GATE Questions

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Given that train K crosses a pole in 30 seconds and train L crosses the same pole in one minute and 15 seconds.

Let the length of train K be Lk and that of train L be Ll

given that Lk = 3/4 Ll

As the train K and L crosses the pole in 30 seconds and 80 seconds respectively,
=> Speed of train K = sk = Lk/30

Speed of train L = sl = Ll/80

Lk = 3/4 Ll
=> sk = 3/4 Ll/(30) = Ll/40

Ratio of their speeds = sk : sl
= Ll/40 : Ll/80

=> 1/40 : 1/80  =  2 : 1

Dry ice is solid form of carbon dioxide, used as a cooling agent.

It lower temperature than that of water ice and not leave any residue.

Let number of boys = B

Number of girls = G

From the given data,

1B/3 + 1G/2 = 300

But given B/3 = 100

=> B = 300

G/2 = 300 - 100

G = 200 x 2

=> G = 400

Therefore, total number of students in the college = B + G = 700.

729 = 9 x 9 x 9

=> Cube root of 729 = 9

Now, required square of 9 = 9 x 9 = 81.

PFD's : Personal Flotation Devices (life jackets).

It is a legal requirement for a PFD to

1. Must be in good, serviceable condition 

2. PFDs must be properly sized for the intended wearer.

3. Sizing for PFDs is based on body weight and chest size.

A rowboat can be put into motion by using oar. Similaarly, a skateboard can be put into motion by using foot.

The other options like walk and running are not objects to be in motion. And loafers are something worn on foot.

Hence, Oar : Rowboat :: Foot : Skateboard.

Let S be the sample space.
Here n(S)= 23 = 8
Let E be the event of getting atmost two heads. Then,
n(E) = {(H,T,T), (T,H,T), (T,T,H), (H,H,T), (T,H,H), (H,T,H)}
Required probability = n(E)/n(S) = 6/8 = 3/4.