GATE Questions

---

The twentieth element in the above arrangement is 'E'.
Then, the sixth element to the left of 'E' is 'L'.

Total no of ways = (14 – 1)! = 13!

Number of favorable ways = (12 – 1)! = 11!

So, required probability = 11!×3!13! = 39916800×66227020800 = 24625

Let the speed of current = 'C' km/hr

Given the speed of boat in still water = 6 kmph

Let 'd' kms be the distance it covers.

According to the given data,

Boat takes thrice as much time in going the same distance against the current than going with the current

i.e, d8 - C = 3 × d8 + C

$$\begin{gathered} ⇒ 24 - 3C = 8 + C \\ ⇒ 4C = 16 \\ ⇒ C = 4 kmph \end{gathered}$$

Hence, the speed of the current C = 4 kmph.

The given series follows the rule,
+(5x1), +(5x2), +(5x3), +(5x4), +(5x5),....

So starting from 37, 37 + 5 = 42, 42 + 10 = 52, 52 + 15 = 67, 67 + 20 = 87,...
So wrong number is 47 which is to be 42.

Work done by the third pipe in 1 min = 1/50 - (1/60 + 1/75) = - 1/100.
[-ve sign means emptying]

The third pipe alone can empty the cistern in 100 min.

For 30 days he receives

30 x 25 = 750
               

Actually he gets 425

Therefore, Fine is 750 - 425 =  325

=> No of days absent = 325/(25+7.50)= 10

Towel gets wetter and wetter the more it dries because we use that towel which is dried after used.

Given, 

25% of three-seventh of 26% of a number is 145.5

Let the required number be 'N'

i.e, 25100x37x26100xN = 145.5

N = 145.5x7x1000075x26

=> N = 5223.07