GATE Questions

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The given letter equation implies that, 

7 C in the R = 7 Colours in a Rainbow.

The given statement implies that 64 Squares on Carrom Board.

Total work is given by L.C.M of 72, 48, 36

Total work = 144 units

Efficieny of A = 144/72 = 2 units/day

Efficieny of B = 144/48 = 3 units/day

Efficieny of C = 144/36 = 4 units/day

According to the given data,

2 x p/2 + 3 x p/2 + 2 x (p+6)/3 + 3 x (p+6)/3 + 4 x (p+6)/3 = 144 x (100 - 125/3) x 1/100

3p + 4.5p + 2p + 3p + 4p = 84 x 3 - 54

p = 198/16.5

p = 12 days.

Now, efficency of D = (144 x 125/3 x 1/100)/10 = 6 unit/day

(C+D) in p days = (4 + 6) x 12 = 120 unit

Remained part of work = (144-120)/144 = 1/6.

Total time taken = k/40 + 2k/20 hours

= 5k/40 = k/8 hours

Average speed = 3k/(k/8) = 24 kmph.

Removing the contaminents if any in the water which causes harm to our health is involved in the purifying of water. 

This process involves chemicals. Chloramines, Hydrogen peroxide, Iodine are the chemicals which are used in purifying water.

The order of basicity in ammonia is different in gaseous phases vs. aqueous phases due to hydrogen bonding.

So in gaseous phases it's the well known: 3' > 2' > 1'> NH3. Just so we're on the same page, this is due to the inductive effect of electron donating alkyl groups--they destabilize the lone pair on nitrogen atom, making nitrogen more basic.

But in aqueous phase, the order is slightly different: 2'> 1'> 3' > NH3.

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

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

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.