Question

Assertion (a) :6ⁿ ends with the digit zero, where n is natural number.

Reason (R) : Any number ends with the digit zero, if its prime factor is of the form 2^m x 5^n, where m&n are natural numbers.

(a) Both A and R are true and R is the correct explanation for A.
(b) Both A and R are true and R is not the correct explanation for A.
(c) A is true but R is false.
(d) A is false but R is true.​

Answer 1

The assertion (a) is true and the reason provided is the correct explanation for it.

Step-by-step explanation:

The given assertion (a) states that 6ⁿ ends with the digit zero, where n is a natural number. The reason (R) provided is that any number ends with the digit zero if its prime factor is of the form 2^m x 5^n, where m and n are natural numbers.

This assertion and reason are both true. Let's examine why. When we calculate 6ⁿ, it can be written as 2³ⁿ x 3ⁿ. The prime factorization of 6 is 2 x 3. So, when we raise 6 to the power of any natural number, we are essentially raising 2³ⁿ x 3ⁿ to that power.

Since 2³ⁿ and 3ⁿ both end with the digit zero (2³=8, 3ⁿ ends with 0 for any n), the product of these two numbers will also end with the digit zero. Therefore, assertion (a) is true, and the reason provided is the correct explanation for assertion (a).