GATE Questions

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The number of letters in the given word CREATIVITY = 10

Here T & I letters are repeated

=> Number of Words that can be formed from CREATIVITY = 10!/2!x2! = 3628800/4 = 907200

Oil from Gnetum spp a gymnosperm belonging to the family Gnetaceae is used to relieve the effects of rheumatism

The lianas and shrubs of Gnetum are found in the rain forests of the western ghats.

When two dice are thrown simultaneously, the probability is n(S) = 6x6 = 36

Required, the sum of the two numbers that turn up is less than 12

That can be done as n(E)

= { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5) }

= 35

Hence, required probability = n(E)/n(S) = 35/36.

ST candidates vacancies can be filled by C35 ways = 10 

Remaining vacancies are 5 that are to be filled by 12 

=> C512= (12x11x10x9x8)/(5x4x3x2x1) = 792 

Total number of filling the vacancies = 10 x 792 = 7920

As per the rule of adverb, the adverb is followed by the third form of verb.

Let the speed of the train be 'S' kmph

From the given data,

Distance = Length of train = D = 200 mts = 200 x 18/5 kms

Time = 10 sec

given speed of the motorcycler = 12 kmph

Relative speed as they are moving in the same direction = (S - 12) kmph

$$\begin{gathered} (S- 12) = 200 x 18515 \\ S - 12 = 48 \\ S = 60 kmph \\ \end{gathered}$$

Hence, the speed of the train = S = 60 kmph

Now,

Let the speed of the jeep be 'x' kmph

$$\begin{gathered} 60 - x = 200 x 18520 \\ 60 - x = 36 \\ x = 60 - 36 \\ x = 24 kmph \end{gathered}$$

Therefore, the speed of the jeep = x = 24 kmph.