If one of the roots of $2x^{2}-5x+k=0$ is $\frac{7}{2}$,then $k=$ .............

Find the roots of the following quadratic equation,if they exist,by the method of completing the square: $4x^{2} + 4\sqrt{3}x + 3 = 0$.

$16x^2 + 40x + k$ is a perfect square polynomial,then $k = \ldots$

Divide $16$ into two parts such that twice the square of the larger part exceeds the square of the smaller part by $164$.

At present,Asha's age (in $years$) is $2$ more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age,Asha's age would be one year less than $10$ times the present age of Nisha. Find the present ages of both Asha and Nisha (in $years$).

Represent the following situation mathematically:
$A$ cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be $55$ minus the number of toys produced in a day. On a particular day,the total cost of production was ₹ $750$. We would like to find out the number of toys produced on that day.