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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 291/350 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 292/350 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 293/350 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 294/350 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 \(\sin \theta-\cos \theta\)?

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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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Question 295/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(3\sin \theta+4\cos \theta\) का अधिकतम मान (M) है, तो (M) क्या है?

If the maximum value of \(3\sin \theta+4\cos \theta\) is (M), what is (M)?

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Correct Answer

A. (5)

Explanation

Simple Explanation

\(a\sin \theta+b\cos \theta\) का अधिकतम \(\sqrt{a^2+b^2}\) होता है, इसलिए (M=5)। परीक्षा में coefficients का square जोड़ें। / The maximum of \(a\sin \theta+b\cos \theta\) is \( \sqrt{a^2+b^2}\), so (M=5). In exams add the squares of coefficients.

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Question 296/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(5\cos \theta-12\sin \theta\) का न्यूनतम मान (m) है, तो (m) क्या है?

If the minimum value of \(5\cos \theta-12\sin \theta\) is (m), what is (m)?

Explanation opens after your attempt
Correct Answer

B. (-13)

Explanation

Simple Explanation

Amplitude (\sqrt{52+(-12)2}=13) है, इसलिए न्यूनतम (-13) होगा। परीक्षा में maximum positive और minimum negative amplitude होता है। / The amplitude is ( \sqrt{52+(-12)2}=13), so the minimum is (-13). In exams maximum is positive amplitude and minimum is negative amplitude.

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Question 297/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\theta\) तृतीय चतुर्थांश में है, तो \(\sin \theta\) और \(\cos \theta\) के चिन्ह कैसे होंगे?

If \(\theta\) is in the third quadrant, what are the signs of \(\sin \theta\) and \(\cos \theta\)?

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Correct Answer

B. \(\sin \theta\) ऋणात्मक और \(\cos \theta\) ऋणात्मक\(\sin \theta\) negative and \(\cos \theta\) negative

Explanation

Simple Explanation

तृतीय चतुर्थांश में sine और cosine दोनों ऋणात्मक होते हैं। परीक्षा में ASTC नियम से signs जल्दी तय करें। / In the third quadrant, both sine and cosine are negative. In exams use the ASTC rule to decide signs quickly.

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Question 298/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

\(\sin 3\theta\) का मूल period क्या है?

What is the fundamental period of \(\sin 3\theta\)?

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Correct Answer

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

Explanation

Simple Explanation

\(\sin k\theta\) का period \(\frac{2\pi}{k}\) होता है, इसलिए यहां \(\frac{2\pi}{3}\) मिलेगा। परीक्षा में coefficient को period formula में लगाएं। / The period of \( \sin k\theta\) is \( \frac{2\pi}{k}\), so here it is \( \frac{2\pi}{3}\). In exams use the coefficient in the period formula.

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Question 299/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

यदि \(\cos \theta=-1\), तो \(\theta\) का सामान्य हल क्या है?

If \(\cos \theta=-1\), what is the general solution for \(\theta\)?

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Correct Answer

B. (\theta=(2n+1)\pi)

Explanation

Simple Explanation

\(\cos \theta=-1\) विषम गुणजों of \(\pi\) पर होता है। परीक्षा में \(\cos \theta=1\) और \(\cos \theta=-1\) के हल अलग पहचानें। / \( \cos \theta=-1\) occurs at odd multiples of \( \pi\). In exams distinguish the solutions of \( \cos \theta=1\) and \( \cos \theta=-1\).

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Question 300/350 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 72

(\cos\(4\theta\)) का मूल period क्या है?

What is the fundamental period of (\cos\(4\theta\))?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

\(\cos k\theta\) का मूल period \(\frac{2\pi}{k}\) होता है, इसलिए यहां \(\frac{\pi}{2}\) मिलेगा। परीक्षा में coefficient को denominator में रखें। / The fundamental period of \( \cos k\theta\) is \( \frac{2\pi}{k}\), so here it is \( \frac{\pi}{2}\). In exams put the coefficient in the denominator.

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