GATE Questions

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When their is a colloid in the solution, then it will show the Brownian movement, such as dust particle in the air will show the Brownian movement.

Hence, Brownian movement arises due to the impact of the molecules of the dispersion medium with the colloidal particles. It has been postulated that the impact of the molecules of dispersion medium on the colloidal particles are unequal.

This leads to the zig-zag (random) motion of the colloidal particles.

The given statement implies that 64 Squares on Carrom Board.

Digits are 0,1,2,3,4,5,6,7,8,9. So no. of digits are 10

First all possible case => 9(0 excluded) x 10 x 10 = 900

Second no repetition allowed =>9 x 9 x 8 = 648

Third all digits are same => 9 (111,222,333,444,555,666,777,888,999)

Three digit numbers where two of the three digits are same = 900 - 648 - 9 = 243 ;

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.

As the distance travelled is constant, the time taken is inversely proportional to speed.

Let 'u' be the speed of the current and 'v' be the speed of the boat.

Speed of the boat downstream = v + u & upstream = v - u

=> v+u/v-u = 30/20 => v/u = 5 => v = 5u

=> v + u = 6u = 10/20/60 miles/hr

=> 6u = 30 m/h

=> u = 5 m/h

Ratio of investment of all the three members = (7 x 12) : (9 x 12) : (2/3 x 9 x 6)

= 7 : 9 : 3

Given Rushi's one year profit = Rs. 5600

=> Let the total profit = Rs. P

Then,

P x 7/19 = 5600

Total profit P = 19 x 5600/7 = Rs. 15,200.

Let Akhil's weight = p kg

=> Shreyon's weight = 2p kg

Nani's weight = 0.9 x 2p = 1.8p kg

=> Arun's weight = 1.4p kg

Required percentage = 1.4p1.8p x 100

= 77.8%

~= 78%