{2}=\frac{1+\cos x}{\sin x}\). Keep the forms of \(\tan \frac{x}{2}\) and \(\cot \frac{x}{2}\) separate.

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Question 204/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

फलन \(4-3\sin x\) का अधिकतम मान क्या है?

What is the maximum value of the function \(4-3\sin x\)?

Explanation opens after your attempt
Correct Answer

C. (7)

Explanation

Simple Explanation

\(\sin x\) का न्यूनतम मान (-1) है। इसलिए अधिकतम मान (4-3(-1)=7) होगा। / The minimum value of \(\sin x\) is (-1). Hence the maximum value is (4-3(-1)=7).

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Question 205/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

फलन \(2+5\cos x\) का न्यूनतम मान क्या है?

What is the minimum value of the function \(2+5\cos x\)?

Explanation opens after your attempt
Correct Answer

A. -(3)

Explanation

Simple Explanation

\(\cos x\) का न्यूनतम मान (-1) होता है। इसलिए न्यूनतम मान (2+5(-1)=-3) है। / The minimum value of \(\cos x\) is (-1). Therefore, the minimum value is (2+5(-1)=-3).

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Question 206/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

फलन \(3\sin 2x-1\) का परिसर क्या है?

What is the range of the function \(3\sin 2x-1\)?

Explanation opens after your attempt
Correct Answer

B. ([-4,2])

Explanation

Simple Explanation

\(\sin 2x\) का परिसर ([-1,1]) है। (3) से गुणा और (-1) जोड़ने पर परिसर ([-4,2]) मिलता है। / The range of \(\sin 2x\) is ([-1,1]). Multiplying by (3) and adding (-1) gives ([-4,2]).

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Question 207/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

फलन \(2\cos 3x+4\) का काल क्या है?

What is the period of the function \(2\cos 3x+4\)?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

ऊर्ध्व बदलाव और आयाम काल नहीं बदलते। \(\cos 3x\) का काल \(\frac{2\pi}{3}\) है। / Vertical shift and amplitude do not change the period. The period of \(\cos 3x\) is \(\frac{2\pi}{3}\).

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Question 208/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

फलन (\tan(2x)) का मूल काल क्या है?

What is the fundamental period of the function (\tan(2x))?

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Correct Answer

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

Explanation

Simple Explanation

\(\tan kx\) का काल \(\frac{\pi}{k}\) होता है। यहाँ (k=2), इसलिए मूल काल \(\frac{\pi}{2}\) है। / The period of \(\tan kx\) is \(\frac{\pi}{k}\). Here (k=2), so the fundamental period is \(\frac{\pi}{2}\).

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Question 209/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

यदि (x) दूसरे चतुर्थांश में है और \(\cos x=-\frac{3}{5}\), तो \(\tan x\) का मान क्या है?

If (x) is in the second quadrant and \(\cos x=-\frac{3}{5}\), what is the value of \(\tan x\)?

Explanation opens after your attempt
Correct Answer

B. -\(\frac{4}{3}\)

Explanation

Simple Explanation

दूसरे चतुर्थांश में \(\sin x\) धनात्मक और \(\cos x\) ऋणात्मक होता है। \(\sin x=\frac{4}{5}\), इसलिए \(\tan x=-\frac{4}{3}\) है। / In the second quadrant, \(\sin x\) is positive and \(\cos x\) is negative. Since \(\sin x=\frac{4}{5}\), \(\tan x=-\frac{4}{3}\).

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Question 210/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 71

यदि (x) तीसरे चतुर्थांश में है और \(\sin x=-\frac{5}{13}\), तो \(\sec x\) का मान क्या है?

If (x) is in the third quadrant and \(\sin x=-\frac{5}{13}\), what is the value of \(\sec x\)?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

तीसरे चतुर्थांश में \(\cos x\) ऋणात्मक होता है। \(\cos x=-\frac{12}{13}\), इसलिए \(\sec x=-\frac{13}{12}\) है। / In the third quadrant, \(\cos x\) is negative. Since \(\cos x=-\frac{12}{13}\), \(\sec x=-\frac{13}{12}\).

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