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Mathematics Domain, range, and graphs of trigonometric functions MCQ Questions for Class 11 Science

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Question 1/3 Hard Mathematics Trigonometric Functions Domain, range, and graphs of trigonometric functions Class 11 Level 36

फलन �\(y=2\sin x\u0000\) का आयाम क्या है?

What is the amplitude of the function �\(y=2\sin x\u0000\)?

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Correct Answer

A. 2

Explanation

Simple Explanation

सामान्य रूप �\(y=a\sin x\u0000\) में आयाम �\(|a|\u0000\) होता है। यहाँ �\(a=2\u0000\) है, इसलिए आयाम �2� है। विकल्प B में �1� केवल �\(\sin x\u0000\) का आयाम है, जबकि उसके आगे का गुणांक 2 है। परीक्षा-युक्ति: �\(a\sin x�\) या �\(a\cos x�\) में आयाम हमेशा �|a|� लें। / For a function of the form �\(y=a\sin x�\), the amplitude is �|a|�. Here �(a=2�), so the amplitude is �2�. Option B is the amplitude of �\(\sin x�\) alone, not of �2\sin x�. Exam tip: for �\(a\sin x�\) or �\(a\cos x�\), the amplitude is always �|a|�.

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Question 2/3 Hard Mathematics Trigonometric Functions Domain, range, and graphs of trigonometric functions Class 11 Level 36

फलन \(y=-\cos x\) के ग्राफ पर \(x=0\) के लिए \(y\) का मान क्या होगा?

For the graph of the function \(y=-\cos x\), what is the value of \(y\) when \(x=0\)?

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Correct Answer

A. -1

Explanation

Simple Explanation

\(x=0\) रखने पर \(y=-\cos 0=-1\), क्योंकि \(\cos 0=1\)। विकल्प B में ऋण चिह्न छूट गया है; वह \(\cos 0\) का मान है, \(-\cos 0\) का नहीं। परीक्षा में पहले विशेष कोण का मान रखें और फिर फलन का बाहरी ऋण चिह्न लागू करें। / Substituting \(x=0\) gives \(y=-\cos 0=-1\), since \(\cos 0=1\). Option B omits the negative sign and gives the value of \(\cos 0\), not \(-\cos 0\). Exam tip: evaluate the standard trigonometric value first, then apply any sign outside the function.

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Question 3/3 Expert Mathematics Trigonometric Functions Domain, range, and graphs of trigonometric functions Class 11 Level 33

फलन \(f(x)=\cos x\) का परिसर (range) क्या है, जब \(x\in[0,\pi]\)?

What is the range of the function \(f(x)=\cos x\) when \(x\in[0,\pi]\)?

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Correct Answer

A. \([-1,1]\)

Explanation

Simple Explanation

अंतराल \([0,\pi]\) में \(\cos x\) लगातार घटता है: \(\cos 0=1\) और \(\cos\pi=-1\)। इसलिए इस अंतराल में \(\cos x\) के सभी मान \(-1\) से \(1\) के बीच आते हैं और दोनों सिरों के मान शामिल हैं; अतः परिसर \([-1,1]\) है। परीक्षा में \([0,\pi]\) पर cosine का मान-परास याद रखें: \([-1,1]\)। / On the interval \([0,\pi]\), \(\cos x\) decreases continuously from \(\cos 0=1\) to \(\cos\pi=-1\). Since both endpoints are included, every value from \(-1\) to \(1\) is attained, so the range is \([-1,1]\). Exam tip: for cosine over \([0,\pi]\), check the endpoint values first; they give the complete range.

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