The set of real numbers includes which of the following ?
The set of real numbers includes which of the following ?
वास्तविक संख्याओं के समूह में निम्नलिखित में स् कौन शामिल हैं?
Detailed Solution & Logic
Both Rational and Irrational Numbers/ परिमेय और अपरिमेय दोनों संख्याएँ
📖 Explanation
The set of real numbers includes:
👉 Rational Numbers (e.g., $\frac{1}{2}, -3, 0.75$)
👉 Irrational Numbers (e.g., $\sqrt{2}, \pi$)
📌 So, real numbers = Rational + Irrational numbers
वास्तविक संख्याएँ (Real Numbers) में शामिल हैं:
👉 परिमेय संख्याएँ (जैसे $\frac{1}{2}, -3, 0.75$)
👉 अपरिमेय संख्याएँ (जैसे $\sqrt{2}, \pi$)
📌 इसलिए, वास्तविक संख्याएँ = परिमेय + अपरिमेय संख्याएँ
⭐ Extra Facts
- Rational numbers can be written as $\frac{p}{q}$ where $q \neq 0$
- Irrational numbers cannot be expressed as fractions
- All real numbers lie on the number line
- परिमेय संख्याएँ $\frac{p}{q}$ के रूप में लिखी जा सकती हैं ($q \neq 0$)
- अपरिमेय संख्याएँ भिन्न के रूप में नहीं लिखी जा सकतीं
- सभी वास्तविक संख्याएँ संख्या रेखा पर स्थित होती हैं
Similar Practice Questions
Find the least number, which, when divided by 20, 25, 35 and 40 leaves remainders 14, 19, 29 and 34, respectively.
Find the least number, which, when divided by 20, 25, 35 and 40 leaves remainders...
Which of the following number is NOT a perfect square?
Which of the following number is NOT a perfect square? निम्नलिखित में से कौन –...
Evaluate :
Evaluate / हल कीजिए : \(41 – [21 -\{11 -(15 – 6 \div 3\times 3)\}]\)
The sum of two numbers is 37, and the difference of their squares is 185. What is the difference between the two numbers?
The sum of two numbers is 37, and the difference of their squares is 185....
What is the smallest number which when divided by 16, 18, 20, and 25 leaves a remainder of 4 in each case, but is exactly divisible by 7?
What is the smallest number which when divided by 16, 18, 20, and 25 leaves...
Simplify
Simplify / मान ज्ञात कीजिए। : \(5\frac{1}{2} +6\frac{1}{2} \:- 8\frac{1}{4} + 24 -\: [9\:- \{6-...
How many natural numbers are there between $ 11^2 $ and $ 12^2 $ ?
How many natural numbers are there between $ 11^2 $ and $ 12^2 $ ?...