If one root of $x^{2}-5x+6=0$ is also the root of $x^{2}+3x+c=0$,then $c = \ldots$

The denominator of a non-zero ratio is one less than twice the numerator. If the sum of the ratio and its reciprocal is $2 \frac{4}{15},$ find the ratio.

In the centre of a rectangular lawn of dimensions $50\, m \times 40\, m$,a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be $1184\, m^{2}$ [see $Fig.$]. Find the length and breadth of the pond. (in $m$)

The difference between the lengths of the sides of a right triangle which form the right angle is $7 \, cm$. If its perimeter is $30 \, cm$,find the lengths of the sides.

For a two-digit number,if the sum of its digits is equal to the product of its digits,then the number is .............

Out of the following triplets,$\ldots \ldots \ldots \ldots$ is not a Pythagorean triplet.