A wire is in the shape of a rectangle. Its length is 42.7m and breadth is 21.8m. If the same wire is re-bent in the shape of a square, what will be the measure of the side of the square?

Let ABC be an equilateral triangle and AX, BY, CZ be the altitudes. Then the right statement out of the four given responses is

In ∆ABC, ∠C=90⁰, Point P and Q are on the sides AC and BC, respectively, such that  AP:PC=BQ:QC=1:2.Then, $${AQ^2+BP^2}\over AB^2$$  is equal to:

In a triangle, if orthocentre, circumcentre, incentre and centroid coincide, then the triangle must be

In ∆PQR, O is the incentre and ∠P = 42°. Then what is the measure of ∠QOR?

In Δ ABC, D and E are points on AB and BC, respectively, such that DE is parallel to AC. If DE = 3 cm, AC = 5 cm and the area of trapezium ACED = 32 cm2, then what will be the area of Δ BDE?

AC is a chord of circle whose centre is at O. If B is any point on the arc AC and ∠OCA=20⁰ , then the magnitude of ∠ABC is

The side of a trapezium pyramid with a square base is 24 cm. and its height is 5 cm. What will be the area of its oblique surface in cm²?