IGNOU MST 1 2026 - State whether the following statements are True or False. Give a reaso

Question

State whether the following statements are True or False. Give a reason in support of your answer.

(a) Between any two different irrational numbers there is another irrational number.
(b) $\int_{-10}^{10} (x^{11} + x^{21} + x^{31}) \, dx = 0$
(c) $\begin{vmatrix} p & x & q + r \\ q & x & r + p \\ r & x & p + q \end{vmatrix} = 0$
(d) The range of the data shown in the following frequency distribution is 350.

Classes	20-25	25-30	30-35	35-40	40-45	45-50	50-55
Frequencies	0	7	3	8	4	0	0

19 Jan 2026

Answer :

Word Count : 118

(a) True. Between any two different irrational numbers, one can always find another irrational number. For example, if ( \sqrt{2} ) and ( \sqrt{3} ) are two irrationals, their average ( \frac{\sqrt{2} + \sqrt{3}}{2} ) is also irrational and

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