A rectangular park is 120 m long and 104 m wide. A 1-m wide path runs along the boundary of the park, remaining completely inside the park area. Thus, the outside edges of the path run along the boundary wall of the park. The inside edges of the path are marked with a white line of negligible thickness. If it costs ₹2.50 to mark each metre with the white line, then how much would it cost (in ₹) to fully mark the inside edges of the path?

The length, breadth and height of a hall are 144 m, 180 m and 384 m respectively. The length of the longest scale that can measure the three dimensions of the hall exactly is:

The side of a square is 8 cm. If a square is made by joining the mid points of each sides of this square and this process goes up to infinity. Calculate the sum of areas of all the squares made.

A copper wire is bent in the shape of a square of area 81 cm². If the same wire is bent in the form of a semicircle, the radius (in cm) of the semicircle is (take π=22/7 ) 

In a triangle ABC, ∠ABC = 75⁰ and ∠ABC = π⁰/4, The circular measure of ∠BAC is :

A hemispherical bowl of internal diameter 54 cm contains a liquid. The liquid is to be filled in cylindrical bottles of radius 3 cm and height 9 cm, then find the number of bottles that can be filled?

The measure of the angles of a triangle are in the ratio 2 : 7 : 11. Measures of angles are : 

∆ DEF is right angle at E. if m∠F = 30⁰ Then Find the value of   $$\left( cos D - {1\over 2}\right)$$ = ?