GATE Questions

---

We need to find the total cost to send r messsages, r > 1000.

The first 1000 messsages will cost Rs.p each (Or) 

The total cost of first 1000 messsages = Rs.1000p

The remaining (r - 1000) messsages will cost Rs.q each (Or)

The cost of the (r - 1000) = Rs.(r - 1000)y

Therefore, total cost = 1000p + rq - 1000q

= 1000(p - q) + qr

We know that,

The equivalent K =  L1 + L2L1K1+L2K2

where L1 & L2 are plate1 & Plate2 thicknesses, K1 & K2 are coefficient thermal conductivity of plate1 & Plate2 respectively.

But here L1 = L2 = L (say)

Then K = L+L/(L/K1 + L/K2)  =  2K1K2K1+K2

An object at rest may have Potential energy.

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.

Milk is an emulsion of oil in water (o/w).

Emulsion: A suspension of droplets of one liquid in another.

Constituents of milk :

The principal constituents of milk are water, fat, proteins, lactose (milk sugar) and minerals (salts). Milk also contains trace amounts of other substances such as pigments, enzymes, vitamins, phospholipids (substances with fatlike properties), and gases.

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

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