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.

If x + y + 3 = 0 , then find the value of x³+y³-9xy+9.

A sold a mobile phone to B at a gain of 25% and B sold it to C at a loss of 10%. If C paid ₹5,625 for it, how much did A pay (in ₹) for the phone?

If 4sin²θ=3(1+cosθ),0⁰<θ<90⁰, then what is the value of (2tanθ+4sinθ-secθ)?

A pole 23 m long reaches a window which is 3 m above the ground on one side of a street. Keeping its foot at the same point, the pole is turned to the other side of the street to reach a window 4 is m high. What is the width (in m) of the street? 

What is the height (in cm) of an equilateral triangle whose each side is 8 cm?

The width of the path around a square field is 4.5 m and its area is 105.75 m². Find the cost of fencing the path at the rate of ₹100 per metre.

In the first 10 overs of a cricket game, the run rate was only 7.2. What should be the average run rate in the remaining 40 overs to reach the target of 272 runs?