| Assertion (A): For no value of n. where n is a natural number, the number \[{{8}^{n}}\] ends with the digit zero. |
| Reason (R): The prime factorisation of a natural number is unique, except for the order of its factors. |
A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A)
C) Assertion (A) is true but reason (R) is false
D) Assertion (A) is false but reason (R) is true
Correct Answer: A
Solution :
| Sol. [a] We have, \[{{8}^{n}}={{({{2}^{3}})}^{n}}={{2}^{3n}},\] so the only prime in the factorisation of \[{{8}^{n}}\] is 2. So, from the uniqueness of the Fundamental Theorem of Arithmetic we can say that there are no other primes in the factorisation of \[{{8}^{n}}\]. So, there is no natural number n for which 8" ends with the digit zero. |
| \[\therefore \] Assertion: True; Reason: True and it is the correct explanation of assertion. |
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