Question

If the divisor and the dividend have the like signs, then the quotient will be:
\[\begin{align}
  & \left( a \right)positive \\
 & \left( b \right)negative \\
 & \left( c \right)zero \\
 & \left( d \right)none \\
\end{align}\]

Answer 1

Hint: For solving this question, we need to note very carefully what the divisor, dividend and quotient means, after that we can very easily get to know what will happen if divisor and dividend have like signs.

Formula used:
The formula used here is
\[divisor{{\left| \!{\overline {\,
 dividend \,}} \right. }^{quotient}}\]
For the division form and
\[\dfrac{dividend}{divisor}=quotient\]for the fraction form
And also,
\[\dfrac{-ve}{-ve}=+ve\]
\[\dfrac{+ve}{+ve}=+ve\]

Complete step by step answer:
In order to solve the question, let us first see what it means,
It is given that the divisor and the dividend have like signs, now, divisor is the number that divides a number completely or with a remainder.
And dividend is the amount or the number to be divided and quotient is the number when multiplied to the divisor, we get the dividend.
So, in division form,
\[divisor{{\left| \!{\overline {\,
 dividend \,}} \right. }^{quotient}}\]
And in the fraction form,
\[\dfrac{dividend}{divisor}=quotient\]
Now as given in the question, the divisor and dividend have like signs
So, if both are positive,
Then the quotient is also positive as on being multiplied to a positive quotient only, divisor can give a positive dividend
And if both are negative,
Then also, the quotient is positive because the both negative signs cancel out.

So, the correct answer is Option A.

Note: Alternatively, the question can be answered orally also without any solving because this is a fact that whenever division or multiplication, the negative signs cancel each other out to give positive and the positive signs stay positive only.