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.
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B. (12) सेमी(12) cm
\(225^\circ=\frac{5\pi}{4}\) रेडियन है। \(r=\frac{s}{\theta}=\frac{15\pi}{5\pi/4}=12\) सेमी। / \(225^\circ=\frac{5\pi}{4}\) radians. \(r=\frac{s}{\theta}=\frac{15\pi}{5\pi/4}=12\) cm.
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A sector perimeter is (3) times its arc length and the radius is (8) cm. What is the central angle?
B. (1)
(2r+s=3s) से (16=2s) और (s=8) मिलता है। इसलिए \(\theta=\frac{s}{r}=1\) रेडियन। / From (2r+s=3s) we get (16=2s) and (s=8). Hence \(\theta=\frac{s}{r}=1\) radian.
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What is the least positive coterminal angle of \(-1025^\circ\)?
C. \(55^\circ\)
\(-1025^\circ+1080^\circ=55^\circ\) है। नकारात्मक बड़े कोण में \(360^\circ\) के गुणज जोड़ें। / \(-1025^\circ+1080^\circ=55^\circ\). Add multiples of \(360^\circ\) to a large negative angle.
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In which quadrant will the terminal side of \(\frac{31\pi}{6}\) lie?
C. तृतीयThird
\(\frac{31\pi}{6}-4\pi=\frac{7\pi}{6}\) है। \(\frac{7\pi}{6}\) तृतीय चतुर्थांश में आता है। / \(\frac{31\pi}{6}-4\pi=\frac{7\pi}{6}\). \(\frac{7\pi}{6}\) lies in the third quadrant.
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Which angle is coterminal with \(\frac{5\pi}{8}\) and lies between \(-4\pi\) and \(-2\pi\)?
D. \(-\frac{27\pi}{8}\)
\(\frac{5\pi}{8}-4\pi=-\frac{27\pi}{8}\) है। यह दिया गया अंतराल पूरा करता है। / \(\frac{5\pi}{8}-4\pi=-\frac{27\pi}{8}\). This satisfies the given interval.
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What is the principal angle of the terminal side passing through the point (\(-\sqrt{3},1\))?
B. \(\frac{5\pi}{6}\)
बिंदु द्वितीय चतुर्थांश में है और संदर्भ कोण \(\frac{\pi}{6}\) है। इसलिए मुख्य कोण \(\frac{5\pi}{6}\) है। / The point is in the second quadrant and the reference angle is \(\frac{\pi}{6}\). Hence the principal angle is \(\frac{5\pi}{6}\).
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What is the principal angle of the fourth-quadrant ray of the line (y=-x)?
D. \(\frac{7\pi}{4}\)
चतुर्थ चतुर्थांश में (y=-x) की किरण का संदर्भ कोण \(\frac{\pi}{4}\) है। इसलिए मुख्य कोण \(\frac{7\pi}{4}\) है। / The fourth-quadrant ray of (y=-x) has reference angle \(\frac{\pi}{4}\). Hence the principal angle is \(\frac{7\pi}{4}\).
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C. \(4080^\circ\)
(11) चक्कर \(3960^\circ\) और \(\frac{2\pi}{3}=120^\circ\) है। कुल कोण \(4080^\circ\) होगा। / (11) revolutions are \(3960^\circ\) and \(\frac{2\pi}{3}=120^\circ\). The total angle is \(4080^\circ\).
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C. (72)
ऋणात्मक (x)-अक्ष पर कोण \(\pi\) और \(3\pi\) होंगे। इसलिए (m=18,54) और योग (72) है। / On the negative (x)-axis the angles are \(\pi\) and \(3\pi\). Hence (m=18,54) and the sum is (72).
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C. \(\frac{7\pi}{8}\)
समकोण \(\frac{\pi}{2}\) है इसलिए संदर्भ कोण \(\frac{\pi}{8}\) है। द्वितीय चतुर्थांश में कोण \(\frac{7\pi}{8}\) होगा। / A right angle is \(\frac{\pi}{2}\) so the reference angle is \(\frac{\pi}{8}\). In the second quadrant the angle is \(\frac{7\pi}{8}\).
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