The length of a rectangle is five times the breadth. If the minimum perimeter of the rectangle is $180 \ cm$,then:

The number of points $P(x, y)$ with natural numbers as coordinates that lie inside the quadrilateral formed by the lines $2x + y = 2$,$x = 0$,$y = 0$,and $x + y = 5$ is

Eleven apples are distributed among a girl and a boy. Then,which one of the following statements is true?

How many litres of water will have to be added to $1125$ litres of the $45 \%$ solution of acid so that the resulting mixture will contain more than $25 \%$ but less than $30 \%$ acid content?

$A$ solution of $9 \%$ acid is to be diluted by adding $3 \%$ acid solution to it. The resulting mixture is to be more than $5 \%$ but less than $7 \%$ acid. If there is $460 \text{ L}$ of the $9 \%$ solution,how many litres of $3 \%$ solution will have to be added?

The cost and revenue functions of a product are given by $C(x) = 20x + 4000$ and $R(x) = 60x + 2000$ respectively,where $x$ is the number of items produced and sold. The value of $x$ to earn profit is