GATE CS 2018

The series starts with 2. We multiply first term with 6 to get second term 12 Then we multiply second term with 5 to get third term 60 Then we multiply third term with 4 to get fourth term 340 Then we multiply fourth term with 3 to get fifth term 720 Then we multiply fifth term with 2 to get fifth term 1440. Then we need to multiply with 1 and we get 1440 again.

We need a number that can be written as 20x + 7, 42y + 7, 76z + 7 for three integers x, y and z. We basically need to find least common multiple of 20 (2 * 2 *5), 42(2 * 3 * 7) and 76(2 * 2 * 19) which is 2 * 2 * 5 * 3 * 7 * 19 = 20 * 21 * 19 = 420 * 19 = 7980 So our number is 7980 + 7 = 7987. Note - You can also verify options using virtual calculator.

"From where are they bringing their books? Who bringing Whose books from Where." Who - A group as subject = They are Whose - of that group = their Where - from a place = there "From where are they bringing their books? They are bringing their books from there." So, option (B) is correct choice.

Meandering (as adjective) = proceeding in a convoluted or undirected fashion. Timely (as adjective) = done or occurring at a favourable or useful time; opportune. Consistent (as adjective) = acting or done in the same way over time, especially so as to be fair or accurate. Systematic (as adjective) = done or acting according to a fixed plan or system; methodical. Therefore, meandering is correct choice, all other options are similar to the word organized.

One important observation to solve 
the question :

Diagonal of Square = Diameter of Circle.

Let side of square be x. 

From Pythogorous theorem.
Diagonal = √(2*x*x)

We know area of square = x * x = d

Diameter = Diagonal =  √(2*d)

Radius = √(d/2)
Area of Circle = π * √(d/2) * √(d/2) = 1/2 * π * d

Option (A) is correct.

Let total males and females be 60x and
40x respectively.

Total number of people = (60x + 40x)
Total number of people who attended : 
                 0.8(60x + 40x) = 80x

Let y males attended. It is given all 
1females attended 

40x + y = 80x
y = 40x which is same as females.

Alternative Approach - Lets total number of people = 100. Therefore, 60 are male and and 40 are female. But total 80 guests are attended and all 40 female attended the party. So, there remaining (80 - 40 = 40) attendees should be male. Then the ration of male to female among attendees is 40 : 40 = 1 : 1

Considering uniformly distributed outcomes, we get 4 greens and 2 reds in six throws. Then in one more throw, green is more likely. So, option (C) is correct.

Taking logs of given three values, we get

1/q = p-x -------(1)
1/r = q-y -------(2)
1/p = r-z -------(3)

1/q = p-x
    = r-xz [Putting value of p from (3)]
    = q-xyz  [Putting value of r from (2)]
    = 1 / qxyz

On comparing power of q both sides, we get xyz = 1

So, option (C) is correct.

Let there be x total men.

Total amount paid = x * 750 * 8/9 + (300 - x)*1000*2/3
                  = x*2000/3 + 300*1000*2/3 - x*2000/3
                  = 200000