Question 1 :
A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 $m^2$ more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m. Find its length and breadth.

Question 2 :
The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

Question 5 :
Find the roots of the following quadratic equation by factorisation: $2x^2 – x + \frac{1}{8} = 0$

Question 6 :
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

Question 7 :
John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Write an equation to find out how many marbles they had to start with.

Question 8 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $2x^2 + x + 4 = 0$

Question 9 :
Find the roots of the quadratic equation (by using the quadratic formula): $x^2-3\sqrt{5}x+10=0$

Question 10 :
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 age of Asha.