Statement A (Assertion): 3" cannot end with digit zero for any natural number n Statement B (Reason): Any positive integer ending with the digit zero is divisible by 2 and 5 both. 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 and 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
Question
Statement A (Assertion): 3" cannot end with digit zero for any natural number n Statement B (Reason): Any positive integer ending with the digit zero is divisible by 2 and 5 both. 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 and 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
Solution
The correct answer is b. Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).
Here's why:
Statement A is true because the cube of any natural number never ends with a zero. This is because the cube of a number is the product of the number multiplied by itself twice. Since no single digit number when multiplied by itself gives a result ending in zero, the cube of any number also cannot end in zero.
Statement B is also true. Any positive integer ending with the digit zero is indeed divisible by both 2 and 5. This is because the factors of 10 are 2 and 5, and any number ending in zero can be divided evenly by 10, and therefore also by 2 and 5.
However, Statement B does not explain Statement A. The divisibility of a number ending in zero by 2 and 5 has no bearing on whether the cube of a number can end in zero. They are two separate mathematical properties. Therefore, the reason (R) is not the correct explanation of the assertion (A).
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