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The stage of cell division in which paired homologous chromosomes get shortened and thickened is prophase I of meiosis. During this stage, the chromosomes condense and become visible as distinct structures, allowing for the homologous chromosomes to pair up and exchange genetic material through a process called crossing over. The shortening and thickening of the chromosomes during prophase I is important for proper alignment and separation of the homologous chromosomes during subsequent...

Water is a vital substance for life on Earth, and it plays numerous important biological roles in living organisms. Some of the key biological roles of water are:

1. Universal solvent: Water is an excellent solvent for many substances, both organic and inorganic. This means that it can dissolve and transport a wide range of nutrients and minerals necessary for the growth and survival of living organisms.

2. Medium for metabolic reactions: Many metabolic reactions in living organisms require water...

The full form of WTO is World Trade Organization.

If a vector A is multiplied by a real number (say n), the vector of same nature is obtained but its magnitude is n times that of A.

There is, for sure, effect of gravity on fire. We know for a fact that fires on Earth are "pointy" while those in zero-gravity are "round". This is because fire is simply glowing gas. Gas is matter and matter has weight. For a body to have weight, gravity must influence it in some way. 

Log_2aa=x    then, a=(2a)^x  ......(1)

Log_3a2a=y    then,2a=(3a)^y ......(2)

Log_4a 3a=z  then, 3a=(4a)^z ......(3)

So, 

a=(2a)^x  [from (1)]

Or, a=(3a)^xy    [from(2)]

Or, a=(4a)^xyz     [from(3)]

Multiplying both sides by 4a,

4a.a=4a.(4a)^xyz  

Or,(2a)² =(4a)^{xyz + 1} 

Or,(3a)^2y =(4a)^xyz+1 

Or,(4a)^2yz =(4a)^xyz+1 

Or, 2yz = xyz+1 .proved.

Pteridophytes