The radius of a circle is 17.5 cm. find the area of the sector of the circle enclosed by two radii and an arc 44 cm in length.

In a lottery, there are 10 prizes and 25 blanks. What is the probability of getting a prize?

An isosceles triangle ABC, with AB = AC, circumscribes a circle, touching Bc at P, AC at Q and AB at R. Prove that the contact point P bisects BC.

Prove thatis an irrational number.

OR

Using Euclid’s algorithm, find the HFC of 272 and 1032.

If x = 3 sinθ + 4 cosθ and y = 3 cosθ – 4 sinθ then prove that x² + y² = 25.

OR

If sinθ + sin²θ = 1;

Thenprovethatcos²θ+cos⁴θ= 1.