निम्नलिखित कथनों पर विचार कीजिए:

1. रेडियन माप में 1°, 0.02 रेडियन से कम है। 

2. डिग्री माप में 1 रेडियन 45° से अधिक है। 

उपरोक्त कथनों में से कौन-सा/कौन-से कथन सही है/हैं?

  1. केवल 1 
  2. केवल 2 
  3. 1 और 2 दोनों 
  4. ना तो 1 और ना ही 2 

Answer (Detailed Solution Below)

Option 3 : 1 और 2 दोनों 
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Detailed Solution

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संकल्पना:

\(1^{0} =\frac{\pi}{180} \text { rad } \\\)

\(\text { 1 radian }=\frac{180}{\pi} \text {degree} \)

गणना:

कथन 1: 

\(\begin{aligned} 1^{0} &=\frac{\pi}{180} \text { rad } \\ &=\frac{3.14}{180}\\&=0.01746 <0.02 \end{aligned}\)

कथन 2:  

\(\text { 1 radian }=\frac{180}{\pi}\\=\frac{180}{3 \cdot 14} \approx 57^{\circ}>45^{\circ}\)

इसलिए, दोनों कथन सही हैं। 

अतः विकल्प (3) सही है।       

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