GATE Questions

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Total number of chairs = (3 + 5 + 4) = 12.

Let S be the sample space.

Then, n(s)= Number of ways of picking 2 chairs out of 12

= 12×11/2×1 = 66

Let n(E) = number of events of selecting 2 chairs for selecting no white chairs.

=> 8C2 = 8×7/2×1 = 28

Therefore required probability = 28/66 = 14/33.

Oligarchy is a form of government in which the power rests with the small group of people.

Number of words with 5 letters from given 9 alphabets formed = 95

Number of words with 5 letters from given 9 alphabets formed such that no letter is repeated is = 9P5

Number of words can be formed which have at least one letter repeated =  95 - 9P5

= 59049 - 15120

= 43929

Cryogenic Engines find applications in Rocket technology. A cryogenic rocket engine is a rocket engine that uses a cryogenic fuel or oxidizer, that is, its fuel or oxidizer are gases liquefied and stored at very low temperatures. Notably, these engines were one of the main factors of NASA's success in reaching the Moon by the Saturn V rocket.

Let age of retirement = S
so according to the given condition 25000(x-20)
=10000 x 3 + 12000 + 14000 + 16000 + 18000 + 20000 + 22000 + 24000 + 26000 + 28000 + 30000 + 30000(S-33)
= 30000 + 210000 + 30000S-990000
= 30000S - 750000
or 25000S - 500000 = 30000x - 750000
or 5000x = 250000
or S = 50 yrs.

In common we all call the systematic name of NH4ClO3 as Ammonium Chlorate. But originally the systematic name is azanium trioxidochlorate.

To find the minimum distance, we have to get the LCM of 75, 80, 85

Now, LCM of 75, 80, 85 = 5 x 15 x 16 x 17 = 20400

Hence, the minimum distance each should walk so that thay can cover the distance in complete steps = 20400 cms = 20400/100 = 204 mts.