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 241-250 of 346 questions.
What is the period of the function (5\cos\(\frac{x}{2}\))?
C. \(4\pi\)
\(\cos kx\) का काल \(\frac{2\pi}{k}\) होता है। यहाँ \(k=\frac{1}{2}\), इसलिए काल \(4\pi\) है। / The period of \(\cos kx\) is \(\frac{2\pi}{k}\). Here \(k=\frac{1}{2}\), so the period is \(4\pi\).
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What is the fundamental period of the function \(\sin^2 x\)?
B. \(\pi\)
(\sin-2\(x+\pi\)=\sin-2 x) होता है। इसलिए \(\sin^2 x\) का मूल काल \(\pi\) है। / (\sin-2\(x+\pi\)=\sin-2 x). Hence the fundamental period of \(\sin^2 x\) is \(\pi\).
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What is the range of the function \(\cos^2 x\)?
C. ([0,1])
\(\cos x\) का मान ([-1,1]) में होता है। वर्ग करने पर परिसर ([0,1]) बनता है। / The value of \(\cos x\) lies in ([-1,1]). Squaring gives the range ([0,1]).
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If \(\sec x-\tan x=\frac{2}{5}\), what is the value of \(\tan x\)?
A. \(\frac{21}{20}\)
क्योंकि (\(\sec x-\tan x\)\(\sec x+\tan x\)=1), इसलिए \(\sec x+\tan x=\frac{5}{2}\)। दोनों समीकरण घटाने पर \(\tan x=\frac{21}{20}\) मिलता है। / Since (\(\sec x-\tan x\)\(\sec x+\tan x\)=1), \(\sec x+\tan x=\frac{5}{2}\). Subtracting the two equations gives \(\tan x=\frac{21}{20}\).
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What is the simplified value of \(\frac{\sin x-\sin^3 x}{\cos^2 x}\)?
C. \(\sin x\)
अंश को (\sin x\(1-\sin^2 x\)) लिखें। क्योंकि \(1-\sin^2 x=\cos^2 x\), इसलिए मान \(\sin x\) है। / Write the numerator as (\sin x\(1-\sin^2 x\)). Since \(1-\sin^2 x=\cos^2 x\), the value is \(\sin x\).
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What is the range of the function \(2-4\cos^2 x\)?
B. ([-2,2])
\(\cos^2 x\) का परिसर ([0,1]) है। इसलिए \(2-4\cos^2 x\) का परिसर ([-2,2]) होगा। / The range of \(\cos^2 x\) is ([0,1]). Therefore, the range of \(2-4\cos^2 x\) is ([-2,2]).
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B. \(\sin \theta+\cos \theta\)
क्योंकि पूरक कोणों में (\sin\left\(\frac{\pi}{2}-\theta\right\)=\cos \theta) और (\cos\left\(\frac{\pi}{2}-\theta\right\)=\sin \theta) होता है। परीक्षा में co-function सूत्र याद रखें। / Because for complementary angles ( \sin\left\(\frac{\pi}{2}-\theta\right\)=\cos \theta) and ( \cos\left\(\frac{\pi}{2}-\theta\right\)=\sin \theta). In exams remember co-function formulas.
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A. \(\sec \theta\) धनात्मक और \(\cosec \theta\) ऋणात्मक\(\sec \theta\) positive and \(\cosec \theta\) negative
चतुर्थ चतुर्थांश में \(\cos \theta\) धनात्मक और \(\sin \theta\) ऋणात्मक होता है, इसलिए उनके व्युत्क्रमों के चिन्ह भी वैसे ही होंगे। परीक्षा में पहले मूल फलनों के चिन्ह तय करें। / In the fourth quadrant, \(\cos \theta\) is positive and \(\sin \theta\) is negative, so their reciprocals have the same signs. In exams decide the signs of basic functions first.
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If \(\tan \theta=3\), what is the value of \(\frac{\sin \theta}{\cos \theta}\)?
B. (3)
\(\tan \theta=\frac{\sin \theta}{\cos \theta}\) होता है। परीक्षा में परिभाषा सीधे लागू करें। / \( \tan \theta=\frac{\sin \theta}{\cos \theta}\). In exams apply the definition directly.
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What is (\tan\(5\pi+\theta\)) equal to?
C. \(\tan \theta\)
\(\tan \theta\) का मूल period \(\pi\) है और \(5\pi\) period का गुणज है, इसलिए मान नहीं बदलता। परीक्षा में tangent में \(\pi\) के गुणज को हटाकर सरल करें। / The fundamental period of \(\tan \theta\) is \(\pi\), and \(5\pi\) is a multiple of the period, so the value does not change. In exams simplify tangent by removing multiples of \(\pi\).
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