GATE Questions

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Alloy of copper and zinc is called as Brass.

According to the given data,

P + Q = 41 ......(1)

R - 1 = P + 2

R = P + 3

and

P + 4 = Q - 1

=> Q = P + 5 ....(2)

From (1)&(2)

P = 18

Q = 18 + 5 = 23

R = 18 + 3 = 21

=> P/S = 3/4

=> S = 4/3 x 18 = 24

Required Difference = S - R = 24 - 21 = 3.

Speed on return trip = 150% of 50 = 75 km/hr.

Average speed = (2 x 50 x 75)/(50 + 75) = 60 km/hr.

Here in 100P2, P says that permutations and is defined as in how many ways 2 objects can be selected from 100 and can be arranged.

That can be done as,

100 P2 = 100!/(100 - 2)!

= 100 x 99 x 98!/98!

= 100 x 99 

= 9900.

Here given soldier shots 7 shots in 12 min

=> 1 shot doen't take any time in 12 min 

=> Only 6 shots take 12 min 

12 min ------ 6 shots 

90 min ------ ? shots 

=> 90 x (6/12) = 45 

Therefore, total shots fired in 90 minutes = 45 + 1 = 46 shots.

Here n(S) = 6 x 6 = 36

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

=> n(E)=20

Required Probability n(P) = n(E)/n(S) = 20/36 = 5/9.

In geometry, we can define plane as a flat surface with no thickness.

The surface extends with no ends.

A plane does not have any edges even if we draw it on paper with edges, it does't mean it has edges.

Hence, A plane is an undefined term because it is described generally, not using a formal definition.

The molar mass of H2O can be calculated as the following.

M(H2O)= [2 x M(H)] + [M(O)].

And we know that M(H) = 1g/mol, M(O) = 16g/mol.

So, M(H2O)= 2x1 + 16 = 18g/mol,

That means 1 mole of H2O contains 18g.

Hence, one mole of H2O corresponds to 18 grams.