GATE Questions

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Let, Distance between A and B = d

Distance travelled by P while it meets Q = d + 11

Distance travelled by Q while it meets P = d – 11

Distance travelled by Q while it meets R = d + 9

Distance travelled by R while it meets Q = d – 9

Here the ratio of speeds of P & Q => SP : SQ = d + 11 : d – 11

The ratio of speeds of Q & R => SQ : SR = d + 9 : d – 9

But given Ratio of speeds of P & R => P : R = 3 : 2

 SPSR = SPSQxSQSR = d+11d+9d-11d-9

=> d+11d+9d-11d-9 = 3/2

=>  d = 1, 99

=> d = 99 satisfies.

Therefore, Distance between A and B = 99

Screws weight = 90x100 = 9000gms
bolts weight = 100 x 150 = 15000gms
weight = screws + bolts => 24000 gms =>24 kg
Given entire box weight = 35.5kg
empty box = entire box weight - weight => 35.5kg - 24kg => 11.5kg
so the empty box is 11.5kg.

Here total parts of milk and water in the solution is 6+2 = 8 parts.

1part = 640/8 = 80

old mixture contains 6parts of milk and 2 parts of water(6:2).

To get new mixture containing half milk and half water, add 4parts of water to the old mixture then 6:(2+4) to make the ratio same.

i.e, 4 x 80 = 320 ml.

Here all the given compounds have both ionic and covalent bonds.

NaNO3 - In Sodium nitrate, Nitrate is covalently bonded as nitrogen is bonded with 3 oxygen atoms. And this nitrate is ionically bonded with sodium.

CaSO4 - In Calcium sulphate, sulphate is covalently bonded as sulphur is bonded with 4 oxygen atoms. And this sulphate is ionically bonded with calcium.

NH4Cl - In Ammonium chloride, ammonium is covalently bonded as nitrogen is bonded with 4 hydrogen atoms. And this ammonium is ionically bonded with chlorine.

N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)

= H.C.F. of 3360, 2240 and 5600 = 1120.

Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4

Ozone molecule has one single bond and one double bond.

Let Speed of boat in still water = b

Let Speed of still water = w

Then we know that,

Speed of Upstream = U = boat - water

Speed of Downstream = D = boat + water

Given, U + D = 82

b - w + b + w = 82

2b = 82

=> b = 41 kmph

From the given data,

41 - w = 105/3 = 35

w = 6 kmph

Now,

b + w = 126/t

=> 41 + 6 = 126/t

=> t = 126/47  = 2.68 hrs.

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.