GATE Questions

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In the given puzzle the logic is

2 x 1 + 1 = 2 + 1 = 3

3 x 2 + 2 = 6 + 2 = 8

4 x 3 + 3 = 12 + 3 = 15

5 x 4 + 4 = 20 + 4 = 24

6 x 5 + 5 = 30 + 5 = 35

Similarly,

7 x 6 + 6 = 42 + 6 = 48

7 = 48.

Let the age of ruler is x so that of son = x/2 (given)
Now according to the given condition
(x/6) + (x/12) + (x/7) + 5 + (x/2) + 4 = x
=> x = 84

The one word substitute for A person of good understanding knowledge and Reasoning power is Intellectual.

Entropy is a measure of disorder . It will be maximum in gases followed by liquids and least in solids.

Hence, here the gas is only hydrogen and it has the highest entropy.

Let Priyatham's age = x

Then, Vishal's age = 2x; Raghu's age = x/2; Veeru's age = 4x ; Karthik's age = x/4

So, the descending order of ages is :

Veeru > Vishal > Priyatham > Raghu > Karthik

Therefore,  Karthik is the youngest.

The cow can graze an area of 2826 sq.m i.e it is able to cover area of circle of 2826 sq.m

Therefore, πr2 =2826
r2 =(2826×7/22) = 899.18 = 900
r = 30 m.

Therefore, the radius of the circle implies the length of the rope = 30 mts.

Probability of occurrence of an event, 

P(E) = Number of favorable outcomes/Numeber of possible outcomes = n(E)/n(S)

⇒ Probability of getting head in one coin = ½, 

⇒ Probability of not getting head in one coin = 1- ½ = ½, 

Hence, 

All the 11 tosses are independent of each other.

∴ Required probability of getting only 2 times heads =122×129=1211

We can select atleast one item from 6 different items = 26-1  

Similarly we can select atleast one item from other set of 6 different items in 26-1 ways. 

Required number of ways = (26-1)26-1 = 26-12 = 3969