For the following questions answer them individually
If $$\left(x^2 + \frac{1}{x^2}\right) = 8.25$$, what is the value of $$\left(x^3 - \frac{1}{x^3}\right)?$$
x varies inversely as $$(2y^2 - 5)$$ and is equal to 25 when y = 15. Find the value of x when y = 10 (approximate value).
Anil climbs a staircase stage by stage. He climbs the first 10 steps at 10 a.m., 11 more steps at 12.00 p.m. and 20 more steps at 2.00 p.m. Find the total number of steps Anil has climbed.
What are coordinates of the point that divides the line segment joining the points (4, 4) and (8, 12) internally in the ratio of 3 : 5?
Seven different coloured lights are fixed on a mast to produce signals by illuminating them. How many signals can be produced, if any number of lights is used?
In a coffee estate there are two varieties of coffee. At what ratio must the two varieties of coffee be mixed together into one at ā¹40 per kg and the other at ā¹50 per kg? The cost of the mixture is ā¹43 per kg.
If a water bill is paid before the due date, overall there is a reduction of 5% on the bill amount. A person paid the bill before the due date he got a reduction of ā¹250. Find the amount of the water bill.
Two mixtures A and B contain petrol and kerosene. A has 40% of petrol and B has 60% of petrol. If 8 litres of A and 12 litres of B are mixed together, what will be the ratio of petrol and kerosene in the new mixture?