GATE Questions

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Total number of possible ways = 

9C5 = 9 x 8 x 7 x 6 x 55 x 4 x 3 x 2 x 1 = 126

Number of favorable cases = 

$$\begin{gathered} 4C2 x 5C3 + 4C3 x 5C2 + 4C4 x 5C1 \\ 4 x 32 x 1 x 5 x 4 x 33 x 2 x 1 + 4 x 3 x 23 x 2 x 1 x 5 x 4 2 x 1 + 1 x 5 \\ = 6 x 10 + 4 x 10 + 5 \\ = 60 + 40 + 5 \\ = 105 \end{gathered}$$

Therefore, required probability = 105/126 = 5/6

If After p years , commodity X will cost 60 rupees more than the commodity Y, then

320 + 60p = 740 + 20p + 60
=> p = 12

So in year (2002 + 12 = 2014), commodity X will cost Rs.60 more than the commodity Y.

A Temper.

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.

Total number of possible ways = 9C3 = 84 ways

Required atleast one girl in the group of three = total possible ways - ways in which none is girl

None of the members in the group is girl = 6C3 = 20

Therefore, number of ways that at least one member is a girl in the group of three

= 84 - 20

= 64 ways.

Remaining % of amount with Rohan

= 100 - (24 + 34 + 17 + 19)

= 100 - 94

= 6%

=> 6% = 540

=> 100% = ?

540 x 100/6 = Rs. 9000

Now, Money spent on insurance and food is

= 34 + 24 = 58% of 9000

= 58 x 9000/100

= 58 x 90

= Rs. 5220

Let 'Y' be the youngest player.

The last song can be sung by any of the remaining 3 players. The first 3 players can sing the song in (3!) ways.

The required number of ways = 3(3!) = 4320.