GATE Questions

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Given number series follows a pattern that,

2

2 x 1.5 + 1 = 4

4 x 1.5 + 1 = 7 (not equal to 8)

7 x 1.5 + 1 = 11.5

11.5 x 1.5 + 1 = 18.25

18.25 x 1.5 + 1 = 28.375

Hence, the odd number in the given number series is 8.

Two sub groups of Himalayan Rivers are Trans Himalayan Rivers and Himalayan Rivers.

• Trans Himalayan Rivers :

These rivers originate beyond the Himalayas. They are The Indus, The Sutlej and The Brahmaputra Rivers.

• Himalayan Rivers :

These are the rivers originate from Himalayas. They are The Ganga, The Yamuna and their tributaries.

114       131     165     216     ?      369

   +17      +34     +51     +68    +85

=> The missing number in the given Number series = 216 + 68 = 284.

The given number series follows the pattern that,

24×0 + 4  = 4  

4×1  + 9   = 13

13×2 + 16 = 42

42×3 + 25  = 151

151×4 + 36 =  640

Therefore, the odd number in the given series is 41

From the beginning, the next term comes by adding prime numbers in a sequence of 2, 3, 5, 7, 9, 11, 13... to its previous term. But 165 will not be in the series as it must be replaced by 166 since 153+13 = 166.

The given number series follows a pattern that

5 x 5 – 1 = 24

24 x 4 – 2 = 94

94 x 3 – 3 = 279

279 x 2 – 4 = 554

Here the given series 7, 11, 19, 35, ?

follows a pattern that (x 2 - 3) i.e,

7

7 x 2 - 3 = 11

11 x 2 - 3 = 19

19 x 2 - 3 = 35

35 x 2 - 3 = 67

67 x 2 - 3 = 131

Hence the next number in the given number series is 67.

17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)
Odd days in 1600 years = 0
Odd days in 300 years = 1
97 years has 24 leap years + 73 ordinary years.
Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.
Jan. Feb. March. April. May. June.
(31 + 28 + 31 + 30 + 31 + 17) = 168 days
168 days = 24 weeks = 0 odd day.
Total number of odd days = (0 + 1 + 2 + 0) = 3.
Given day is Wednesday.