Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 131-140 of 346 questions.
What is the period of the function \(\sec x\)?
C. \(2\pi\)
\(\sec x\) का काल \(\cos x\) जैसा \(2\pi\) होता है। व्युत्क्रम फलन का काल मूल फलन से जुड़ा रहता है। / The period of \(\sec x\) is \(2\pi\), like \(\cos x\). The reciprocal function keeps the related basic period.
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What is the period of the function \(\cot x\)?
A. \(\pi\)
\(\cot x\) हर \(\pi\) के बाद अपना मान दोहराता है। \(\tan x\) और \(\cot x\) दोनों का काल \(\pi\) है। / \(\cot x\) repeats its value after every \(\pi\). Both \(\tan x\) and \(\cot x\) have period \(\pi\).
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What is the period of the function \(\cosec x\)?
C. \(2\pi\)
\(\cosec x\) \(\sin x\) का व्युत्क्रम है और इसका काल \(2\pi\) है। व्युत्क्रम संबंध से काल पहचानें। / \(\cosec x\) is the reciprocal of \(\sin x\) and its period is \(2\pi\). Use reciprocal relation to identify the period.
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What is the range of \(\sec x\)?
D. (\(-\infty,-1]\cup[1,\infty\))
\(\sec x=\frac{1}{\cos x}\) है और \(\cos x\) का मान ([-1,1]) में होता है। इसलिए \(\sec x\) का मान (1) से बड़ा या (-1) से छोटा होता है। / \(\sec x=\frac{1}{\cos x}\) and \(\cos x\) lies in ([-1,1]). Hence \(\sec x\) is greater than or equal to (1) or less than or equal to (-1).
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What is the range of \(\cosec x\)?
A. (\(-\infty,-1]\cup[1,\infty\))
\(\cosec x=\frac{1}{\sin x}\) है। इसलिए इसका परिसर (\(-\infty,-1]\cup[1,\infty\)) होता है। / \(\cosec x=\frac{1}{\sin x}\). Therefore, its range is (\(-\infty,-1]\cup[1,\infty\)).
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Where is \(\tan x\) undefined?
A. \(\cos x=0\)
\(\tan x=\frac{\sin x}{\cos x}\) है, इसलिए \(\cos x=0\) पर यह अपरिभाषित होता है। हर शून्य होने पर भिन्न परिभाषित नहीं रहती। / \(\tan x=\frac{\sin x}{\cos x}\), so it is undefined when \(\cos x=0\). A fraction is not defined when the denominator is zero.
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Where is \(\cot x\) undefined?
B. \(\sin x=0\)
\(\cot x=\frac{\cos x}{\sin x}\) है, इसलिए \(\sin x=0\) पर यह अपरिभाषित होता है। हर को हमेशा ध्यान से देखें। / \(\cot x=\frac{\cos x}{\sin x}\), so it is undefined when \(\sin x=0\). Always check the denominator carefully.
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Where is \(\sec x\) undefined?
C. \(\cos x=0\)
\(\sec x=\frac{1}{\cos x}\) है, इसलिए \(\cos x=0\) पर यह अपरिभाषित होता है। व्युत्क्रम फलनों में हर शून्य नहीं हो सकता। / \(\sec x=\frac{1}{\cos x}\), so it is undefined when \(\cos x=0\). In reciprocal functions, the denominator cannot be zero.
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Where is \(\cosec x\) undefined?
B. \(\sin x=0\)
\(\cosec x=\frac{1}{\sin x}\) है, इसलिए \(\sin x=0\) पर यह अपरिभाषित होता है। व्युत्क्रम में नीचे वाला फलन शून्य नहीं होना चाहिए। / \(\cosec x=\frac{1}{\sin x}\), so it is undefined when \(\sin x=0\). In a reciprocal, the denominator function must not be zero.
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If \(\sin x=\frac{3}{5}\) and (x) is in the first quadrant, what is the value of \(\cos x\)?
C. \(\frac{4}{5}\)
\(\sin^2 x+\cos^2 x=1\) से \(\cos x=\frac{4}{5}\) मिलता है। प्रथम चतुर्थांश में \(\cos x\) धनात्मक होता है। / Using \(\sin^2 x+\cos^2 x=1\), \(\cos x=\frac{4}{5}\). In the first quadrant, \(\cos x\) is positive.
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