Tuesday, May 26, 2015
Sunday, March 1, 2015
Saturday, October 25, 2014
Thursday, October 23, 2014
Wednesday, October 22, 2014
Wednesday, April 9, 2014
In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics,
In a class of 120 students numbered 1 to 120, all even
numbered students opt for Physics, whose numbers are divisible by 5 opt for
Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt
for none of the three subjects?
Answer
M : mathematics
P :
physics
C : chemistry
We have the formula for arithmetic series
an = a+(n-1)d here
an = last term
a=
first term
n =
number of term and
d = difference
subtract a both side and divide by (n-1)
we get
number of term n= (an- a)/d
+ 1
use this formula to get the number of student
Student numbered for physics ={2,4,6,8,……….120}
Number of student n(P) =(120- 20)/6 +1 = 60
Student numbered
for chemistry ={5,10,15,20………..120}
Number of student n(C) = (120 – 5)/5 +1=24
Student number for mathematics = {7,14,21,28………119}
Number of student n(M) =(119-7)/7 +1 =17
Student of Physics and chemistry will have number which
will be divisible by 2*5 = 10
Hence student for the physics and chemistry will have the
number = {10,20,30,40…….120 }
Number of student n(P∩C) = (120-10)/10 +1 = 12
Student of Physics and mathematics will have number which
will be divisible by of 2*7 = 14
Hence student for the physics and mathematics will have
the number = {14,28,42…….112 }
Number of student n(P∩C) = (112-14)/10 +1 = 8
Student of mathematics and chemistry will have number
which will be divisible by 7*5 = 35
Hence student for the mathematics and chemistry will have
the number = {35,70,105 }
Number of student n(M∩C) = 3
Student of mathematics, physics and chemistry will have
the number which will be divisible by 2*5*7
= 70
Hence Student of mathematics, physics and chemistry will
have the number ={70}
There are only
1 such student hence
n(M∩P∩C) = 1
We have the
formula.
n (AUBUC) =
n(A) + n(B) +n(c) – n(A∩B) – n(B∩C) –n(C∩A) + n(A∩B∩C)
replace A,B and
C by C,P and M respectively and plug the value we get
n(PUCUM) =
60 + 24+17 -12-3-8 + 1
=79
Number of
student which non of above subject =
total - n(CUPUM)
=
120-79
=41 students
Friday, May 31, 2013
Difference between Amorphous and Crystalline solids
Difference between Amorphous and Crystalline solids
Property
|
Crystalline solids
|
Amorphous solids
|
Shape
|
Definite characteristic geometrical shape
|
Irregular shape
|
Melting point
|
Melt at a sharp and characteristic
temperature
|
Gradually soften over a range of
temperature
|
Cleavage
property
|
When cut with a sharp edged tool, they
split into two pieces and the newly
generated surfaces are plain and
smooth
|
When cut with a sharp edged tool, they
cut into two pieces with irregular
surfaces
|
Heat of fusion
|
They have a definite and characteristic
heat of fusion
|
They do not have definite heat of fusion
|
Anisotropy
|
Anisotropic in nature
|
Isotropic in nature
|
Nature
|
True solids
|
Pseudo solids or super cooled liquids
|
arrangement
of constituent
particles
|
Long range order
|
Only short range order.
|
anisotropic and isotropic nature of solid
Crystalline solids are anisotropic in nature, that is, some of their physical properties like electrical resistance or refractive index show different values when measured along different directions in the same crystals. This arises from different arrangement of particles in different directions. This is illustrated in figure .
Since the arrangement of particles is different along different directions, the value of same physical property is found to be different along each direction.
Amorphous solids on the other hand are isotropic in nature. It is because there is no long range order in them and arrangement is irregular along all the directions. Therefore, value of any physical property would be same along any direction.
Since the arrangement of particles is different along different directions, the value of same physical property is found to be different along each direction.
Amorphous solids on the other hand are isotropic in nature. It is because there is no long range order in them and arrangement is irregular along all the directions. Therefore, value of any physical property would be same along any direction.
pseudo solids or super cooled liquids (why glass is called pseudo solids or super cooled liquids ?)
Like liquids, amorphous solids have a tendency to flow, though very slowly. Therefore, sometimes these are called pseudo solids or super cooled liquids. Glass panes fixed to windows or doors of old buildings are invariably found to be slightly thicker at the bottom than at the top. This is because the glass flows down very slowly and makes the bottom portion slightly thicker.
amorphous solid properties examples structure
An amorphous solid (Greek amorphos = no form) consists of particles of irregular shape. The arrangement of constituent particles (atoms, molecules or ions) in such a solid has only short range order. In such an arrangement, a regular and periodically repeating pattern is observed over short distances only. Such portions are scattered and in between the arrangement is disordered.
Glass, rubber and plastics are typical examples of amorphous solids.
 |
| amorphous of structure |
Glass, rubber and plastics are typical examples of amorphous solids.
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