Quantitative Ab...

Two circles are drawn such that the smaller circle touches the bigger circle internally at one point. Triangle PQR is drawn such that it circumscribes the smaller triangle. Side RQ is tangent to both the circle and sides PR and PQ intersect each other at the centre of the bigger circle. Side RP is extended to touch the bigger circle at point T such that RT = 20 cm. What is the radius of the smaller circle if the radius of the bigger circle is 7.5 cm?

Raghu bought 3 oranges, 2 apples and a banana and paid 20 rupees. If it is known that the prices of the fruits are positive integers, how many different combinations of prices is possible?

15 employees started working on a project and worked on it for 15 days. From the sixteenth day onwards, a new employee joined the existing team every day till the project was finished. It took 25 days to finish the entire project. The same project needed to be completed starting with the minimum possible even number of employees. Considering this how many days will it take to complete the project if two employees quit the project every day starting from the second day ?

Bourne is relaxing in the Caribbean Islands in a hammock. The hammock is tied to two trees which are 10 meters apart at height of 4m above the ground. Due to his weight, the hammock sags and it is in the shape of the parabola. The centre of the hammock touches the ground. At distance of 2m from the right tree, find the height of the hammock above the ground.

[The general equation of a parabola is y = ax² + bx + c, where a, b, and c are real numbers and a≠0]

(Assume hammock as a thin rope for calculations)

A set X consists of 507 elements which are squares of natural numbers selected at random. List Y consists of elements that are remainders when the elements of set X are divided by 11. The least number of times the element that gets repeated the most can appear in the list Y is _______ .

Amar and Balu run around a circular track. If they decide to run in the opposite directions, the distance covered by Amar will be 90 m more than the distance covered by Balu when they meet for the first time. The length of the track is 60 m more than the distance covered by Amar. What will be the difference between the distances covered by Amar and Balu when they meet for the first time had they decided to run in the same direction?

In a factory, 40% of the bulbs produced are blue in colour, 20% of the bulbs are green in colour and the rest are red in colour. 30% of the red bulbs are defective while the total percentage of defective bulbs is 24%. 80% of the blue bulbs are not defective. If the number of defective blue bulbs is 120, what is the number of non-defective green bulbs?