GATE Questions

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      It is a case of shifting as given below:

      1  2  3  4  5                    2  1  3  5  4

      O  F  T  E  N   →  F  O  T  N  E

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       1  2  3  4  5                   5  4  3  1  2

1.    H  E  A  R  T       →      T  R  A  H  E    

2.    O  P  E  N  S  →  S  N  E  O  P

        1  2  3  4  5         2  1  3  5  4

3.    R  I  S  K  Y  →   I  R  S  Y  K

4.    F  I  R  S  T  →   I  F  R  S  T

Hence option 3 is correct.

19 C in a CB means 19 Coins in a Carrom Board.

We have 9 white coins, 9 black coins and one red coin in a carrom board.

Daughter of your mother's father's mother => Maternal grandmother => Renu's Aunt.

Hence, Laxmi is Renu's Aunt and Vishal is Renu's Uncle.

".INI" is an extention for all the configuration files in the system. 

Hence, .ini is an extension for System files.

1001 A N means 1001 Arabian Nights.

These are same as 12 S of the Z, 64 S on a C, 19 C in CB, 8 S on SS, ...

There are total 5 ways.
we have only one kg of weight so,
2kg = 1kg + 1kg
4kg = 1 + 2 + 1
8kg = 1 + 2 + 4 + 1
16kg = 1 + 2 + 4 + 8 + 1
31kg = 1 + 2 + 4 + 8 + 16
So 5 weights are needed.

Here the given series follows a pattern that,

2² - 0 = 4  

3² - 1 = 8  

4² - 2 = 14

5² - 3 = 22

6² - 4 = 32

Hence, the missing number is 32

Method 2 ::

The difference between 4 and 8 is 4, the difference between 8 and 14 is 6, the difference between 14 and 22 is 8. So the next difference between 22 and the next number will be 10 since it follows (4,6,8,10 - add +2 each time)

Hence, 22 + 10 = 32 is the missing number.

The 8 letters can be written in 8! ways.
n(S) = 8!
Let E be the event that the letters b,c,d,e always come together when the first 8 alphabets are written down.
Now the letters a, (bcde), f, g and h can be arranged in 5! ways.
The letters b,c,d and e can be arranged themselves in 4! ways.
n(E) = 5! x 4!
Now, the required P(E) = n(E)/n(S) = 5! x 4!/8! = 1/14
Hence the answer is 1/14.