GATE Questions

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Speed = 78 x 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (900 + x)/60 = 65/3
x = 400 m.

Non collision can happen only when all the cars move in same direction.

That is either all cars moving in clockwise direction or all cars moving in anti clockwise direction.
P(all cars not colliding)

= P(all cars moving in the same direction)

= P(all cars moving in clockwise direction)  +  P(all cars moving in anticlockwise direction)

= [p(A --> C) x p(C --> B) x p(B --> A)]  +  [p(A --> B) x p(B --> C) x p(C --> A)]

= [1/2 x 1/2 x 1/2] + [1/2 x 1/2 x 1/2]

= 1/8 + 1/8

= 1/4

6.72/100 = 672/10000 = 42/625

Let the distance in one direction = k kms

Speed in still water = 4.5 kmph

Speed of river = 1.5

Hence, speed in upstream = 4.5 - 1.5 = 3 kmph

Speed in downstream = 4.5 + 1.5 = 6 kmph

Time taken by Rajesh to row upwards = k/3 hrs

Time taken by Rajesh to row downwards = k/6 hrs

Now, required Average speed =$$\begin{gathered} Total distanceTotal speed = 2kk3 + k6 \\ = 2k x 186k + 3k = 4 kmph \end{gathered}$$ 

Therefore, the average speed of the whole journey = 4kmph.

Given P = 54 and M = 80

According to the question,

Let ‘A’ years ago, M = 3P

=> M - A/P - A = 3

=> 80 - A = 3(54 - A)

=> 80 - A = 162 - 3A

=> 2A = 82

=> A = 41

Therefore, A = 41 years ago Sweety’s mother was 3 times of Sweety’s age.

Hence, at the age S = 13 and M = 39.

That man's son means Mukesh

=> Mukesh father's son is Mukesh

=> It is Mukesh's father.

Given speed of the person = 8 1/2 = 17/2 kmph
Let the speed of the stream = x kmph
speed of upstream = 17/2 - x
speed of downstream = 17/2 + x
But given that,
2(17/2 - x) = 17/2 + x
=> 3x = 17/2
=> x = 2.83 kmph.

Let marks obtained by N = x

M's marks = 0.80x

L's marks = 1.25 (0.80x)

K's marks = (0.90) (1.25) (0.80x)

= 0.9x

But 0.9x = 360 ⇒ x = 400

Percentage of Marks obtained by N

= 400 x 100/500 = 80%