Assertion (A): never ends with the digit zero, where n is natural number.

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Q.
Assertion (A): $6^{n}$ never ends with the digit zero, where n is natural number.
Reason (R): Any number ends with digit zero, if its prime factor is of the form $2^{m} \times 5^{n}$ , where m, n are natural numbers.

1 Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2 Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

3 Assertion (A) is true but Reason (R) is false.

4 Assertion (A) is false but Reason (R) is true.

Ans.
(1)

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

$6^{n} = {(2 \times 3)}^{n} = 2^{n} \times 3^{n}$ , Its prime factors do not contain 5 i.e., of the form $2^{m} \times 5^{n}$ ,

where m, n are natural numbers. Hence, $6^{n}$ never ends with the digit zero.

Solution

Q.
Assertion (A): $6^{n}$ never ends with the digit zero, where n is natural number.
Reason (R): Any number ends with digit zero, if its prime factor is of the form $2^{m} \times 5^{n}$ , where m, n are natural numbers.

1 Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2 Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

3 Assertion (A) is true but Reason (R) is false.

4 Assertion (A) is false but Reason (R) is true.

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Solution

Q. Assertion (A): 6n never ends with the digit zero, where n is natural number. Reason (R): Any number ends with digit zero, if its prime factor is of the form 2m×5n, where m, n are natural numbers.

1 Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2 Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

3 Assertion (A) is true but Reason (R) is false.

4 Assertion (A) is false but Reason (R) is true.

Ans. (1) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). 6n=(2×3)n=2n×3n , Its prime factors do not contain 5 i.e., of the form 2m×5n, where m, n are natural numbers. Hence, 6n never ends with the digit zero.

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Q.
Assertion (A): $6^{n}$ never ends with the digit zero, where n is natural number.
Reason (R): Any number ends with digit zero, if its prime factor is of the form $2^{m} \times 5^{n}$ , where m, n are natural numbers.