'The total surface area of a cube is 600 sq cm, what will be the length of its diagonal?

ABC is an isosceles triangle such that AB = AC and ∠B = 35°. AD is the median to the base BC. Then ∠BAD 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:

PK is the median and M is a centroid of triangle PQR. If PK is 15 cm, then find length of PM?

In ∆ABC, the bisector of ∠A intersects side BC at D. If AB = 12 cm, AC = 15 cm and BC= 18 cm, then the length of BD is:

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

AB is a chord of a circle in minor segment with center O.C is a point on the minorarc of the circle between the points A and B. The tangents to the circle at A and B meet at the point P. If ∠ACB = 102⁰ , then what is the measure of ∠APB?

O is the centre of this circle. Tangent drawn from a point P, touches the circle at Q. If PQ = 24 cm and OQ = 10 cm, then what is the value of OP?