Question

Assertion (a) :

6^n 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

Answer:

A is false but R is true

Answer 2

Given,

Assertion (a) :

$6^{n}$ 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.

To find,

Which of the following is correct?

(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.​

Solution,

We know that,

Any number of the form $6^{n}$ has prime factors of the form $2^{m}$ x $3^{n}$ where m and n are natural numbers.

So, the assertion that $6^{n}$ ends with the digit zero is false.

Also,

Any number of the form $10^{n}$ ends with 0 at the end and has prime factors of the form $2^{m}$ x $5^{n}$ where m and n are natural numbers.

So, the reason is true.

Hence, (d) A is false but R is true is the correct option.