B. उसके कण बहुत पास होते हैं/Its particles are very close
Step 1
Concept
There is very little empty space between solid particles. Exam tip: remember solids are nearly incompressible.
Step 2
Why this answer is correct
The correct answer is B. उसके कण बहुत पास होते हैं / Its particles are very close. There is very little empty space between solid particles. Exam tip: remember solids are nearly incompressible.
Step 3
Exam Tip
ठोस के कणों के बीच बहुत कम रिक्त स्थान होता है। परीक्षा में ठोस की असंपीड्यता याद रखें।
A. क्योंकि कण बहुत दूर होते हैं/Because particles are far apart
Step 1
Concept
Gas particles have large empty spaces between them. Exam tip: connect distance with compressibility.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि कण बहुत दूर होते हैं / Because particles are far apart. Gas particles have large empty spaces between them. Exam tip: connect distance with compressibility.
Step 3
Exam Tip
गैस के कणों के बीच अधिक रिक्त स्थान होता है। परीक्षा में दूरी और संपीड्यता को जोड़कर पढ़ें।
Ice is solid and water is liquid. Exam tip: change of state does not always change substance identity.
Step 2
Why this answer is correct
The correct answer is B. भौतिक अवस्था का / Physical state. Ice is solid and water is liquid. Exam tip: change of state does not always change substance identity.
Step 3
Exam Tip
बर्फ ठोस और जल द्रव अवस्था है। परीक्षा में अवस्था बदलने पर पदार्थ की पहचान तुरंत न बदलें।
Solid liquid and gas are common states of matter. Exam tip: keep states and classification separate.
Step 2
Why this answer is correct
The correct answer is A. ठोस द्रव गैस / Solid liquid gas. Solid liquid and gas are common states of matter. Exam tip: keep states and classification separate.
Step 3
Exam Tip
ठोस द्रव और गैस पदार्थ की सामान्य अवस्थाएँ हैं। परीक्षा में अवस्था और वर्गीकरण अलग रखें।
B. जिसमें द्रव्यमान हो और स्थान घेरता हो/Has mass and occupies space
Step 1
Concept
Matter has mass and occupies space. Exam tip: remember this basic definition.
Step 2
Why this answer is correct
The correct answer is B. जिसमें द्रव्यमान हो और स्थान घेरता हो / Has mass and occupies space. Matter has mass and occupies space. Exam tip: remember this basic definition.
Step 3
Exam Tip
पदार्थ में द्रव्यमान होता है और वह स्थान घेरता है। परीक्षा में पदार्थ की परिभाषा याद रखें।
\(30^\circ-15'=29^\circ45'=\frac{119}{4}^\circ\), so the radian measure is \(\frac{119\pi}{720}\). In exams, convert minutes into a fraction of a degree.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{119\pi}{720}\). \(30^\circ-15'=29^\circ45'=\frac{119}{4}^\circ\), so the radian measure is \(\frac{119\pi}{720}\). In exams, convert minutes into a fraction of a degree.
Step 3
Exam Tip
\(30^\circ-15'=29^\circ45'=\frac{119}{4}^\circ\), इसलिए रेडियन माप \(\frac{119\pi}{720}\) है। परीक्षा में मिनट को डिग्री के अंश में बदलें।
\(\frac{7\pi}{18}=70^\circ\), so the original angle is \(70^\circ-20^\circ=50^\circ\). In exams, first convert the final measure into degrees.
Step 2
Why this answer is correct
The correct answer is D. \(50^\circ\). \(\frac{7\pi}{18}=70^\circ\), so the original angle is \(70^\circ-20^\circ=50^\circ\). In exams, first convert the final measure into degrees.
Step 3
Exam Tip
\(\frac{7\pi}{18}=70^\circ\), इसलिए मूल कोण \(70^\circ-20^\circ=50^\circ\) है। परीक्षा में अंतिम माप को पहले डिग्री में बदलें।
The first angle gives \(\frac{\pi}{4}\) and the second gives \(\frac{\pi}{6}\), so the sum is \(\frac{5\pi}{12}\). In exams, reduce both angles separately.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{5\pi}{12}\). The first angle gives \(\frac{\pi}{4}\) and the second gives \(\frac{\pi}{6}\), so the sum is \(\frac{5\pi}{12}\). In exams, reduce both angles separately.
Step 3
Exam Tip
पहले कोण का मान \(\frac{\pi}{4}\) और दूसरे का \(\frac{\pi}{6}\) है, इसलिए योग \(\frac{5\pi}{12}\) है। परीक्षा में दोनों कोणों को अलग-अलग घटाएं।
A. पहला चतुर्थांश और \(45^\circ\)/First quadrant and \(45^\circ\)
Step 1
Concept
\(765^\circ-720^\circ=45^\circ\), which lies in the first quadrant. In exams, first find the coterminal angle and then the reference angle.
Step 2
Why this answer is correct
The correct answer is A. पहला चतुर्थांश और \(45^\circ\) / First quadrant and \(45^\circ\). \(765^\circ-720^\circ=45^\circ\), which lies in the first quadrant. In exams, first find the coterminal angle and then the reference angle.
Step 3
Exam Tip
\(765^\circ-720^\circ=45^\circ\), जो पहले चतुर्थांश में है। परीक्षा में पहले सह-टर्मिनल कोण निकालकर संदर्भ कोण देखें।
Since (a-b=4b) must be a multiple of \(360^\circ\), the least \(b=90^\circ\). In exams, apply the coterminal condition to the difference.
Step 2
Why this answer is correct
The correct answer is D. \(90^\circ\). Since (a-b=4b) must be a multiple of \(360^\circ\), the least \(b=90^\circ\). In exams, apply the coterminal condition to the difference.
Step 3
Exam Tip
क्योंकि (a-b=4b) को \(360^\circ\) का गुणज होना चाहिए, सबसे छोटा \(b=90^\circ\) है। परीक्षा में सह-टर्मिनल शर्त को अंतर पर लगाएं।
The difference of coterminal angles is \(2\pi n\), so \(\frac{\theta-\phi}{2\pi}\) is an integer. In exams, check the difference, not the sum.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{\theta-\phi}{2\pi}\). The difference of coterminal angles is \(2\pi n\), so \(\frac{\theta-\phi}{2\pi}\) is an integer. In exams, check the difference, not the sum.
Step 3
Exam Tip
सह-टर्मिनल कोणों का अंतर \(2\pi n\) होता है, इसलिए \(\frac{\theta-\phi}{2\pi}\) पूर्णांक होगा। परीक्षा में अंतर को देखें, योग को नहीं।
(1) radian is approximately \(57.2958^\circ\), which is close to \(57^\circ 18'\). In exams, multiply the decimal part by (60).
Step 2
Why this answer is correct
The correct answer is A. \(57^\circ 18'\). (1) radian is approximately \(57.2958^\circ\), which is close to \(57^\circ 18'\). In exams, multiply the decimal part by (60).
Step 3
Exam Tip
(1) रेडियन लगभग \(57.2958^\circ\) होता है, जो \(57^\circ 18'\) के निकट है। परीक्षा में दशमलव भाग को (60) 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 \(2\pi\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{9\pi}{2}\). \(2.25=\frac{9}{4}\) revolutions, so the angle is \(\frac{9}{4}\times2\pi=\frac{9\pi}{2}\). In exams, multiply revolutions by \(2\pi\).
Step 3
Exam Tip
\(2.25=\frac{9}{4}\) चक्कर है, इसलिए कोण \(\frac{9}{4}\times2\pi=\frac{9\pi}{2}\) है। परीक्षा में चक्कर को \(2\pi\) से गुणा करें।
\(72^\circ=\frac{2\pi}{5}\) and \(r=\frac{s}{\theta}=\frac{4\pi}{2\pi/5}=10\) cm. In exams, keep the angle in radians when using the formula.
Step 2
Why this answer is correct
The correct answer is D. (10) सेमी / (10) cm. \(72^\circ=\frac{2\pi}{5}\) and \(r=\frac{s}{\theta}=\frac{4\pi}{2\pi/5}=10\) cm. In exams, keep the angle in radians when using the formula.
Step 3
Exam Tip
\(72^\circ=\frac{2\pi}{5}\) और \(r=\frac{s}{\theta}=\frac{4\pi}{2\pi/5}=10\) सेमी है। परीक्षा में कोण को रेडियन में रखकर सूत्र लगाएं।
\(\theta=\frac{11}{21}\) radians and the degree measure is \(\frac{11}{21}\times\frac{180^\circ\times7}{22}=30^\circ\). In exams, convert radians to degrees carefully.
Step 2
Why this answer is correct
The correct answer is B. \(30^\circ\). \(\theta=\frac{11}{21}\) radians and the degree measure is \(\frac{11}{21}\times\frac{180^\circ\times7}{22}=30^\circ\). In exams, convert radians to degrees carefully.
Step 3
Exam Tip
\(\theta=\frac{11}{21}\) रेडियन और डिग्री माप \(\frac{11}{21}\times\frac{180^\circ\times7}{22}=30^\circ\) है। परीक्षा में रेडियन से डिग्री में सावधानी से बदलें।
\(-\frac{5\pi}{3}+2\pi=\frac{\pi}{3}\). In exams, add \(2\pi\) to convert a negative angle into a positive principal angle.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\pi}{3}\). \(-\frac{5\pi}{3}+2\pi=\frac{\pi}{3}\). In exams, add \(2\pi\) to convert a negative angle into a positive principal angle.
Step 3
Exam Tip
\(-\frac{5\pi}{3}+2\pi=\frac{\pi}{3}\) है। परीक्षा में ऋणात्मक कोण को धनात्मक बनाने के लिए \(2\pi\) जोड़ें।
The remainder of \(540^\circ\) is \(180^\circ\), so \(180^\circ+\theta\equiv 70^\circ\) and \(\theta=250^\circ\). In exams, reduce the fixed part first.
Step 2
Why this answer is correct
The correct answer is B. \(250^\circ\). The remainder of \(540^\circ\) is \(180^\circ\), so \(180^\circ+\theta\equiv 70^\circ\) and \(\theta=250^\circ\). In exams, reduce the fixed part first.
Step 3
Exam Tip
\(540^\circ\) का शेष \(180^\circ\) है, इसलिए \(180^\circ+\theta\equiv 70^\circ\) और \(\theta=250^\circ\) है। परीक्षा में पहले स्थिर भाग को घटाएं।
\(75^\circ+360^\circ=435^\circ=\frac{29\pi}{12}\), which lies between \(2\pi\) and \(3\pi\). In exams, add revolutions according to the given interval.
Step 2
Why this answer is correct
The correct answer is D. \(\frac{29\pi}{12}\). \(75^\circ+360^\circ=435^\circ=\frac{29\pi}{12}\), which lies between \(2\pi\) and \(3\pi\). In exams, add revolutions according to the given interval.
Step 3
Exam Tip
\(75^\circ+360^\circ=435^\circ=\frac{29\pi}{12}\), जो \(2\pi\) और \(3\pi\) के बीच है। परीक्षा में दी गई सीमा के अनुसार चक्कर जोड़ें।
Adding \(2\pi\) three times to \(-\frac{41\pi}{10}\) gives \(\frac{19\pi}{10}\). In exams, keep adding \(2\pi\) until the angle enters the interval.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{19\pi}{10}\). Adding \(2\pi\) three times to \(-\frac{41\pi}{10}\) gives \(\frac{19\pi}{10}\). In exams, keep adding \(2\pi\) until the angle enters the interval.
Step 3
Exam Tip
\(-\frac{41\pi}{10}\) में (3) बार \(2\pi\) जोड़ने पर \(\frac{19\pi}{10}\) मिलता है। परीक्षा में सीमा पूरी होने तक \(2\pi\) जोड़ें।
C. नहीं, क्योंकि यह \(2\pi\) का पूर्णांक गुणज नहीं है/No, because it is not an integral multiple of \(2\pi\)
Step 1
Concept
\(\frac{35\pi}{3}\div2\pi=\frac{35}{6}\), which is not an integer. In exams, check \(2\pi n\) for coterminal angles.
Step 2
Why this answer is correct
The correct answer is C. नहीं, क्योंकि यह \(2\pi\) का पूर्णांक गुणज नहीं है / No, because it is not an integral multiple of \(2\pi\). \(\frac{35\pi}{3}\div2\pi=\frac{35}{6}\), which is not an integer. In exams, check \(2\pi n\) for coterminal angles.
Step 3
Exam Tip
\(\frac{35\pi}{3}\div2\pi=\frac{35}{6}\), जो पूर्णांक नहीं है। परीक्षा में सह-टर्मिनल के लिए \(2\pi n\) जांचें।
