In a ∆ ABC, points P, Q and R are taken on AB, BC and CA, respectively, such that BQ=PQ and QC=QR. If ∠BAC = 75⁰, what is the measure of ∠PQR (in degress)?

A spherical metallic shell with 6 cm external radius weighs 6688 g. What is the thickness of the shell if the density of metal is 10.5 g per cm3? (Take л = 22/7)

A conical vessel, whose internal radius is 20 cm and height is 27 cm, is full of water. If this water is poured into a cylindrical vessel with internal radius 15cm, what will be the height to which the water rises in it?

A hemispherical bowl of internal radius 18 cm is full of liquid. This liquid is to be filled in cylindrical bottles each of radius 3 cm and height 6 cm. How many bottles are required to empty the bowl

The base of a triangle is 16 cm and its area is $${144cm^2}$$. Find its corresponding height, with respect to the given base.

The diagonal of a square A is (a+b). The diagonal of a square whose area is twice the area of square A, is

The curved surface area of a right cylinder is 3696 cm². Its height is three times its radius. What is the capacity (in litres) of the cylinder? (Take π =22/7)

O, G, I and H are respectively the circumcentre, centroid, incentre and orthocentre of an equilateral triangle. Which of these points are identical?