Chord AB of circle of radius 10 cm is at a distance 8 cm from the centre O. If tangents drawn at A and B intersect at P, then the length of the tangent AP (in cm) is:

If a + b + c = 2, a² + b² + c² = 26 then the value of a³ + b³ + c³ – 3abc is

Directions : The pie graph indicates the break-up of the cost of construction of a house. Assuming that the total cost of construction is Rs 6,00,000, answer the following questions. 

The amount spent on labour exceeds the amount spent on steel by : 

Average of the test scores of a class of 'x' students is 80 and that of 'y' student is 94. When the scores of both the classes are combined, the average becomes 86. What is the ratio of x to y?

If the cost price of 25 perts is equal to the selling price of 20 pens, then profit percent is

AB is a diameter of a circle with centre O. A tangent is drawn at point A. C is a point on the circle such that BC produced meets the tangent at P. If ∠APC = 62⁰, then find the measure of the minor arc AC.

In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. x² + 31x + 240 = 0

II. 5y²+ 60y + 135 = 0

If $${45\over53}={1\over{a+{1\over b+{1\over c-{2\over 5}}}}}$$  , where a, b and c are positive integers, then what is the value of (4a-b+3c)?