CAT Questions

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Here given formula is 

a2 + b2 + c2 -ab- bc - ca = 0

and it is possible if and only if a = b = c.

From the trial and error method, 

1) Let a = b = c = 1

Now substitute these values of a, b, c in the above formula.

We get 1 + 1 + 1 - 1 - 1 - 1 = 3 - 3 = 0

2) Now, let a = b = c = 4

Now substitute these values of a, b, c in the above formula.

We get 16 + 16 + 16 - 16 - 16 - 16 = 48 - 48 = 0.

Hence, it is possible that 

a2 + b2 + c2 -ab- bc - ca = 0 iff a = b = c.

A Jigsaw puzzle.

The US state California's  economy has surpassed that of the UK to become the world’s fifth largest, according to new federal data released.

With a GDP of $2.7 trillion, California is now only behind the US, China, Japan and Germany.

Conditions suitable for the formation of a tornado develop when varying temperatures and humidity come together and form thunderclouds. This refers to the presence of warm and moist condition in the lower atmosphere and cold and dry conditions in the upper atmosphere. The place where these varying masses of air meet is known as the dry-line. Such conditions, which are suitable for the formation of a tornado, are most often observed just before a low pressure system develops.

Once the ideal conditions occur, the warm air tries to rise in the atmosphere, while the cold air blocks it. This makes the air in between rotate horizontally. In the meanwhile, the land is heated by the Sun, and hence, the air near the ground becomes warm and starts rising. Continuous fueling by the heat energy from the Sun ensures that the warm air has an upper hand over cold air. As a result of this, the cold air at the top starts sinking and the warm air below starts rising in a spinning motion. As the amount of warm air increases, the formation gains height and becomes intense. The intensity of these devastating tornadoes is such that they can clear off anything that comes in their path.

Photosynthesis is a process used by plants and other organisms to convert light energy into chemical energy that can later be released to fuel the organisms activities.

Photosynthesis can be represented using a chemical equation.

The overall balanced equation is

              $$\begin{gathered} 6CO2 + 6H2O →Sunlight C6H12O6 + 6O2 \\ Source of Carbon & Oxygen + \\ Source of Electrons & Hydrogen + \\ Energy that drives Photosynthesis ----> \\ Sugar + Gas produced by splitting water. \end{gathered}$$

Where 

CO2 = carbon dioxide 

H2O = water

C6H12O6 = glucose 

O2 = oxygen.

Charles Babbage, the father of computer, invented the first general-purpose computer in an effort to prevent the mathematical errors that were prevalent in the human-calculated mathematics of his time.

Neeraj Chopra became the first Indian javelin thrower to claim a gold medal at the Commonwealth Games, with a season’s best effort of 86.47m in the final. The 20-year-old junior world champion had made the final after achieving the qualifying mark in his very first throw.