\(35^\circ+360^\circ=395^\circ\) lies in the given interval. Add or subtract \(360^\circ\) for coterminal angles.
Step 2
Why this answer is correct
The correct answer is B. \(395^\circ\). \(35^\circ+360^\circ=395^\circ\) lies in the given interval. Add or subtract \(360^\circ\) for coterminal angles.
Step 3
Exam Tip
\(35^\circ+360^\circ=395^\circ\) दिए अंतराल में आता है। सहप्रारंभी कोण के लिए \(360^\circ\) जोड़ें या घटाएं।
For fixed arc length \(\theta\) is inversely proportional to radius. The new radius is \(\frac{5}{4}\) times so the new angle is \(\frac{\pi}{2}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{\pi}{2}\). For fixed arc length \(\theta\) is inversely proportional to radius. The new radius is \(\frac{5}{4}\) times so the new angle is \(\frac{\pi}{2}\).
Step 3
Exam Tip
चाप लंबाई स्थिर हो तो \(\theta\) त्रिज्या के व्युत्क्रमानुपाती है। नई त्रिज्या \(\frac{5}{4}\) गुना है इसलिए नया कोण \(\frac{\pi}{2}\) होगा।
The minute hand is at \(228^\circ\) and the hour hand is at \(229^\circ\). The smaller difference is \(1^\circ\).
Step 2
Why this answer is correct
The correct answer is A. \(1^\circ\). The minute hand is at \(228^\circ\) and the hour hand is at \(229^\circ\). The smaller difference is \(1^\circ\).
Step 3
Exam Tip
मिनट सुई \(228^\circ\) पर और घंटे की सुई \(229^\circ\) पर होती है। छोटा अंतर \(1^\circ\) है।
\(125^\circ15'30''=\frac{450930}{3600}^\circ\). Multiplying by \(\frac{\pi}{180}\) gives \(\frac{15031\pi}{21600}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{15031\pi}{21600}\). \(125^\circ15'30''=\frac{450930}{3600}^\circ\). Multiplying by \(\frac{\pi}{180}\) gives \(\frac{15031\pi}{21600}\).
Step 3
Exam Tip
\(125^\circ15'30''=\frac{450930}{3600}^\circ\) है। इसे \(\frac{\pi}{180}\) से गुणा करने पर \(\frac{15031\pi}{21600}\) मिलता है।
One third of the circumference gives one third of the full angle \(2\pi\). Hence the central angle is \(\frac{2\pi}{3}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{2\pi}{3}\). One third of the circumference gives one third of the full angle \(2\pi\). Hence the central angle is \(\frac{2\pi}{3}\).
Step 3
Exam Tip
परिधि का \(\frac{1}{3}\) भाग पूरे कोण \(2\pi\) का \(\frac{1}{3}\) भाग देगा। इसलिए केंद्रीय कोण \(\frac{2\pi}{3}\) है।
The difference \(4\theta-120^\circ\) must be a multiple of \(360^\circ\). For the least positive value \(\theta=120^\circ\).
Step 2
Why this answer is correct
The correct answer is C. \(120^\circ\). The difference \(4\theta-120^\circ\) must be a multiple of \(360^\circ\). For the least positive value \(\theta=120^\circ\).
Step 3
Exam Tip
अंतर \(4\theta-120^\circ\) को \(360^\circ\) का गुणज होना चाहिए। सबसे छोटे धनात्मक मान के लिए \(\theta=120^\circ\) है।
In the second quadrant the angle is \(180^\circ-18^\circ=162^\circ\). \(162^\circ=\frac{9\pi}{10}\) radians.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{9\pi}{10}\). In the second quadrant the angle is \(180^\circ-18^\circ=162^\circ\). \(162^\circ=\frac{9\pi}{10}\) radians.
Step 3
Exam Tip
द्वितीय चतुर्थांश में कोण \(180^\circ-18^\circ=162^\circ\) है। \(162^\circ=\frac{9\pi}{10}\) रेडियन होता है।
\(18^\circ24'=\frac{92}{5}^\circ\). In radians it is \(\frac{92}{5}\times\frac{\pi}{180}=\frac{23\pi}{225}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{23\pi}{225}\). \(18^\circ24'=\frac{92}{5}^\circ\). In radians it is \(\frac{92}{5}\times\frac{\pi}{180}=\frac{23\pi}{225}\).
Step 3
Exam Tip
\(18^\circ24'=\frac{92}{5}^\circ\) है। रेडियन में \(\frac{92}{5}\times\frac{\pi}{180}=\frac{23\pi}{225}\) होगा।
\(\frac{7\pi}{5}\) lies in the third quadrant. The reference angle is \(\frac{7\pi}{5}-\pi=\frac{2\pi}{5}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{2\pi}{5}\). \(\frac{7\pi}{5}\) lies in the third quadrant. The reference angle is \(\frac{7\pi}{5}-\pi=\frac{2\pi}{5}\).
Step 3
Exam Tip
\(\frac{7\pi}{5}\) तृतीय चतुर्थांश में है। संदर्भ कोण \(\frac{7\pi}{5}-\pi=\frac{2\pi}{5}\) है।
The time difference is \(\frac{11}{2}\) hours and the hour hand turns \(30^\circ\) per hour. The total angle is \(165^\circ=\frac{11\pi}{12}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{11\pi}{12}\). The time difference is \(\frac{11}{2}\) hours and the hour hand turns \(30^\circ\) per hour. The total angle is \(165^\circ=\frac{11\pi}{12}\).
Step 3
Exam Tip
समय अंतर \(\frac{11}{2}\) घंटे है और घंटे की सुई \(30^\circ\) प्रति घंटा घूमती है। कुल कोण \(165^\circ=\frac{11\pi}{12}\) है।
The point is in the second quadrant and the reference angle is \(\frac{\pi}{6}\). Hence the principal angle is \(\frac{5\pi}{6}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{5\pi}{6}\). The point is in the second quadrant and the reference angle is \(\frac{\pi}{6}\). Hence the principal angle is \(\frac{5\pi}{6}\).
Step 3
Exam Tip
बिंदु द्वितीय चतुर्थांश में है और संदर्भ कोण \(\frac{\pi}{6}\) है। इसलिए मुख्य कोण \(\frac{5\pi}{6}\) है।
The fourth-quadrant ray of (y=-x) has reference angle \(\frac{\pi}{4}\). Hence the principal angle is \(\frac{7\pi}{4}\).
Step 2
Why this answer is correct
The correct answer is D. \(\frac{7\pi}{4}\). The fourth-quadrant ray of (y=-x) has reference angle \(\frac{\pi}{4}\). Hence the principal angle is \(\frac{7\pi}{4}\).
Step 3
Exam Tip
चतुर्थ चतुर्थांश में (y=-x) की किरण का संदर्भ कोण \(\frac{\pi}{4}\) है। इसलिए मुख्य कोण \(\frac{7\pi}{4}\) है।
A right angle is \(\frac{\pi}{2}\) so the reference angle is \(\frac{\pi}{8}\). In the second quadrant the angle is \(\frac{7\pi}{8}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{7\pi}{8}\). A right angle is \(\frac{\pi}{2}\) so the reference angle is \(\frac{\pi}{8}\). In the second quadrant the angle is \(\frac{7\pi}{8}\).
Step 3
Exam Tip
समकोण \(\frac{\pi}{2}\) है इसलिए संदर्भ कोण \(\frac{\pi}{8}\) है। द्वितीय चतुर्थांश में कोण \(\frac{7\pi}{8}\) होगा।
The area ratio is \(\frac{\theta}{2\pi}\). From \(\frac{\theta}{2\pi}=\frac{3}{4}\) we get \(\theta=\frac{3\pi}{2}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{3\pi}{2}\). The area ratio is \(\frac{\theta}{2\pi}\). From \(\frac{\theta}{2\pi}=\frac{3}{4}\) we get \(\theta=\frac{3\pi}{2}\).
Step 3
Exam Tip
क्षेत्रफल का अनुपात \(\frac{\theta}{2\pi}\) होता है। \(\frac{\theta}{2\pi}=\frac{3}{4}\) से \(\theta=\frac{3\pi}{2}\) है।
\(-75^\circ15'=-\frac{301}{4}^\circ\). In radians it is \(-\frac{301}{4}\times\frac{\pi}{180}=-\frac{301\pi}{720}\).
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{301\pi}{720}\). \(-75^\circ15'=-\frac{301}{4}^\circ\). In radians it is \(-\frac{301}{4}\times\frac{\pi}{180}=-\frac{301\pi}{720}\).
Step 3
Exam Tip
\(-75^\circ15'=-\frac{301}{4}^\circ\) है। रेडियन में \(-\frac{301}{4}\times\frac{\pi}{180}=-\frac{301\pi}{720}\) होगा।
The difference is \(5x+60^\circ\) and it must be a multiple of \(360^\circ\). For the least positive value \(x=60^\circ\).
Step 2
Why this answer is correct
The correct answer is C. \(60^\circ\). The difference is \(5x+60^\circ\) and it must be a multiple of \(360^\circ\). For the least positive value \(x=60^\circ\).
Step 3
Exam Tip
अंतर \(5x+60^\circ\) है और यह \(360^\circ\) का गुणज होना चाहिए। सबसे छोटे धनात्मक मान के लिए \(x=60^\circ\) है।
C. \(\frac{360}{11}\) मिनट बाद/after \(\frac{360}{11}\) minutes
Step 1
Concept
After (m) minutes the angle difference is \(90^\circ-5.5m\). For the next right angle \(m=\frac{360}{11}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{360}{11}\) मिनट बाद / after \(\frac{360}{11}\) minutes. After (m) minutes the angle difference is \(90^\circ-5.5m\). For the next right angle \(m=\frac{360}{11}\).
Step 3
Exam Tip
(m) मिनट बाद कोण अंतर \(90^\circ-5.5m\) होता है। अगले समकोण के लिए \(m=\frac{360}{11}\) मिलता है।
(5) radians \(=5\times\frac{180^\circ}{\pi}\). Using \(\pi=\frac{22}{7}\) gives approximately \(286^\circ21'49''\).
Step 2
Why this answer is correct
The correct answer is B. \(286^\circ21'49''\). (5) radians \(=5\times\frac{180^\circ}{\pi}\). Using \(\pi=\frac{22}{7}\) gives approximately \(286^\circ21'49''\).
Step 3
Exam Tip
(5) रेडियन \(=5\times\frac{180^\circ}{\pi}\) है। \(\pi=\frac{22}{7}\) रखने पर लगभग \(286^\circ21'49''\) मिलता है।
D. नहीं क्योंकि \(\frac{1980}{360}\) पूर्णांक नहीं है/No because \(\frac{1980}{360}\) is not an integer
Step 1
Concept
The difference of coterminal angles is an integer multiple of \(360^\circ\). \(\frac{1980}{360}=\frac{11}{2}\) is not an integer.
Step 2
Why this answer is correct
The correct answer is D. नहीं क्योंकि \(\frac{1980}{360}\) पूर्णांक नहीं है / No because \(\frac{1980}{360}\) is not an integer. The difference of coterminal angles is an integer multiple of \(360^\circ\). \(\frac{1980}{360}=\frac{11}{2}\) is not an integer.
Step 3
Exam Tip
सहप्रारंभी कोणों का अंतर \(360^\circ\) का पूर्णांक गुणज होता है। \(\frac{1980}{360}=\frac{11}{2}\) पूर्णांक नहीं है।
The perimeter is \(24+12\theta\) and the area is \(72\theta\). From \(24+12\theta=72\theta\) we get \(\theta=\frac{2}{5}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{2}{5}\). The perimeter is \(24+12\theta\) and the area is \(72\theta\). From \(24+12\theta=72\theta\) we get \(\theta=\frac{2}{5}\).
Step 3
Exam Tip
परिमाप \(24+12\theta\) और क्षेत्रफल \(72\theta\) है। \(24+12\theta=72\theta\) से \(\theta=\frac{2}{5}\) मिलता है।
The minute hand is at \(324^\circ\) and the hour hand is at \(357^\circ\). The smaller difference is \(33^\circ\).
Step 2
Why this answer is correct
The correct answer is C. \(33^\circ\). The minute hand is at \(324^\circ\) and the hour hand is at \(357^\circ\). The smaller difference is \(33^\circ\).
Step 3
Exam Tip
मिनट सुई \(324^\circ\) पर और घंटे की सुई \(357^\circ\) पर होती है। छोटा अंतर \(33^\circ\) है।
The difference \(\frac{5\pi}{2}-2\theta\) must be a multiple of \(2\pi\). In the given interval \(\theta=\frac{\pi}{4}\) is suitable.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\pi}{4}\). The difference \(\frac{5\pi}{2}-2\theta\) must be a multiple of \(2\pi\). In the given interval \(\theta=\frac{\pi}{4}\) is suitable.
Step 3
Exam Tip
अंतर \(\frac{5\pi}{2}-2\theta\) को \(2\pi\) का गुणज होना चाहिए। दिए अंतराल में \(\theta=\frac{\pi}{4}\) उपयुक्त है।
A. कोई अशून्य कोण संभव नहीं/No non-zero angle is possible
Step 1
Concept
Degree measure is \(x\cdot\frac{180}{\pi}\). \(x\cdot\frac{180}{\pi}=60x\) is possible only for (x=0).
Step 2
Why this answer is correct
The correct answer is A. कोई अशून्य कोण संभव नहीं / No non-zero angle is possible. Degree measure is \(x\cdot\frac{180}{\pi}\). \(x\cdot\frac{180}{\pi}=60x\) is possible only for (x=0).
Step 3
Exam Tip
डिग्री माप \(x\cdot\frac{180}{\pi}\) होता है। \(x\cdot\frac{180}{\pi}=60x\) केवल (x=0) पर संभव है।
B. \(40^\circ\) और \(\frac{11\pi}{9}\)/\(40^\circ\) and \(\frac{11\pi}{9}\)
Step 1
Concept
\(220^\circ\) is in the third quadrant so the reference angle is \(40^\circ\). \(220^\circ=\frac{11\pi}{9}\) radians.
Step 2
Why this answer is correct
The correct answer is B. \(40^\circ\) और \(\frac{11\pi}{9}\) / \(40^\circ\) and \(\frac{11\pi}{9}\). \(220^\circ\) is in the third quadrant so the reference angle is \(40^\circ\). \(220^\circ=\frac{11\pi}{9}\) radians.
Step 3
Exam Tip
\(220^\circ\) तृतीय चतुर्थांश में है इसलिए संदर्भ कोण \(40^\circ\) है। \(220^\circ=\frac{11\pi}{9}\) रेडियन होता है।
The interior angle of a regular polygon is (\frac{(n-2)\pi}{n}). From (\frac{(n-2)\pi}{n}=\frac{5\pi}{6}) we get (n=12).
Step 2
Why this answer is correct
The correct answer is C. (12). The interior angle of a regular polygon is (\frac{(n-2)\pi}{n}). From (\frac{(n-2)\pi}{n}=\frac{5\pi}{6}) we get (n=12).
Step 3
Exam Tip
समबहुभुज का आंतरिक कोण (\frac{(n-2)\pi}{n}) होता है। (\frac{(n-2)\pi}{n}=\frac{5\pi}{6}) से (n=12) मिलता है।
The net angle is \(\frac{17\pi}{6}-\frac{5\pi}{3}=\frac{7\pi}{6}\). Take counterclockwise as positive and clockwise as negative.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{7\pi}{6}\). The net angle is \(\frac{17\pi}{6}-\frac{5\pi}{3}=\frac{7\pi}{6}\). Take counterclockwise as positive and clockwise as negative.
Step 3
Exam Tip
नेट कोण \(\frac{17\pi}{6}-\frac{5\pi}{3}=\frac{7\pi}{6}\) है। वामावर्त को धनात्मक और दक्षिणावर्त को ऋणात्मक लें।
The clockwise angle is \(-\frac{14\pi}{3}\). Adding \(6\pi\) gives the principal angle \(\frac{4\pi}{3}\).
Step 2
Why this answer is correct
The correct answer is D. \(\frac{4\pi}{3}\). The clockwise angle is \(-\frac{14\pi}{3}\). Adding \(6\pi\) gives the principal angle \(\frac{4\pi}{3}\).
Step 3
Exam Tip
दक्षिणावर्त कोण \(-\frac{14\pi}{3}\) है। इसमें \(6\pi\) जोड़ने पर \(\frac{4\pi}{3}\) मुख्य कोण मिलता है।
समान त्रिज्या वाले दो त्रिज्यखंडों के क्षेत्रफलों का अनुपात (5:8) है। यदि छोटे त्रिज्यखंड का कोण \(75^\circ\) है तो बड़े त्रिज्यखंड का कोण रेडियन में क्या है?
For equal radii sector area is proportional to angle. The larger angle is \(75^\circ\times\frac{8}{5}=120^\circ=\frac{2\pi}{3}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{2\pi}{3}\). For equal radii sector area is proportional to angle. The larger angle is \(75^\circ\times\frac{8}{5}=120^\circ=\frac{2\pi}{3}\).
Step 3
Exam Tip
समान त्रिज्या में क्षेत्रफल कोण के समानुपाती होता है। बड़ा कोण \(75^\circ\times\frac{8}{5}=120^\circ=\frac{2\pi}{3}\) है।
