State whether the following statements are True or False. Give reason

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) $\int_{-1000}^{1000}(x^{100120013001}+\cos(x))\,dx=0$

(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

20 Feb 2025

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} _________ ________ ________ ____ ___.
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