If two irrational numbers i.e. $\sqrt{2},\sqrt{5},2+\sqrt{3},2-\sqrt{3}$ etc. are added it is not necessary that sum comes out to be an irrational number always, or a rational nnumber always, or a rational number always...
Since $\sqrt{2}+\sqrt{5}=$ an irrational number
$2+\sqrt{\not\text{3}}+2-\sqrt{\not\text{3}}=4=$ a rational number
So we see that $\sqrt{2}$ and $\sqrt{5}$ are irrational numbers, and their sum is also irrational.
But $2+\sqrt{3}$ and $2-\sqrt{3}$ are also irrational numbers, and their sum is rational number $'4'.$
So sum of two irrational numbers can be either an irrational number or a rational number depending which numbers are being added.
So options $(a)$ and $(b)$ are totally wrong, because they are not 'always' true.
Option $(c)$ is correcrt because sum can be either irrational or rational and option $(c)$ is verifying this statement.
Option $(d) -$ again it is not always true, if we add two irrational numbers like $2+\sqrt{3}$ and $2-\sqrt{3}.$
Sum is an integer $= 4,$ but if we add $\sqrt{3}$ and $\sqrt{3},$ sum is $2\sqrt{3}$ which is not an integer but again an irrational number.
So option $(d)$ is also incorrect.
Hence, correct option is $(c).$
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Number of heads
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$2$
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$1$
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$0$
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Frequency
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$200$
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$550$
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$250$
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