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.

1/15 + 1/12 + 1/R = 1/6, we got R = 60 (it means R will take 60 days to complete the work alone)

so ratio of work done by P:Q:R = 1/15 : 1/12 : 1/60 = 5 : 4 : 1

so R share = (1/10) x 1200 = 120.

By trial and error method from the given options,

as 54 - 45 =  (1/11) x (45+54)  = 99/11  = 9

Hence this satisfies the given conditions.

Then the woman's husband age is 54.

Let the age of ruler is x so that of son = x/2 (given)
Now according to the given condition
(x/6) + (x/12) + (x/7) + 5 + (x/2) + 4 = x
=> x = 84

Ozone molecule has one single bond and one double bond.

p=d×1002R2 

Where d is difference, r is rate of interest. 

=> (48 x 100 x 100) / 8 x 8 = Rs.7500

100
65
-------
65 ------- 35
100 ------ ? => 53.84 %

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