GATE Questions

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Rewrite equation as 122x+1 = 120

Leads to 2x + 1 = 0 

Solve for x : x = -1/2

PRINCE.

1/2 as a percentage means

1/2 = 0.5 in decimal

Now, in percentage means 0.5 x 100% = 50%.

The logic in the given puzzle is 

Addition of numeric values of corresponding letters in the first three figures gives respective corresponding letter in fourth figure. 

i.e, A = 1 , W = 23 , B = 2 => 2 + 1 + 23 =26 = 'Z'

Similarly, L = 12, K = 11 , A = 1 => 1 + 11 + 12 = 24 = 'X'

Here the missing letter is 'X'.

OKG
Remaining all are not in series
only OKG is in series of(15,11,7)

Here it follows the random difference of '4'.

One fathom = 1.8288 meters = 6 feet

A fathom is a unit of length used especially for measuring the depth of water.

Let their present ages be 13x and 17x.
Then, 13x-4/17x-4 = 11/15.
Solving this, we get x = 2.
Required ratio = 13x2 + 6/17x2 + 6 = 32/40 = 4/5.

The letter 'E'.

As of the above given data,

It is in the 1st place in Earth, 2nd in Heaven and in the middle of the Sea.

It appears once in a Year and twice in a Week.

It is present in February, June, September, October, November & December.

But not in the Month.

Hence, it is the letter 'E'.