GATE Questions

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The term gram formula mass is synonymous with molecular mass. So, to get this, we must add molar mass of all the elements in this compound.

Given compound is Lithium Sulphate - Li2SO4

Elemental calculation ::

Li  -  Lithium   -   6.941    -     2   -   13.88200 %
S  -  Sulfur     -    32.065   -    1   -   32.065 %
O  -  Oxygen   -   15.9994  -    4   -   63.9976 %

Now, total = 12.6264 + 29.1647 + 58.2090 = 109.9446 

Hence, the gram formula mass of Li2SO4 = 109.9446.

Let the Oranges be 'O', Bananas be 'B' and Apples be 'A'

From the given data,

2O + 3B + 4A = 15 ...... (I)

3O + 2B + A = 10 ..... (II)

On adding (I) and (II),

5O + 5B + 5A = 25

O + B + A = 5

4O + 4B + 4A = 20.

The given series follows the rule,
+(11x1), +(11x3), +(11x5), +(11x7), +(11x9),....

So starting from 7, 7 + 11 = 18, 18 + 33 = 51, 51 + 55 = 106, ...
So wrong number is 40 which is to be 51.

2 engines of former type for one hour consumes (2 x 24)/(6 x8) = 1 metric ton 

i.e. 3 engines of latter type consumes 1 ton for one hour

Hence 9 engines consumes 3 tons for one hour

For 15 hours it is 15 x 3 = 45 metric tonnes.

Speed of lorry = 36012 = 30 kmph

Speed of van =250100 x 30 = 75 kmph

Speed of bike = 35 x 75 = 45 kmph

Therefore, now required average speed of bike and van  = 75 + 452= 60 kmph.

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.

100
65
-------
65 ------- 35
100 ------ ? => 53.84 %

Non collision can happen only when all the cars move in same direction.

That is either all cars moving in clockwise direction or all cars moving in anti clockwise direction.
P(all cars not colliding)

= P(all cars moving in the same direction)

= P(all cars moving in clockwise direction)  +  P(all cars moving in anticlockwise direction)

= [p(A --> C) x p(C --> B) x p(B --> A)]  +  [p(A --> B) x p(B --> C) x p(C --> A)]

= [1/2 x 1/2 x 1/2] + [1/2 x 1/2 x 1/2]

= 1/8 + 1/8

= 1/4