Complex Numbers

Vectors (common to physics and mathematics)

Mole concept

1. The inequality |z-4|<|z-2| represents the region given by

a. Re(z)>0

b. Re(z)<2

c. Re(z)<0

d. none of these

Answer (d)

Answer

Let z = x+iy then

|z-4|<|z-2|

=> |z-4²|<|z-2|²

=> (x-4) ²+y²<(x-2) ²+y²

=> -8x+16<-4x+4

=>12<4x

=> x>3

Means Re(z)>3

2. The points with the position vectors 60

**i**+3

**j**, 40

**i**-8

**j**, a

**i**-52

**j**are collinear if

a. a = -40

b. a = 40

c. a = 20

d. none of these

If the vectors

**x**and

**y**are collinear,

x = py

If we take given position vectors m.n,o, it implies

**o**-

**m**= p(

**n**-

**m**)

[(a

**i**-52

**j**)-( 60

**i**+3

**j**)] = k[(40

**i**-8

**j**)-( 60

**i**+3

**j**)]

=> (a-60)

**i**– 55

**j**= k(-20

**i**-11

**j**)

=> a-60 = -20k and -55 = -11k

=> k = 55/11

=> a = -20*5 + 60

=> a = -40

3. One molal solution is one that contains one mole of a solute in :

a. 1000 g of the solvent

b. one litre of the solvent

c. one litre of the solution

d. 22.4 litres of the solution

Answer (a)

As per the definition, molality is amount of solute per kg of solvent.

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