GATE Questions

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$$\begin{gathered} [(K-L)2-K+L2]4K = ab \\ K2+L2-2KL-K2+L2+2KL4K= ab \end{gathered}$$

=> - 4KL/4K = a/b

=> L = - a/b

=> bL = -a

The given number series follows a pattern that,

9

9 x 0.5 + 0.5 = 5

5 x 1 + 1 = 6

6 x 2 + 2 = 14

14 x 4 + 4 = 60 (not equals to 56)

60 x 8 + 8 = 488.

Hence, the odd one in the given number series is 56.

Here the given number series  3, 10.5, 36.75, 128.625, ? follows a pattern that

3

3 x 3.5 = 10.5

10.5 x 3.5 = 36.75

36.75 x 3.5 = 128.625

128.625 x 3.5 = 450.187

Hence the next number in the given number series is 450.187.

Here Grass is to Erosion and whereas Dam is to Water.

Since Grass prevents Erosion similarly Dam prevents Water flow.

Hence, Grass : Erosion :: Dam : Water.

Let first no. be "k" and multiple be "l"...start value of y with 3
then,
[(k x y) + {l x (l-1)}]
Thus, we get

15 x 3 + 3 x 2 = 51
51 x 4 + 4 x 3 = 216
216 x 5 + 5 x 4 = 1100
1100 x 6 + 6 x 5 = 6630
6630 x 7 + 7 x 6 = 46452

Therefore, the missing number is 6630.

'Rhythm of eyes' logically means Nainital in India.

The other cities are:

No Zip - Chennai

Mr. City - Srinagar

Do Acting - Karnataka.

The given series follows the pattern that,

×5+5,   ×5+5,   ×5+5,   ×5+5,   ×5+5

38 x 5 + 5  = 195

195 x 5 + 5 = 980

980 x 5 + 5 = 4905

4905 x 5 + 5 = 24530

24530 x 5 + 5 = 122655

So the missing number is 980 .

Cup is used to drink something with the help of lips. Similarly, birds collect grass with the help of beak to make her nest.

Hence, Cup : Lip :: Bird : Grass.