Exams

It is useful to have a property of a material that is independent of the size of the sample and can be use to compare its elastic properties with another - this is called the Modulus of Elasticity for the material.

The modulus of elasticity is defined as:

Modulus of elasticity = Stress / Strain

There are three types of moduli. They are :

(a) the Young Modulus - tensile and compression longitudinal stress

(b) the shear modulus - a shearing stress

(c) the bulk modulus - volume changes of the specimen.

Ratio C1:C2 = 3:5 and C2:C3 = 7:11
So C1:C2:C3 = 21 : 35 : 55
Let the strength of three classes are 21x, 35x and 55x respectively, then
Given that 21x + 35x + 55x = 333
=> 111x = 333 or x=3
So strength of the class with highest number of students =55x = 55x3 = 165.

Given 45 kg for painting 

And 6% 0f 45 for wasting => 6x45/100 = 2.7 kg

Now total paint required = 45+2.7 = 47.7 kgs

But tins are available in only 4kgs

Then, no. of tins req = 47.7/4 = 11.4 => 12 tins

Here 5, 7 & 9 are repeating after modulation.

(Total numbers of cubes in a line  x  Number of stack / tower) + ...

= (6x1)+(5x2)+(4x3)+(3x4)+(5x2)+(6x1)

= 6+10+12+12+10+6 = 56

50 men can build a tank in 40 days 

Assume 1 man does 1 unit of work in 1 day

Then the total work is 50×40 = 2000 units

50 men work in the first 10 days and completes 50×10 = 500 units of work

45 men work in the next 10 days and completes 45×10 = 450 units of work

40 men work in the next 10 days and completes 40×10 = 400 units of work

35 men work in the next 10 days and completes 35×10 = 350 units of work

So far 500 + 450 + 400 + 350 = 1700 units of work is completed and

Remaining work is 2000 - 1700 = 300 units

30 men work in the next 10 days. In each day, they does 30 units of work.

Therefore, additional days required = 300/30 =10

Thus, total 10+10+10+10+10 = 50 days required.