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CBSE Class 10 Basic Math 2026 All Sets Solved Paper

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Question : 19 of 20
Marks: +1, -0
Assertion (A): 4n4^n can not end with the digit zero.
Reason (R): Prime factorisation of 4n is unique.
A statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:
Solution:  
Assertion (A): For a number to end with the digit zero, its prime factorisation must contain both 2 and 5.
Prime factorisation of 4n=(22)n=22n4^n = (2^2)^n = 2^{2n}
The only prime factor of 4n4^n is 2. Since 5 is not a prime factor, 4n4^n can never end with the digit zero for any natural number n.
So, Assertion is true.
Reason (R):The Fundamental Theorem of Arithmetic states that the prime factorisation of every composite number is unique, apart from the order of its factors.
So, Reason is true.
However, the uniqueness of prime factorisation (Reason) is the underlying principle used to confirm that no other prime (like 5) can exist in the factorisation of 4n4^n.
Thus, Reason is the correct explanation for Assertion.
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