100 results found for "supplementary-radian" in all classes.
If \(\frac{7\pi}{18}\) and (x) are supplementary angles then what is (x)?
C. \(\frac{11\pi}{18}\)
संपूरक कोणों का योग \(\pi\) होता है। इसलिए \(x=\pi-\frac{7\pi}{18}=\frac{11\pi}{18}\) है। / Supplementary angles add to \(\pi\). Hence \(x=\pi-\frac{7\pi}{18}=\frac{11\pi}{18}\).
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If \( \theta=\frac{7\pi}{12} \), what is its supplementary angle in radians?
A. \( \frac{5\pi}{12} \)
पूरक कोणों का योग \( \pi \) होता है इसलिए \( \pi-\frac{7\pi}{12}=\frac{5\pi}{12} \) है। रेडियन में \(180^\circ\) की जगह \( \pi \) लें। / Supplementary angles sum to \( \pi \), so \( \pi-\frac{7\pi}{12}=\frac{5\pi}{12} \). In radians use \( \pi \) instead of \(180^\circ\).
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Two supplementary angles are in the ratio (5:7). What is the radian measure of the smaller angle?
A. \(\frac{5\pi}{12}\)
संपूरक कोणों का योग \(180^\circ\) है, इसलिए छोटा कोण \(75^\circ=\frac{5\pi}{12}\) है। परीक्षा में \(180^\circ\) को अनुपात में बांटें। / Supplementary angles sum to \(180^\circ\), so the smaller angle is \(75^\circ=\frac{5\pi}{12}\). In exams, divide \(180^\circ\) in the given ratio.
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D. \(96^\circ\)
मूल कोण \(\pi-\frac{7\pi}{15}=\frac{8\pi}{15}\) है, जो \(96^\circ\) के बराबर है। परीक्षा में संपूरक कोणों का योग \(180^\circ\) रखें। / The original angle is \(\pi-\frac{7\pi}{15}=\frac{8\pi}{15}\), which equals \(96^\circ\). In exams, keep the sum of supplementary angles as \(180^\circ\).
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If \( \theta=112^\circ30' \), what is its supplementary angle?
A. \(67^\circ30'\)
पूरक कोण \(180^\circ-112^\circ30'=67^\circ30'\) है। मिनट वाले घटाव में उधार लेने का ध्यान रखें। / The supplementary angle is \(180^\circ-112^\circ30'=67^\circ30'\). Be careful with borrowing in minute subtraction.
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What is the importance of asking a supplementary question to a minister?
A. मुख्य उत्तर की स्पष्टता और जवाबदेही बढ़ानाTo increase clarity and accountability after the main answer
मंत्री मुख्य प्रश्न का उत्तर देता है। / A minister answers the main question.
पूरक प्रश्न से अस्पष्ट बात साफ की जा सकती है। / A supplementary question can clarify unclear points.
इससे सरकार पर वास्तविक निगरानी बढ़ती है। / This increases real scrutiny of the government.
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What can be called a supplementary source of income?
A. मुख्य आय के साथ छोटा अतिरिक्त कामA small additional work along with main income
पूरक आय मुख्य आय के साथ अतिरिक्त सहारा देती है। परीक्षा में इसे जीविका विविधता से जोड़ें। / Supplementary income gives extra support along with main income. In exams connect it with livelihood diversity.
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If the radian measure of \(1^\circ\) is \(\frac{\pi}{180}\), what is the radian measure of (1')?
A. \(\frac{\pi}{10800}\)
\(1'=\frac{1}{60}^\circ\), इसलिए रेडियन मान \(\frac{\pi}{180\times60}\) है। परीक्षा में मिनट को पहले डिग्री में बदलें। / \(1'=\frac{1}{60}^\circ\), so its radian measure is \(\frac{\pi}{180\times60}\). In exams, first convert minutes into degrees.
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In which situation would a photograph be the best supplementary evidence for an observation?
A. जब समय के साथ पत्ती के आकार परिवर्तन की तुलना करनी होWhen comparing changes in leaf shape over time
छायाचित्र दृश्य आकार और संरचना का स्थायी अभिलेख देता है। मात्रात्मक गुणों के लिए उपयुक्त यंत्र भी चाहिए। / A photograph provides a permanent record of visual shape and structure. Appropriate instruments are still needed for quantitative properties.
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When is it wrong to call women work only supplementary income?
A. जब उनकी आय परिवार की मुख्य जरूरतें पूरी कर रही होWhen their income is meeting main family needs
महिलाओं की आय को कमतर कहना उनके आर्थिक योगदान को घटाता है। परीक्षा में contribution recognition लिखें। / Calling women income secondary reduces their economic contribution. In exams write contribution recognition.
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If \(\alpha=220^\circ\) then which reference angle and principal radian angle are correct?
B. \(40^\circ\) और \(\frac{11\pi}{9}\)\(40^\circ\) and \(\frac{11\pi}{9}\)
\(220^\circ\) तृतीय चतुर्थांश में है इसलिए संदर्भ कोण \(40^\circ\) है। \(220^\circ=\frac{11\pi}{9}\) रेडियन होता है। / \(220^\circ\) is in the third quadrant so the reference angle is \(40^\circ\). \(220^\circ=\frac{11\pi}{9}\) radians.
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A. कोई अशून्य कोण संभव नहींNo non-zero angle is possible
डिग्री माप \(x\cdot\frac{180}{\pi}\) होता है। \(x\cdot\frac{180}{\pi}=60x\) केवल (x=0) पर संभव है। / Degree measure is \(x\cdot\frac{180}{\pi}\). \(x\cdot\frac{180}{\pi}=60x\) is possible only for (x=0).
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What is the radian measure of \(-75^\circ15'\)?
A. \(-\frac{301\pi}{720}\)
\(-75^\circ15'=-\frac{301}{4}^\circ\) है। रेडियन में \(-\frac{301}{4}\times\frac{\pi}{180}=-\frac{301\pi}{720}\) होगा। / \(-75^\circ15'=-\frac{301}{4}^\circ\). In radians it is \(-\frac{301}{4}\times\frac{\pi}{180}=-\frac{301\pi}{720}\).
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Which is the correct geometrical interpretation of (1) radian?
A. जब चाप लंबाई त्रिज्या के बराबर होWhen arc length equals radius
(1) रेडियन तब बनता है जब (s=r) हो। परिभाषा आधारित प्रश्नों में \(s=r\theta\) को याद रखें. / (1) radian is formed when (s=r). For definition based questions remember \(s=r\theta\).
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What is the radian measure of \(\frac{3}{8}\) of a complete revolution?
C. \(\frac{3\pi}{4}\)
पूर्ण चक्कर \(2\pi\) रेडियन है। \(\frac{3}{8}\times2\pi=\frac{3\pi}{4}\) होता है। / A complete revolution is \(2\pi\) radians. \(\frac{3}{8}\times2\pi=\frac{3\pi}{4}\).
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What is the radian measure of \(72^\circ\)?
B. \(\frac{2\pi}{5}\)
\(72^\circ\times\frac{\pi}{180}=\frac{2\pi}{5}\) होता है। सरलीकरण में (72) और (180) को (36) से भाग दें। / \(72^\circ\times\frac{\pi}{180}=\frac{2\pi}{5}\). Divide (72) and (180) by (36) while simplifying.
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Approximately (1) radian is equal to how many degrees?
C. \(57.3^\circ\)
(1) रेडियन \(=\frac{180^\circ}{\pi}\approx57.3^\circ\) होता है। अनुमान वाले प्रश्नों में \(\pi\approx3.14\) लें। / (1) radian \(=\frac{180^\circ}{\pi}\approx57.3^\circ\). In approximation questions use \(\pi\approx3.14\).
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What is the degree measure of the radian angle \(\frac{17\pi}{12}\)?
B. \(255^\circ\)
रेडियन को डिग्री में बदलने के लिए \(\frac{180}{\pi}\) से गुणा करें। \(\frac{17\pi}{12}\times\frac{180}{\pi}=255^\circ\) है। / Multiply radians by \(\frac{180}{\pi}\) to convert into degrees. \(\frac{17\pi}{12}\times\frac{180}{\pi}=255^\circ\).
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What is the radian measure of an angle equal to (2.75) complete revolutions?
B. \(\frac{11\pi}{2}\)
एक चक्कर \(2\pi\) रेडियन होता है। \(2.75\times2\pi=\frac{11\pi}{2}\) लिखें। / One revolution is \(2\pi\) radians. Write \(2.75\times2\pi=\frac{11\pi}{2}\).
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Which is the correct radian measure of (1'')?
D. \(\frac{\pi}{648000}\)
\(1''=\frac{1}{3600}^\circ\), इसलिए रेडियन मान \(\frac{\pi}{180\times3600}\) है। परीक्षा में सेकंड को डिग्री में बदलना न भूलें। / \(1''=\frac{1}{3600}^\circ\), so the radian measure is \(\frac{\pi}{180\times3600}\). In exams, do not forget to convert seconds into degrees.
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If \( \theta=2^\circ 30' 45'' \), which is the radian measure of \( \theta \)?
A. \( \frac{1003\pi}{72000} \) रेडियन\( \frac{1003\pi}{72000} \) radians
\(2^\circ30'45''=\frac{1003}{400}^\circ\) और रेडियन \( \frac{1003\pi}{72000} \) है। पहले डिग्री में बदलकर \( \frac{\pi}{180} \) से गुणा करें। / \(2^\circ30'45''=\frac{1003}{400}^\circ\) and the radian value is \( \frac{1003\pi}{72000} \). First convert to degrees and multiply by \( \frac{\pi}{180} \).
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Which is the correct radian value of \(33^\circ 45'\)?
C. \( \frac{3\pi}{16} \) रेडियन\( \frac{3\pi}{16} \) radians
\(33^\circ45'=33.75^\circ=\frac{135^\circ}{4}\) और रेडियन मान \( \frac{3\pi}{16} \) है। पहले मिनट को डिग्री में बदलें। / \(33^\circ45'=33.75^\circ=\frac{135^\circ}{4}\) and the radian value is \( \frac{3\pi}{16} \). Convert minutes into degrees first.
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What is the radian form of \(198^\circ\)?
D. \( \frac{11\pi}{10} \) रेडियन\( \frac{11\pi}{10} \) radians
\(198^\circ=\frac{198\pi}{180}=\frac{11\pi}{10}\) है। \(180^\circ\) से थोड़ा बड़ा कोण \(\pi\) से थोड़ा बड़ा रेडियन देता है। / \(198^\circ=\frac{198\pi}{180}=\frac{11\pi}{10}\). An angle slightly greater than \(180^\circ\) gives a radian value slightly greater than \(\pi\).
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Which is the radian measure of \(54^\circ\)?
B. \( \frac{3\pi}{10} \) रेडियन\( \frac{3\pi}{10} \) radians
\(54^\circ=\frac{54\pi}{180}=\frac{3\pi}{10}\) होता है। भिन्न को सबसे सरल रूप में लिखना जरूरी है। / \(54^\circ=\frac{54\pi}{180}=\frac{3\pi}{10}\). It is important to write the fraction in simplest form.
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What is the correct radian value of \(18^\circ\)?
A. \( \frac{\pi}{10} \) रेडियन\( \frac{\pi}{10} \) radians
\(18^\circ=\frac{18\pi}{180}=\frac{\pi}{10}\) है। डिग्री से रेडियन में बदलते समय \( \frac{\pi}{180} \) से गुणा करें। / \(18^\circ=\frac{18\pi}{180}=\frac{\pi}{10}\). Multiply by \( \frac{\pi}{180} \) to convert degrees to radians.
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What is the correct radian value of \(7^\circ 30'\)?
C. \( \frac{\pi}{24} \) रेडियन\( \frac{\pi}{24} \) radians
\(30'=\frac{1}{2}^\circ\) इसलिए \(7^\circ 30'=7.5^\circ\) और \(7.5^\circ\times\frac{\pi}{180}=\frac{\pi}{24}\) है। पहले मिनट को डिग्री में बदलें। / \(30'=\frac{1}{2}^\circ\) so \(7^\circ 30'=7.5^\circ\) and \(7.5^\circ\times\frac{\pi}{180}=\frac{\pi}{24}\). Convert minutes into degrees first.
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Which is the radian form of \(405^\circ\)?
D. \( \frac{9\pi}{4} \) रेडियन\( \frac{9\pi}{4} \) radians
\(405^\circ=\frac{405\pi}{180}=\frac{9\pi}{4}\) होता है। \(360^\circ\) से बड़े कोणों को भी उसी नियम से बदलें। / \(405^\circ=\frac{405\pi}{180}=\frac{9\pi}{4}\). Use the same rule even for angles greater than \(360^\circ\).
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What is the radian measure of \(37.5^\circ\)?
B. \( \frac{5\pi}{24} \) रेडियन\( \frac{5\pi}{24} \) radians
\(37.5^\circ=\frac{37.5\pi}{180}=\frac{5\pi}{24}\) होता है। \(37.5^\circ\) को \( \frac{75^\circ}{2} \) मानकर भी हल कर सकते हैं। / \(37.5^\circ=\frac{37.5\pi}{180}=\frac{5\pi}{24}\). You can also treat \(37.5^\circ\) as \( \frac{75^\circ}{2} \).
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Which angle has radian measure \( \frac{3}{2} \) if arc (s=18) cm and radius (r=12) cm?
D. \( \frac{3}{2} \) रेडियन\( \frac{3}{2} \) radians
\( \theta=\frac{s}{r}=\frac{18}{12}=\frac{3}{2} \) रेडियन है। चाप और त्रिज्या की इकाई समान होनी चाहिए। / \( \theta=\frac{s}{r}=\frac{18}{12}=\frac{3}{2} \) radians. The arc length and radius must have the same unit.
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What is the radian measure of \(285^\circ\)?
B. \( \frac{19\pi}{12} \) रेडियन\( \frac{19\pi}{12} \) radians
\(285^\circ=\frac{285\pi}{180}=\frac{19\pi}{12}\) है। ऐसे कोणों में \( \frac{\pi}{12} \) की गिनती काम आती है। / \(285^\circ=\frac{285\pi}{180}=\frac{19\pi}{12}\). Counting in \( \frac{\pi}{12} \) steps helps for such angles.
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Which is the radian form of \(195^\circ\)?
D. \( \frac{13\pi}{12} \) रेडियन\( \frac{13\pi}{12} \) radians
\(195^\circ=\frac{195\pi}{180}=\frac{13\pi}{12}\) है। डिग्री को (180) से भाग देकर \( \pi \) लगाएं। / \(195^\circ=\frac{195\pi}{180}=\frac{13\pi}{12}\). Divide the degree measure by (180) and attach \( \pi \).
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What is the correct simplified radian form of \(75^\circ\)?
A. \( \frac{5\pi}{12} \) रेडियन\( \frac{5\pi}{12} \) radians
\(75^\circ=\frac{75\pi}{180}=\frac{5\pi}{12}\) है। डिग्री से रेडियन में \( \frac{\pi}{180} \) से गुणा करें। / \(75^\circ=\frac{75\pi}{180}=\frac{5\pi}{12}\). Multiply by \( \frac{\pi}{180} \) to convert degrees to radians.
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What will be the radian measure of \(30^\circ\)?
D. \( \frac{\pi}{6} \) रेडियन\( \frac{\pi}{6} \) radians
\(30^\circ=\frac{30\pi}{180}=\frac{\pi}{6}\) है। डिग्री से रेडियन में \( \frac{\pi}{180} \) से गुणा करें। / \(30^\circ=\frac{30\pi}{180}=\frac{\pi}{6}\). Multiply degrees by \( \frac{\pi}{180} \) to convert to radians.
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(1) radian is approximately equal to how many degrees?
A. \(57.3^\circ\)
(1) रेडियन \(=\frac{180^\circ}{\pi}\approx57.3^\circ\) होता है। अनुमान में \(\pi\approx3.14\) लें। / (1) radian \(=\frac{180^\circ}{\pi}\approx57.3^\circ\). For approximation take \(\pi\approx3.14\).
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What is the radian measure of \(75^\circ\)?
B. \(\frac{5\pi}{12}\)
\(75^\circ\times\frac{\pi}{180^\circ}=\frac{5\pi}{12}\) होता है। (75) और (180) को (15) से घटाएं। / \(75^\circ\times\frac{\pi}{180^\circ}=\frac{5\pi}{12}\). Reduce (75) and (180) by (15).
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If an angle is \(300^\circ\) then what is its radian measure?
B. \(\frac{5\pi}{3}\)
\(300^\circ\times\frac{\pi}{180^\circ}=\frac{5\pi}{3}\) होता है। (300:180) को (5:3) में घटाएं। / \(300^\circ\times\frac{\pi}{180^\circ}=\frac{5\pi}{3}\). Reduce (300:180) to (5:3).
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What is the radian measure of \(225^\circ\)?
A. \(\frac{5\pi}{4}\)
\(225^\circ \times \frac{\pi}{180^\circ}=\frac{5\pi}{4}\) होता है। \(45^\circ=\frac{\pi}{4}\) याद रखने से भी उत्तर मिलता है। / \(225^\circ \times \frac{\pi}{180^\circ}=\frac{5\pi}{4}\). Remembering \(45^\circ=\frac{\pi}{4}\) also helps.
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What is the radian measure of \(120^\circ\)?
C. \(\frac{2\pi}{3}\)
\(120^\circ \times \frac{\pi}{180^\circ}=\frac{2\pi}{3}\) होता है। पहले भिन्न को घटाएं फिर उत्तर लिखें। / \(120^\circ \times \frac{\pi}{180^\circ}=\frac{2\pi}{3}\). Reduce the fraction before writing the answer.
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What is the radian measure of \(30^\circ\)?
A. \(\frac{\pi}{6}\)
\(30^\circ \times \frac{\pi}{180^\circ}=\frac{\pi}{6}\) होता है। डिग्री से रेडियन में \(\frac{\pi}{180^\circ}\) से गुणा करें। / \(30^\circ \times \frac{\pi}{180^\circ}=\frac{\pi}{6}\). Multiply by \(\frac{\pi}{180^\circ}\) to convert degrees to radians.
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What is the radian measure of \(90^\circ\)?
B. \(\frac{\pi}{2}\)
\(90^\circ\), \(180^\circ\) का आधा है इसलिए रेडियन \(\frac{\pi}{2}\) होगा। आधे कोण में रेडियन भी आधा होता है। / \(90^\circ\) is half of \(180^\circ\), so its radian measure is \(\frac{\pi}{2}\). Half the angle means half the radian measure.
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What is the radian measure of an angle (15') less than \(30^\circ\)?
A. \(\frac{119\pi}{720}\)
\(30^\circ-15'=29^\circ45'=\frac{119}{4}^\circ\), इसलिए रेडियन माप \(\frac{119\pi}{720}\) है। परीक्षा में मिनट को डिग्री के अंश में बदलें। / \(30^\circ-15'=29^\circ45'=\frac{119}{4}^\circ\), so the radian measure is \(\frac{119\pi}{720}\). In exams, convert minutes into a fraction of a degree.
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To the nearest minute, approximately how many degrees is (1) radian equal to?
A. \(57^\circ 18'\)
(1) रेडियन लगभग \(57.2958^\circ\) होता है, जो \(57^\circ 18'\) के निकट है। परीक्षा में दशमलव भाग को (60) से गुणा करें। / (1) radian is approximately \(57.2958^\circ\), which is close to \(57^\circ 18'\). In exams, multiply the decimal part by (60).
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What is the radian measure of (2.25) complete revolutions?
C. \(\frac{9\pi}{2}\)
\(2.25=\frac{9}{4}\) चक्कर है, इसलिए कोण \(\frac{9}{4}\times2\pi=\frac{9\pi}{2}\) है। परीक्षा में चक्कर को \(2\pi\) से गुणा करें। / \(2.25=\frac{9}{4}\) revolutions, so the angle is \(\frac{9}{4}\times2\pi=\frac{9\pi}{2}\). In exams, multiply revolutions by \(2\pi\).
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If the radian measure of \(x^\circ\) is \(\frac{11\pi}{9}\), what is (x)?
D. (220)
\(\frac{11\pi}{9}\times\frac{180^\circ}{\pi}=220^\circ\), इसलिए (x=220) है। परीक्षा में डिग्री रूपांतरण सीधा लगाएं। / \(\frac{11\pi}{9}\times\frac{180^\circ}{\pi}=220^\circ\), so (x=220). In exams, apply degree conversion directly.
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What is the radian measure of \(27^\circ 45'\)?
B. \(\frac{37\pi}{240}\)
\(27^\circ 45'=\frac{111}{4}^\circ\), इसलिए रेडियन माप \(\frac{111\pi}{720}=\frac{37\pi}{240}\) है। परीक्षा में मिनट को \(\frac{45}{60}^\circ\) लिखें। / \(27^\circ 45'=\frac{111}{4}^\circ\), so the radian measure is \(\frac{111\pi}{720}=\frac{37\pi}{240}\). In exams, write minutes as \(\frac{45}{60}^\circ\).
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Two complementary angles are in the ratio (2:3). What is the radian measure of the larger angle?
B. \(\frac{3\pi}{10}\)
पूरक कोणों का योग \(90^\circ\) है, इसलिए बड़ा कोण \(54^\circ=\frac{3\pi}{10}\) है। परीक्षा में अनुपात का कुल भाग पहले निकालें। / Complementary angles sum to \(90^\circ\), so the larger angle is \(54^\circ=\frac{3\pi}{10}\). In exams, first find the total parts of the ratio.
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What is the radian measure of an angle \(15^\circ\) less than \(\frac{\pi}{3}\) radians?
B. \(\frac{\pi}{4}\)
\(\frac{\pi}{3}=60^\circ\), इसलिए नया कोण \(45^\circ=\frac{\pi}{4}\) है। परीक्षा में मिश्रित इकाइयों को एक ही इकाई में बदलें। / \(\frac{\pi}{3}=60^\circ\), so the new angle is \(45^\circ=\frac{\pi}{4}\). In exams, convert mixed units into one unit.
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Can there be a non-zero angle whose degree measure is (2) times its radian measure?
C. नहींNo
अशून्य कोण के लिए अनुपात हमेशा \(180/\pi\) होता है, जो (2) नहीं है। परीक्षा में डिग्री और रेडियन के संख्यात्मक अनुपात को पहचानें। / For a non-zero angle, the numerical ratio is always \(180/\pi\), not (2). In exams, identify the numerical ratio between degree and radian measures.
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What is the radian measure of an angle \(54^\circ\) more than \(\frac{1}{5}\) of a straight angle?
B. \(\frac{\pi}{2}\)
सीधा कोण \(180^\circ\) है, इसलिए \(\frac{1}{5}\) भाग \(36^\circ\) और कुल \(90^\circ\) है। परीक्षा में शब्दों को चरणों में बदलें। / A straight angle is \(180^\circ\), so \(\frac{1}{5}\) is \(36^\circ\) and the total is \(90^\circ\). In exams, translate words step by step.
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If \(3\theta=450^\circ\), what is the radian measure of \(\theta\)?
C. \(\frac{5\pi}{6}\)
\(\theta=150^\circ\) और \(150^\circ=\frac{5\pi}{6}\) होता है। परीक्षा में पहले कोण निकालें, फिर रेडियन में बदलें। / \(\theta=150^\circ\), and \(150^\circ=\frac{5\pi}{6}\). In exams, first find the angle, then convert into radians.
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If an angle is \(\frac{11}{6}\) of a complete revolution, what is its radian measure?
A. \(\frac{11\pi}{3}\)
एक पूर्ण चक्कर \(2\pi\) रेडियन होता है, इसलिए माप \(\frac{11}{6}\times2\pi=\frac{11\pi}{3}\) है। परीक्षा में पूर्ण चक्कर को \(2\pi\) मानें। / One complete revolution is \(2\pi\) radians, so the measure is \(\frac{11}{6}\times2\pi=\frac{11\pi}{3}\). In exams, take a full turn as \(2\pi\).
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What is the correct radian measure of \(112^\circ 30'\)?
B. (5\pi8)
\(112^\circ 30'\) का अर्थ \(112.5^\circ\) है, इसलिए मान \(5\pi/8\) मिलता है। परीक्षा में मिनट को पहले डिग्री में बदलें। / \(112^\circ 30'\) means \(112.5^\circ\), so the value is \(5\pi/8\). In exams, first convert minutes into degrees.
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What is the principal radian angle for a rotation of \(-\frac{11}{8}\) revolution?
B. \(\frac{5\pi}{4}\)
घूर्णन \(-\frac{11}{8}\times2\pi=-\frac{11\pi}{4}\) है और \(4\pi\) जोड़ने पर \(\frac{5\pi}{4}\) मिलता है। परीक्षा में चक्कर को पहले रेडियन में बदलें। / The rotation is \(-\frac{11}{8}\times2\pi=-\frac{11\pi}{4}\), and adding \(4\pi\) gives \(\frac{5\pi}{4}\). In exams, first convert revolutions into radians.
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What is the radian measure of a total rotation of (7) complete revolutions and \(135^\circ\)?
C. \(\frac{59\pi}{4}\)
(7) चक्कर \(14\pi\) हैं और \(135^\circ=\frac{3\pi}{4}\), इसलिए कुल \(\frac{59\pi}{4}\) है। परीक्षा में चक्कर और अतिरिक्त कोण अलग-अलग बदलें। / (7) revolutions are \(14\pi\) and \(135^\circ=\frac{3\pi}{4}\), so the total is \(\frac{59\pi}{4}\). In exams, convert revolutions and extra angle separately.
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What is the radian measure of \(12^\circ30'\)?
A. \(\frac{5\pi}{72}\)
\(12^\circ30'=12.5^\circ=\frac{25}{2}^\circ\) होता है। रेडियन में \(\frac{25}{2}\times\frac{\pi}{180}=\frac{5\pi}{72}\) है। / \(12^\circ30'=12.5^\circ=\frac{25}{2}^\circ\). In radians it is \(\frac{25}{2}\times\frac{\pi}{180}=\frac{5\pi}{72}\).
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C. \(\frac{3\pi}{2}\)
ऋणात्मक (y)-अक्ष \(270^\circ\) पर होता है। इसका रेडियन माप \(\frac{3\pi}{2}\) है। / The negative (y)-axis is at \(270^\circ\). Its radian measure is \(\frac{3\pi}{2}\).
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If an angle is (3150') then what is its radian measure?
B. \(\frac{7\pi}{24}\)
\(3150'=52.5^\circ\) और \(52.5^\circ=\frac{7\pi}{24}\) है। पहले मिनट को डिग्री में बदलें। / \(3150'=52.5^\circ\) and \(52.5^\circ=\frac{7\pi}{24}\). Convert minutes into degrees first.
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C. \( \frac{17\pi}{9} \)
चतुर्थ चतुर्थांश में \( \theta=2\pi-\frac{\pi}{9}=\frac{17\pi}{9} \) है। रेडियन में पूर्ण चक्कर \(2\pi\) होता है। / In the fourth quadrant \( \theta=2\pi-\frac{\pi}{9}=\frac{17\pi}{9} \). A full revolution in radians is \(2\pi\).
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What is the radian measure of \(137^\circ 30'\)?
B. \( \frac{23\pi}{24} \) रेडियन\( \frac{23\pi}{24} \) radians
\(137^\circ30'=137.5^\circ\) और \(137.5^\circ\times\frac{\pi}{180}=\frac{55\pi}{72}\) है। / \(137^\circ30'=137.5^\circ\), and \(137.5^\circ\times\frac{\pi}{180}=\frac{55\pi}{72}\).
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What will be the radian measure of \(-315^\circ\)?
B. \(-\frac{7\pi}{4}\) रेडियन\(-\frac{7\pi}{4}\) radians
\(-315^\circ=\frac{-315\pi}{180}=-\frac{7\pi}{4}\) है। ऋणात्मक चिह्न को अंतिम उत्तर तक बनाए रखें। / \(-315^\circ=\frac{-315\pi}{180}=-\frac{7\pi}{4}\). Keep the negative sign until the final answer.
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B. \( \frac{5\pi}{6} \) रेडियन\( \frac{5\pi}{6} \) radians
\(150^\circ=\frac{150\pi}{180}=\frac{5\pi}{6}\) है। \( \frac{2\pi}{3} \) का अर्थ \(120^\circ\) होता है। / \(150^\circ=\frac{150\pi}{180}=\frac{5\pi}{6}\). \( \frac{2\pi}{3} \) means \(120^\circ\).
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If (1) radian is written approximately in degrees then which is the nearest correct value?
D. \(57.3^\circ\)
(1) रेडियन \( \frac{180^\circ}{\pi} \approx 57.3^\circ \) होता है। अनुमान में \( \pi\approx 3.14 \) लें। / (1) radian is \( \frac{180^\circ}{\pi} \approx 57.3^\circ \). Use \( \pi\approx 3.14 \) for approximation.
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Which is the radian measure of \(-135^\circ\)?
D. \(-\frac{3\pi}{4}\) रेडियन\(-\frac{3\pi}{4}\) radians
\(-135^\circ=\frac{-135\pi}{180}=-\frac{3\pi}{4}\) होता है। ऋणात्मक कोण का चिह्न बनाए रखें। / \(-135^\circ=\frac{-135\pi}{180}=-\frac{3\pi}{4}\). Keep the negative sign while converting.
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What will be the radian measure of \(105^\circ\)?
B. \( \frac{7\pi}{12} \) रेडियन\( \frac{7\pi}{12} \) radians
\(105^\circ=\frac{105\pi}{180}=\frac{7\pi}{12}\) होता है। पहले भिन्न को सरल करें फिर उत्तर चुनें। / \(105^\circ=\frac{105\pi}{180}=\frac{7\pi}{12}\). Simplify the fraction before choosing the answer.
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What is the radian form of \(315^\circ\)?
C. \( \frac{7\pi}{4} \) रेडियन\( \frac{7\pi}{4} \) radians
\(315^\circ=\frac{315\pi}{180}=\frac{7\pi}{4}\) होता है। \(45^\circ\) के गुणजों का अभ्यास करें। / \(315^\circ=\frac{315\pi}{180}=\frac{7\pi}{4}\). Practice multiples of \(45^\circ\).
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Which is the radian measure of \(240^\circ\)?
D. \( \frac{4\pi}{3} \) रेडियन\( \frac{4\pi}{3} \) radians
\(240^\circ=\frac{240\pi}{180}=\frac{4\pi}{3}\) होता है। भाग देकर भिन्न को कम करें। / \(240^\circ=\frac{240\pi}{180}=\frac{4\pi}{3}\). Reduce the fraction after division.
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Which is the radian measure of \(270^\circ\)?
A. \( \frac{3\pi}{2} \) रेडियन\( \frac{3\pi}{2} \) radians
\(270^\circ=\frac{270\pi}{180}=\frac{3\pi}{2}\) होता है। \(90^\circ\) के गुणजों को जल्दी पहचानें। / \(270^\circ=\frac{270\pi}{180}=\frac{3\pi}{2}\). Quickly identify multiples of \(90^\circ\).
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What is the radian measure of a right angle?
B. \( \frac{\pi}{2} \) रेडियन\( \frac{\pi}{2} \) radians
समकोण \(90^\circ\) होता है और इसका रेडियन माप \( \frac{\pi}{2} \) है। मानक रूपांतरण याद रखें। / A right angle is \(90^\circ\) and its radian measure is \( \frac{\pi}{2} \). Remember standard conversions.
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What is the radian measure of \(330^\circ\)?
A. \(\frac{11\pi}{6}\)
\(330^\circ\times\frac{\pi}{180^\circ}=\frac{11\pi}{6}\) होता है। \(30^\circ=\frac{\pi}{6}\) से भी याद रख सकते हैं। / \(330^\circ\times\frac{\pi}{180^\circ}=\frac{11\pi}{6}\). You can also remember it using \(30^\circ=\frac{\pi}{6}\).
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What is the radian measure of \(240^\circ\)?
D. \(\frac{4\pi}{3}\)
\(240^\circ\times\frac{\pi}{180^\circ}=\frac{4\pi}{3}\) होता है। (240:180) को (4:3) करें। / \(240^\circ\times\frac{\pi}{180^\circ}=\frac{4\pi}{3}\). Reduce (240:180) to (4:3).
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What is the radian measure of \(105^\circ\)?
C. \(\frac{7\pi}{12}\)
\(105^\circ\times\frac{\pi}{180^\circ}=\frac{7\pi}{12}\) होता है। अनुपात को सरल करना मुख्य चरण है। / \(105^\circ\times\frac{\pi}{180^\circ}=\frac{7\pi}{12}\). Simplifying the ratio is the main step.
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What is the radian measure of \(135^\circ\)?
C. \(\frac{3\pi}{4}\)
\(135^\circ \times \frac{\pi}{180^\circ}=\frac{3\pi}{4}\) होता है। (135:180) को (3:4) करें। / \(135^\circ \times \frac{\pi}{180^\circ}=\frac{3\pi}{4}\). Reduce (135:180) to (3:4).
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What is the radian measure of \(15^\circ\)?
B. \(\frac{\pi}{12}\)
\(15^\circ \times \frac{\pi}{180^\circ}=\frac{\pi}{12}\) होता है। (15) और (180) को (15) से सरल करें। / \(15^\circ \times \frac{\pi}{180^\circ}=\frac{\pi}{12}\). Simplify (15) and (180) by (15).
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What is the radian measure of \(270^\circ\)?
C. \(\frac{3\pi}{2}\)
\(270^\circ=\frac{270\pi}{180}=\frac{3\pi}{2}\) होता है। \(90^\circ\) को \(\frac{\pi}{2}\) मानकर भी सोच सकते हैं। / \(270^\circ=\frac{270\pi}{180}=\frac{3\pi}{2}\). You can also think of \(90^\circ\) as \(\frac{\pi}{2}\).
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What is the radian measure of \(150^\circ\)?
A. \(\frac{5\pi}{6}\)
\(150^\circ \times \frac{\pi}{180^\circ}=\frac{5\pi}{6}\) होता है। (150) और (180) को (30) से सरल करें। / \(150^\circ \times \frac{\pi}{180^\circ}=\frac{5\pi}{6}\). Simplify (150) and (180) by (30).
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What is the radian measure of \(60^\circ\)?
B. \(\frac{\pi}{3}\)
\(60^\circ \times \frac{\pi}{180^\circ}=\frac{\pi}{3}\) होता है। (180) से सरल करना न भूलें। / \(60^\circ \times \frac{\pi}{180^\circ}=\frac{\pi}{3}\). Do not forget to simplify by (180).
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What is the radian measure of \(45^\circ\)?
C. \(\frac{\pi}{4}\)
\(45^\circ\), \(180^\circ\) का \(\frac{1}{4}\) भाग है इसलिए \(\frac{\pi}{4}\) रेडियन होगा। अनुपात विधि आसान रहती है। / \(45^\circ\) is \(\frac{1}{4}\) of \(180^\circ\), so it is \(\frac{\pi}{4}\) radians. The ratio method is simple.
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If the complement of an angle is \(\frac{1}{5}\) of its supplement then what is the angle?
C. \(67^\circ30'\)
यदि कोण (x) है तो (90^\circ-x=\frac{1}{5}\(180^\circ-x\))। हल करने पर \(x=67^\circ30'\) मिलता है। / If the angle is (x) then (90^\circ-x=\frac{1}{5}\(180^\circ-x\)). Solving gives \(x=67^\circ30'\).
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The supplement of an angle is \(40^\circ\) less than twice the angle. What is the angle?
C. \(\frac{220^\circ}{3}\)
यदि कोण (x) है तो \(180^\circ-x=2x-40^\circ\) होगा। इससे \(x=\frac{220^\circ}{3}\) मिलता है। / If the angle is (x) then \(180^\circ-x=2x-40^\circ\). This gives \(x=\frac{220^\circ}{3}\).
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The supplement of an angle is (3) times the angle. What is the angle?
C. \(45^\circ\)
यदि कोण (x) है तो \(180^\circ-x=3x\) से \(x=45^\circ\) मिलता है। संपूरक कोणों का योग \(180^\circ\) होता है। / If the angle is (x) then \(180^\circ-x=3x\) gives \(x=45^\circ\). Supplementary angles add to \(180^\circ\).
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A. सुरक्षित मुख सेवन के साथ पूरक नली आहारSupplementary tube feeding with safe oral intake
दो मार्ग मिलकर कुल जरूरत पूरी कर सकते हैं। परीक्षा में कुल सेवन और सुरक्षा दोनों देखें। / Two routes together can meet total needs. In exams check total intake and safety.
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If oral intake is safe but inadequate how can tube feeding be used?
A. पूरक पोषण के रूप मेंAs supplementary nutrition
नली आहार मुख सेवन की कमी पूरी करने में सहायक हो सकता है। परीक्षा में पूरक मार्ग को पर्याप्तता से जोड़ें। / Tube feeding can help complete the gap in oral intake. In exams connect supplementary route with adequacy.
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If a patient eats a little orally but needs are not met which option may be appropriate?
A. पूरक नली आहारSupplementary tube feeding
मुख सेवन कम हो तो पूरक नली आहार पर विचार हो सकता है। परीक्षा में पर्याप्तता और सुरक्षा दोनों देखें। / If oral intake is low supplementary tube feeding may be considered. In exams consider adequacy and safety.
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If a patient is eating a little orally but needs are not being met what can be done?
A. पूरक नली आहार पर विचार किया जा सकता हैSupplementary tube feeding may be considered
मुख सेवन पर्याप्त न हो तो अतिरिक्त पोषण मार्ग की जरूरत हो सकती है। परीक्षा में पर्याप्तता और सुरक्षा दोनों देखें। / If oral intake is inadequate an additional feeding route may be needed. In exams consider both adequacy and safety.
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A. \(\frac{\pi}{4}\)
अंतर \(\frac{5\pi}{2}-2\theta\) को \(2\pi\) का गुणज होना चाहिए। दिए अंतराल में \(\theta=\frac{\pi}{4}\) उपयुक्त 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.
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If \(\pi=\frac{22}{7}\) and (5) radians are converted into degrees what is the approximate value?
B. \(286^\circ21'49''\)
(5) रेडियन \(=5\times\frac{180^\circ}{\pi}\) है। \(\pi=\frac{22}{7}\) रखने पर लगभग \(286^\circ21'49''\) मिलता है। / (5) radians \(=5\times\frac{180^\circ}{\pi}\). Using \(\pi=\frac{22}{7}\) gives approximately \(286^\circ21'49''\).
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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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Through how many radians does the hour hand turn from (1:20) to (6:50)?
B. \(\frac{11\pi}{12}\)
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 time difference is \(\frac{11}{2}\) hours and the hour hand turns \(30^\circ\) per hour. The total angle is \(165^\circ=\frac{11\pi}{12}\).
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Through how many radians does the minute hand turn from (4:12) to (4:47)?
C. \(\frac{7\pi}{6}\)
समय अंतर (35) मिनट है। कोण \(\frac{35}{60}\times2\pi=\frac{7\pi}{6}\) रेडियन है। / The time difference is (35) minutes. The angle is \(\frac{35}{60}\times2\pi=\frac{7\pi}{6}\) radians.
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B. (2)
\(75^\circ=\frac{5\pi}{12}\) है और \(\frac{53\pi}{12}=4\pi+\frac{5\pi}{12}\)। \(4\pi\) में (2) पूर्ण चक्कर होते हैं। / \(75^\circ=\frac{5\pi}{12}\) and \(\frac{53\pi}{12}=4\pi+\frac{5\pi}{12}\). \(4\pi\) contains (2) complete revolutions.
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What is the reference angle of \(\frac{7\pi}{5}\)?
B. \(\frac{2\pi}{5}\)
\(\frac{7\pi}{5}\) तृतीय चतुर्थांश में है। संदर्भ कोण \(\frac{7\pi}{5}-\pi=\frac{2\pi}{5}\) है। / \(\frac{7\pi}{5}\) lies in the third quadrant. The reference angle is \(\frac{7\pi}{5}-\pi=\frac{2\pi}{5}\).
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Convert the angle \(18^\circ24'\) into radians.
B. \(\frac{23\pi}{225}\)
\(18^\circ24'=\frac{92}{5}^\circ\) है। रेडियन में \(\frac{92}{5}\times\frac{\pi}{180}=\frac{23\pi}{225}\) होगा। / \(18^\circ24'=\frac{92}{5}^\circ\). In radians it is \(\frac{92}{5}\times\frac{\pi}{180}=\frac{23\pi}{225}\).
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B. \(\frac{\pi}{4}\)
(\frac{\pi}{2}-x=\frac{1}{3}\(\pi-x\)) रखें। इससे \(x=\frac{\pi}{4}\) मिलता है। / Set (\frac{\pi}{2}-x=\frac{1}{3}\(\pi-x\)). This gives \(x=\frac{\pi}{4}\).
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Which value is correct when \(125^\circ15'30''\) is converted into radians?
A. \(\frac{15031\pi}{21600}\)
\(125^\circ15'30''=\frac{450930}{3600}^\circ\) है। इसे \(\frac{\pi}{180}\) से गुणा करने पर \(\frac{15031\pi}{21600}\) मिलता है। / \(125^\circ15'30''=\frac{450930}{3600}^\circ\). Multiplying by \(\frac{\pi}{180}\) gives \(\frac{15031\pi}{21600}\).
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What is the coterminal angle of \(-\frac{41\pi}{9}\) between (0) and \(2\pi\)?
D. \(\frac{13\pi}{9}\)
\(-\frac{41\pi}{9}+6\pi=\frac{13\pi}{9}\) है। नकारात्मक कोण में \(2\pi\) के गुणज जोड़ें। / \(-\frac{41\pi}{9}+6\pi=\frac{13\pi}{9}\). Add multiples of \(2\pi\) to a negative angle.
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Which value is obtained when the angle \(137^\circ30'\) is converted into radians?
B. \(\frac{55\pi}{72}\)
\(137^\circ30'=\frac{275}{2}^\circ\) होता है। रेडियन के लिए \(\frac{\pi}{180}\) से गुणा करें। / \(137^\circ30'=\frac{275}{2}^\circ\). Multiply by \(\frac{\pi}{180}\) for radians.
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Which value is obtained when \(218^\circ24'\) is converted into radians?
A. \(\frac{91\pi}{75}\)
\(218^\circ24'=218.4^\circ=\frac{1092}{5}^\circ\), इसलिए रेडियन \(\frac{91\pi}{75}\) है। परीक्षा में (24') को \(0.4^\circ\) में बदलें। / \(218^\circ24'=218.4^\circ=\frac{1092}{5}^\circ\), so the radian measure is \(\frac{91\pi}{75}\). In exams, convert (24') into \(0.4^\circ\).
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If \(x^\circ=\frac{11\pi}{36}\) radians, what is the value of (x)?
D. (55)
\(\frac{11\pi}{36}\times\frac{180^\circ}{\pi}=55^\circ\)। परीक्षा में \(\pi\) को पहले काटें। / \(\frac{11\pi}{36}\times\frac{180^\circ}{\pi}=55^\circ\). In exams, cancel \(\pi\) first.
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B. \(14\pi\) मीटर\(14\pi\) m
\(40^\circ=\frac{2\pi}{9}\) रेडियन है। दूरी \(s=63\times\frac{2\pi}{9}=14\pi\) मीटर होगी। / \(40^\circ=\frac{2\pi}{9}\) radians. The distance is \(s=63\times\frac{2\pi}{9}=14\pi\) m.
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What is the approximate degree measure of (4) radians?
C. \(229.2^\circ\)
(4) रेडियन \(=4\times\frac{180^\circ}{\pi}\approx229.2^\circ\) है। अनुमान में \(\pi\approx3.14\) रखें। / (4) radians \(=4\times\frac{180^\circ}{\pi}\approx229.2^\circ\). Use \(\pi\approx3.14\) for approximation.
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