## A tank fills completely in 2 hours if both the taps are open. If only one of the taps is open at the given time, the smaller tap takes 3 hours more than the larger one to fill the tank. How much time does each tap take to fill the tank completely?

## Mr. Dinesh owns an agricultural farm at village Talvel. The length of the farm is 10 meters more than twice the breadth. In order to harvest rain water, he dug a square shaped pond inside the farm. The side of pond is 1/3 of the breadth of the farm. The area of the farm is 20 times the area of the pond. Find the length and breadth of the farm and of the pond.

## Ranjana wants to distribute 540 oranges among some students. If 30 students were more each would get 3 oranges less. Find the number of students.

## The difference between squares of two numbers is 120. The square of smaller number is twice the greater number. Find the numbers.

## Mukund possesses ₹50 more than what Sagar possesses. The product of the amount they have is 15,000. Find the amount each one has.

## Find quadratic equation such that its roots are square of sum of the roots and square of difference of the roots of equation

## The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35, find the equation.

## Find m if (m – 12) x2 + 2 (m – 12) x + 2 = 0 has real and equal roots.

## Solve the following quadratic equation.

Solution: Solution: The roots are (3) (2x + 3)2 = 25 Solution: (4) m2 + 5m + 5 = 0 Solution: (5) 5m2 + 2m + 1 = 0 Solution: (6) x2 – 4x – 3 = 0 Solution:

## Determine the nature of roots for each of the quadratic equation.

(1) 3×2 – 5x + 7 = 0 Solution: (2) √3×2 + √2x – 2 √ 3 = 0 Solution: (3) m2 – 2m + 1 = 0 Solution: