Question
State whether the following statements are True or False. Give reason in support of your answer.
(a) Between any two different rational numbers there is another rational number.
(b)
(c) 210 is 51st term of the sequence 10, 15, 20, 25, ...
(e) The range of the data shown in the following frequency distribution is 350.
| Classes | 200-250 | 250-300 | 300-350 | 350-400 | 400-450 | 450-500 | 500-550 |
| Frequencies | 0 | 7 | 3 | 8 | 4 | 0 | 0 |
Answer :
Word Count : 369
Let's analyze each statement one by one. --- ### (a) Between any two different rational numbers, there is another rational number. ✅ True Reason: The set of rational numbers (\(\mathbb{Q}\)) is dense in the real number system, meaning that between any two distinct rational numbers, there always exists another rational number. For instance, if \(a\) and \(b\) are two different rational numbers such that \(a < b\), then their arithmetic mean \[ \frac{a+b}{2} \] is also a rational number and lies strictly between \(a\) and \(b\). --- ### (b) \(\int_{-1000}^{1000} (x^{100120013001} + _____ _______ _______ _____ __________ __________ __________ ______ __________ ____ ________.
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Let's analyze each statement one by one. --- ### (a) Between any two different rational numbers, there is another rational number. ✅ True Reason: The set of rational numbers (\(\mathbb{Q}\)) is dense in the real number system, meaning that between any two distinct rational numbers, there always exists another rational number. For instance, if \(a\) and \(b\) are two different rational numbers such that \(a < b\), then their arithmetic mean \[ \frac{a+b}{2} \] is also a rational number and lies strictly between \(a\) and \(b\). --- ### (b) \(\int_{-1000}^{1000} (x^{100120013001} + _____ _______ _______ _____ __________ __________ __________ ______ __________ ____ ________.
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