Instructions

For the following questions answer them individually

Question 81

If $$\left(x^2 + \frac{1}{x^2}\right) = 8.25$$, what is the value of $$\left(x^3 - \frac{1}{x^3}\right)?$$

Question 82

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).

Question 84

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.

Question 85

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?

Question 86

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?

Question 87

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 â‚¹40 per kg and the other at â‚¹50 per kg? The cost of the mixture is â‚¹43 per kg.

Question 89

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 â‚¹250. Find the amount of the water bill.

Question 90

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?