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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 321/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\sin x=\sin y\), तो सामान्यतः कौन-सा संबंध सही हो सकता है?

If \(\sin x=\sin y\), which relation can generally be true?

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Correct Answer

A. \(x=2n\pi+y\) या (x=(2n+1)\pi-y)\(x=2n\pi+y\) or (x=(2n+1)\pi-y)

Explanation

Simple Explanation

\(\sin x=\sin y\) के लिए (x=n\pi+(-1)^n y) होता है। इसी से दिए गए दोनों रूप मिलते हैं। / For \(\sin x=\sin y\), (x=n\pi+(-1)^n y). This gives the two stated forms.

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Question 322/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\cos x=\cos y\), तो सामान्य हल का सही रूप क्या है?

If \(\cos x=\cos y\), what is the correct form of the general solution?

Explanation opens after your attempt
Correct Answer

B. \(x=2n\pi\pm y\)

Explanation

Simple Explanation

\(\cos x=\cos y\) के लिए कोण \(2n\pi\pm y\) के रूप में आते हैं। परीक्षा में cosine की सम प्रकृति याद रखें। / For \(\cos x=\cos y\), angles are of the form \(2n\pi\pm y\). In exams, remember the even nature of cosine.

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Question 323/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\tan x=\tan y\), तो सामान्य हल क्या है?

If \(\tan x=\tan y\), what is the general solution?

Explanation opens after your attempt
Correct Answer

C. \(x=n\pi+y\)

Explanation

Simple Explanation

\(\tan x\) का आवर्त \(\pi\) है, इसलिए \(x=n\pi+y\) होगा। परीक्षा में tangent के लिए \(n\pi\) जोड़ें। / The period of \(\tan x\) is \(\pi\), so \(x=n\pi+y\). In exams, add \(n\pi\) for tangent.

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Question 324/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

(\tan\left\(\frac{\pi}{4}+x\right\)\tan\left\(\frac{\pi}{4}-x\right\)) का मान क्या है?

What is the value of (\tan\left\(\frac{\pi}{4}+x\right\)\tan\left\(\frac{\pi}{4}-x\right\))?

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Correct Answer

D. (1)

Explanation

Simple Explanation

(\tan\left\(\frac{\pi}{4}+x\right\)) और (\tan\left\(\frac{\pi}{4}-x\right\)) के सूत्र लगाने पर गुणनफल (1) आता है। यह एक उपयोगी standard result है। / Using the formulas for (\tan\left\(\frac{\pi}{4}+x\right\)) and (\tan\left\(\frac{\pi}{4}-x\right\)), the product is (1). This is a useful standard result.

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Question 325/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

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

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

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Correct Answer

A. \( \frac{7}{25} \)

Explanation

Simple Explanation

समकोण त्रिभुज में लम्ब (7), आधार (24), कर्ण (25) होगा। इसलिए \(\sin x=\frac{7}{25}\)। / In a right triangle, perpendicular is (7), base is (24), and hypotenuse is (25). Hence \(\sin x=\frac{7}{25}\).

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Question 326/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

फलन (f(x)=\cos x+\cos 2x) का आवर्त क्या है?

What is the period of (f(x)=\cos x+\cos 2x)?

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Correct Answer

B. \(2\pi\)

Explanation

Simple Explanation

\(\cos x\) का आवर्त \(2\pi\) और \(\cos 2x\) का \(\pi\) है। इनका सामान्य मूल आवर्त \(2\pi\) है। / The period of \(\cos x\) is \(2\pi\) and that of \(\cos 2x\) is \(\pi\). Their common fundamental period is \(2\pi\).

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Question 327/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

\(\sin x\) का मान किस अंतराल में हमेशा रहता है?

In which interval does the value of \(\sin x\) always lie?

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Correct Answer

C. ( [-1,1] )

Explanation

Simple Explanation

किसी भी वास्तविक (x) के लिए \(-1\leq \sin x\leq 1\) होता है। परीक्षा में sine और cosine का basic range सबसे पहले लगाएं। / For any real (x), \(-1\leq \sin x\leq 1\). In exams, apply the basic range of sine and cosine first.

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Question 328/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

\(\tan x\) किस अंतराल में परिभाषित नहीं है?

At which values is \(\tan x\) not defined?

Explanation opens after your attempt
Correct Answer

D. \(x=\frac{\pi}{2}+n\pi\)

Explanation

Simple Explanation

\(\tan x=\frac{\sin x}{\cos x}\) है, इसलिए \(\cos x=0\) पर यह अपरिभाषित होता है। अतः \(x=\frac{\pi}{2}+n\pi\)। / Since \(\tan x=\frac{\sin x}{\cos x}\), it is undefined when \(\cos x=0\). Thus \(x=\frac{\pi}{2}+n\pi\).

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Question 329/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

\(\cosec x\) कहाँ परिभाषित नहीं है?

Where is \(\cosec x\) not defined?

Explanation opens after your attempt
Correct Answer

B. \(x=n\pi\)

Explanation

Simple Explanation

\(\cosec x=\frac{1}{\sin x}\) है, इसलिए \(\sin x=0\) पर यह अपरिभाषित होता है। अतः \(x=n\pi\)। / Since \(\cosec x=\frac{1}{\sin x}\), it is undefined when \(\sin x=0\). Thus \(x=n\pi\).

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Question 330/346 Hard Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\sin x+\cos x=\sqrt{2}\), तो \(0\leq x<2\pi\) में (x) का मान क्या है?

If \(\sin x+\cos x=\sqrt{2}\), what is (x) in \(0\leq x<2\pi\)?

Explanation opens after your attempt
Correct Answer

C. \( \frac{\pi}{4} \)

Explanation

Simple Explanation

(\sin x+\cos x=\sqrt{2}\sin\left\(x+\frac{\pi}{4}\right\)) है। अधिकतम \(\sqrt{2}\) तब मिलता है जब \(x=\frac{\pi}{4}\)। / We use (\sin x+\cos x=\sqrt{2}\sin\left\(x+\frac{\pi}{4}\right\)). The maximum \(\sqrt{2}\) occurs at \(x=\frac{\pi}{4}\).

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