Find the average of the variable.
The diameters of five pipes are : `13(3)/(4)` mm, `11(7)/(16)`mm , `6(1)/(2)`mm , `7(3)/(4)`mm

Find the inverse of matrices using elementary column transformations: [(1,2,3),(1,3,-1),(-1,1,-7)]

Find the sum of n term of the series 2+4+7+11+16+.....

Find the molecular weight of a solute when 1.2 gm of the solute is dissolved in water at 25^@C in 37.4 mm of Hg.

An air bubble of diameter 1 mm is formed at the bottom of a lake and when it rises to the surface of the water, its diameter becomes 2 mm. If the atmospheric pressure is 760 cm of mercury, then find the depth of the lake. (Density of mercury = 13.6g*cm^(-3) )

Find the number of atoms of hydrogen and oxygen present in one spherical drop of water with radius 1 mm at 4^(@)C .

Let L be the length and d be the diameter of cross section of a wire. Wires of the same material with different L and d are subjected to the same tension along the length of the wire. In which of the following cases, the extension of wire will be the maximum? L= 200 cm, d=0.5 mm L= 300 cm, d=1.0 mm L= 50 cm, d= 0.05 mm L=100 cm, d=0.2 mm

A cylindrical container is to be made from certain solid material with the following constraints : It has a fixed inner volume of V "mm"^(3) , has a 2 mm thick solid wall andis open at the top. The bottom of the container is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of the container. If the volume of the material used to make the container is minimum when the inner radius of the container is 10 mm, then the value of (V)/(250pi) is-

A and B are two thermometers made of glass and both contains the same liquid. Both thermometers have spherical bulbs. The internal diameter of the bulb of A is 7.5 mm and radius of the capillary tube is 1.25 mm. The corresponding values for B are 6.2 mm and 0.9 mm. Find the ratio of the lengths between two consecutive graduations in thermometers A and B.