Questions

Starting with the top 3 digit number, the first digit increases by 2 as you descend,from 1 to 11. The middle digit decreases by 1 each time,and the right hand digit alternates between 5 and 3

Two series alternate here, with every third number following a different pattern.
In the main series, 4 is added to each number to arrive the next.
In alternate series, 5 is subtracted from each number t arrive the next number.
Here in the main series 
3 + 4 = 7
7 + 4 = 11
11 + 4 = 15
15 + 4 = 19

In alternate series 
24 - 5 = 19
19 - 5 = 14...

1 mole of CO2 contain 12gms of carbon and 44 gms of CO2

therefore  24 gms of carbon is present in 88 gms of CO2 or 2 moles of CO2

To produce controlled energy i.e energy at a controlled or steady rate, the number of fissions per second must be controlled and maintained at that rate. Excess neutrons should be absorbed by control roads like cadmium.

It is ABACUS.

Words formed are as below 

BUS
CAB
CUB
US

The logical answer for a puzzle is that the letter 'W'.

A rainbow is a spectrum of light that appears in the sky when sunlight is refracted through raindrops or other drops of moisture in the Earth's atmosphere. They have inspired much popular folklore, including the belief that a leprechaun can be found with a pot of gold at the end of a rainbow.

Public relations includes promotional activities that work to create a strong public image of the company. Public relations activities include helping the public to understand the company and its products. Public relations if done right can reach a large audience without the expensive cost of traditional advertising and marketing.