GATE Questions

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We know that,

$$\begin{gathered} i2 = -1 \\ i3 = i2 x i = -1 x i = -i \\ i4 = i2 x i2 = -1 x -1 = 1 \\ Hence, i233 =i4 x 58 + 1 = i232 x i1 = 1 x i = i \end{gathered}$$

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 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.

The monomer of polythene is ethylene.

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.

Ozone molecule has one single bond and one double bond.

Let the total Profit be Z.
Ramu's profit share is 2/3 of profit (i.e 2Z/3)
Ravi's profit is (Z-2Z/3) =Z/3
Hence the profit ratio is , Ravi : Ramu = Z/3 : 2Z/3 = 1:2

Let total Capital be Rs.X and Ramu has contributed for Y months.Since Ramu's profit share is 2/3, his invest share will be 2/3 in capital.

Ravi's invest for 16 months / Ramu's invest for Y months = Ravi's profit share / Ramu's profit share
i.e. (X/6 x 16) / (2X/3 x Y) = 1/2

Solving the above equation, we get Y = 8.
So Ramu's money has been used for 8 months.

1/15 + 1/12 + 1/R = 1/6, we got R = 60 (it means R will take 60 days to complete the work alone)

so ratio of work done by P:Q:R = 1/15 : 1/12 : 1/60 = 5 : 4 : 1

so R share = (1/10) x 1200 = 120.