Every positive even integer is of the form ........ for some inte… - Vidyadip

MCQ

Every positive even integer is of the form $........$ for some integer $'q\ '$.

A
$2q + 1$
✓
$2q$
C
$2q - 1$
D
None of these

✓

Answer

Correct option: B.

$2q$

Let a be any positive integer and $b = 2$
Then by applying Euclid’s Division Lemma, we have,
$a = 2q + r$ where $0\leq\text{r}<2\text{ r}=0\text{ r}1$
Therefore, $a = 2q$ or $2q + 1$
Thus, it is clear that $a = 2q$
i.e. $a$ is an even integer in the form of $2q$

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