O is a point inside a rectangle ABCD such that OB = 6 cm, OD = 8 cm and OA = 5 cm. Find OC.

State and prove Pythagoras theorem.

In a triangle PQR, ∠P = 90° and PS is perpendicular to QR. Then prove that

Find the median of the data from the following distribution. Marks Obtained No. of Students Less than 10 8 Less than 20 15 Less than 30 29 Less than 40 42 Less than 50 60 Less than 60 70

Find the mode from the following data. Class Interval Frequency 0 - 5 2 5 - 10 6 10 - 15 10 15 - 20 16 20 - 25 22 25 - 30 11 30 - 35 8 35 - 40 5

If 75 buckets of water of equal measure are taken out from the water of a cubical water-filled-tank, then th of the water remains in the tank. If the length of one edge of the tank is 1.5 metres, then calculate the quantity of water in litre that can be held in each bucket.

Difference of outer and inner curved surface area of a hollow cylindrical pipe is 44 sq.cm and length is 14 cm. If the Volume of the material of the pipe be 99 cubic cm. Find inner and outer radius.

The lower part of an ice-cream is conical and upper part is hemispheric with same circular base. If the height of the cone is 9cm and radius of the base 2.5 cm. Find the volume of the ice-cream.

Two pillars of equal heights are at the point A and B on the opposite side of the road which is 120 m wide. From a point C on the line joining the foots of the pillars, the angle of elevation of the top of the pillar at A and B are 60° and 30° respectively. Find AC.

The angle of elevation of the top of a pillar of height h from two points in the same horizontal line through the foot of the pillar and in the same side of the pillar are θ and φ respectively. Find the distance between two points.

If 5 sin² θ + 4 cos² θ = , then from this relation find the value of tan θ.

The difference of acute angles of a right angled triangle is 72°. Determine these acute angles in circular measure