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 151-160 of 346 questions.
What is the simplified value of \(\frac{1-\cos^2 x}{\sin^2 x}\)?
A. (1)
क्योंकि \(1-\cos^2 x=\sin^2 x\), इसलिए अनुपात (1) है। पहचान को पहले बदलकर देखें। / Since \(1-\cos^2 x=\sin^2 x\), the ratio is (1). First convert using identities.
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What is the simplified value of \(\frac{1-\sin^2 x}{\cos^2 x}\)?
B. (1)
क्योंकि \(1-\sin^2 x=\cos^2 x\), इसलिए मान (1) होगा। \(\sin^2 x+\cos^2 x=1\) सबसे जरूरी पहचान है। / Since \(1-\sin^2 x=\cos^2 x\), the value is (1). \(\sin^2 x+\cos^2 x=1\) is the most important identity.
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What is the period of the function \(\sin 3x\)?
C. \(\frac{2\pi}{3}\)
\(\sin kx\) का काल \(\frac{2\pi}{k}\) होता है। यहाँ (k=3), इसलिए काल \(\frac{2\pi}{3}\) है। / The period of \(\sin kx\) is \(\frac{2\pi}{k}\). Here (k=3), so the period is \(\frac{2\pi}{3}\).
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What is the period of the function \(\tan 4x\)?
D. \(\frac{\pi}{4}\)
\(\tan kx\) का काल \(\frac{\pi}{k}\) होता है। (k=4) रखने पर काल \(\frac{\pi}{4}\) मिलता है। / The period of \(\tan kx\) is \(\frac{\pi}{k}\). Substituting (k=4) gives period \(\frac{\pi}{4}\).
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What is the range of the function \(2\cos x\)?
A. ([-2,2])
\(\cos x\) का परिसर ([-1,1]) है। (2) से गुणा करने पर परिसर ([-2,2]) हो जाता है। / The range of \(\cos x\) is ([-1,1]). Multiplying by (2) changes the range to ([-2,2]).
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What is the maximum value of the function \(3\sin x+1\)?
C. (4)
\(\sin x\) का अधिकतम मान (1) है। इसलिए \(3\sin x+1\) का अधिकतम मान (4) होगा। / The maximum value of \(\sin x\) is (1). Hence the maximum value of \(3\sin x+1\) is (4).
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What is the minimum value of the function \(5-2\cos x\)?
B. (3)
\(\cos x\) का अधिकतम मान (1) है। इसलिए न्यूनतम मान (5-2=3) होगा। / The maximum value of \(\cos x\) is (1). Therefore, the minimum value is (5-2=3).
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If \(\sin x=\frac{5}{13}\) and (x) is in the first quadrant, what is the value of \(\tan x\)?
C. \(\frac{5}{12}\)
\(\cos x=\frac{12}{13}\) और \(\tan x=\frac{\sin x}{\cos x}\) होगा। इसलिए \(\tan x=\frac{5}{12}\)। / \(\cos x=\frac{12}{13}\) and \(\tan x=\frac{\sin x}{\cos x}\). Hence \(\tan x=\frac{5}{12}\).
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If \(\cos x=\frac{8}{17}\) and (x) is in the first quadrant, what is the value of \(\cot x\)?
A. \(\frac{8}{15}\)
\(\sin x=\frac{15}{17}\) मिलता है और \(\cot x=\frac{\cos x}{\sin x}\) होता है। इसलिए \(\cot x=\frac{8}{15}\)। / \(\sin x=\frac{15}{17}\) and \(\cot x=\frac{\cos x}{\sin x}\). Therefore, \(\cot x=\frac{8}{15}\).
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If \(\tan x=\frac{3}{4}\) and (x) is in the first quadrant, what is the value of \(\sin x\)?
B. \(\frac{3}{5}\)
\(\tan x=\frac{3}{4}\) से समकोण त्रिभुज में कर्ण (5) होगा। इसलिए \(\sin x=\frac{3}{5}\)। / From \(\tan x=\frac{3}{4}\), the hypotenuse in a right triangle is (5). Hence \(\sin x=\frac{3}{5}\).
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