Mathematics
1. if |z-1| /|z-4| = 2, the locus of z = x+iy in Argand plane will be:
a. parabola
b. hyperbola
c. circle
d. straight line
2.
Let a,b,c be three non-coplanar vectors and p,q,r are vectors defined by the relations
p = b×c/[abc]
q = c×a/[abc]
r = a×b/[abc]
then the value of the expression
[(a+b).p +(b+c).q +(c+a).r] is equal to
a. 3
b. 1
c. 0
d. 2
Physics
3. A particle moving eastwards with a velocity 5 m/s. In 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is
a. zero
b. 1/SQRT(2) m/s² towards north-west
c. ½ m/s² toward north-west
d. ½ m/s² towards north
Chemistry
4. Which of the following has maximum number of atoms?
a. 24 g of C (M=12 g mol^-1
b. 23 g of Na (M = 23 g mol^-1)
c. 48 g of S (M = 32 b mol^-1)
d. 108 g of Ag (M = 108 mol ^-1)
5. The wave number of the shortest wavelength transition in the Balmer series of atomic hydrogen is.
a. 27420 cm^-1
b. 28420 cm^-1
c. 29420 cm^-1
d. 12186 cm^-1
Showing posts with label June 2008. Show all posts
Showing posts with label June 2008. Show all posts
Saturday, June 7, 2008
Solutions to June 1 2008 practice set
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.
Answer: true
At the top of the path, the vertical component of velocity is zero and the particle has only horizontal component. Hence the speed (the magnitude of the velocity) is minimum at the top of the 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
Answer (b)
If vector (x,y,z) is a unit vector perpendicular to (1,1,0) their scalar product is zero
=> x +y = 0
=> y = -x
If vector (x,y,z) is a unit vector perpendicular to (0,1,1) their scalar product is zero
=> y+z = 0
=> y = -z
As it is a unit vector x²+y²+z² = 1
=> 3y² = 1
=> y = ±1/SQRT(3)
This gives two value of y and hence there are two vectors
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
Answer: (b) and (d)
Assume z1 = a+ib, a is positive means a>0,
z2 = c+id, d<0
|z1| = |z2|
=> a²+b² = c²+d²
(z1+z2)/(z1-z2) = [(a+c) + i(b+d)]/ [(a-c) + i(b-d)]
Taking the multiplicative inverse of denominator and multiplying the numerator
= [(a+c) + i(b+d)]* [(a-c) - i(b-d)]/[(a-c) ² + (b-d) ²]
= [(a²-c²)+(b²-d²)]+i[(b+d)(a-c)-(a+c)(b-d)]/ [(a-c) ² + (b-d) ²]
=[{(a²+b²)-(c²+d²)}+i{(b+d)(a-c)-(a+c)(b-d)}]/ [(a-c) ² + (b-d) ²]
As a²+b² = c²+d² the first term of the numerator is zero.
Hence
(z1+z2)/(z1-z2)
= i[(b+d)(a-c)-(a+c)(b-d)]/ [(a-c) ² + (b-d) ²]
So this is a pure imaginary number.
If b+d as well as a+c are equal zero, the expression can be zero also.
4. If two compounds have the same empirical formula but different molecular formulae they must have ------
a. different percentage composition
b. different molecular weights
c. same viscosity
d. same vapour density
answer (b)
Different molecular formulae but same empirical formula imply same empirical mass but different molecular masses
A projectile fired form the ground follows a parabolic path. The speed of the projectile is minimum at the top of its path.
Answer: true
At the top of the path, the vertical component of velocity is zero and the particle has only horizontal component. Hence the speed (the magnitude of the velocity) is minimum at the top of the 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
Answer (b)
If vector (x,y,z) is a unit vector perpendicular to (1,1,0) their scalar product is zero
=> x +y = 0
=> y = -x
If vector (x,y,z) is a unit vector perpendicular to (0,1,1) their scalar product is zero
=> y+z = 0
=> y = -z
As it is a unit vector x²+y²+z² = 1
=> 3y² = 1
=> y = ±1/SQRT(3)
This gives two value of y and hence there are two vectors
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
Answer: (b) and (d)
Assume z1 = a+ib, a is positive means a>0,
z2 = c+id, d<0
|z1| = |z2|
=> a²+b² = c²+d²
(z1+z2)/(z1-z2) = [(a+c) + i(b+d)]/ [(a-c) + i(b-d)]
Taking the multiplicative inverse of denominator and multiplying the numerator
= [(a+c) + i(b+d)]* [(a-c) - i(b-d)]/[(a-c) ² + (b-d) ²]
= [(a²-c²)+(b²-d²)]+i[(b+d)(a-c)-(a+c)(b-d)]/ [(a-c) ² + (b-d) ²]
=[{(a²+b²)-(c²+d²)}+i{(b+d)(a-c)-(a+c)(b-d)}]/ [(a-c) ² + (b-d) ²]
As a²+b² = c²+d² the first term of the numerator is zero.
Hence
(z1+z2)/(z1-z2)
= i[(b+d)(a-c)-(a+c)(b-d)]/ [(a-c) ² + (b-d) ²]
So this is a pure imaginary number.
If b+d as well as a+c are equal zero, the expression can be zero also.
4. If two compounds have the same empirical formula but different molecular formulae they must have ------
a. different percentage composition
b. different molecular weights
c. same viscosity
d. same vapour density
answer (b)
Different molecular formulae but same empirical formula imply same empirical mass but different molecular masses
Saturday, May 31, 2008
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
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
Subscribe to:
Comments (Atom)