IIT JEE June 1 st Weekly Cumulative Practice Test

1. State whether the statement is true or false

A projectile fired form the ground follows a parabolic path. The speed of the projectile is minimum at the top of its path.


2. The number of vectors of unit length perpendicular to vectors a = (1,1,0) and b = (0,1,1) is

a. three
b. two
c. one
d. infinite
e. none of these






3. Let z1 and z2 be complex numbers such that z1≠z2 and |z1| = |z2|. If z1 has positive real part and z2 has negative imaginary part, then (z1+z2)/(z1-z2) may be

a. real and positive
b. zero
c. real and negative
d. purely imaginary
e. none of these



4. If two compounds have the same empirical formula but different molecular formulae they must have ------

a. different percentage composition
b. different molecular weight
c. same viscosity
d. same vapour density

Solutions for May 25 Practice set

covers topics
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 60i +3j, 40i-8j, ai-52j 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)

[(ai-52j)-( 60i +3j)] = k[(40i-8j)-( 60i +3j)]

=> (a-60)i – 55j = k(-20i-11j)
=> 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.

May 25 2008 Question set 1

covers topics
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


2. The points with the position vectors 60i +3j, 40i-8j, ai-52j are collinear if

a. a = -40
b. a = 40
c. a = 20
d. none of these

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


For solution see
http://iit-jee-nrao.blogspot.com/2008/05/solutions-for-may-25-practice-set.html