Download PTU M-Sc -Chemistry 1st Semester May 2019 72262 MATHEMATICS IN CHEMISTRY Question Paper

Download PTU (I. K. Gujral Punjab Technical University) MSc -Chemistry 1st Semester May 2019 72262 MATHEMATICS IN CHEMISTRY Question Paper.

1 | M-72262 (S17)-2191

Roll No. Total No. of Pages : 03
Total No. of Questions : 09
M.Sc.(Chemistry) (2015 to 2017) (Sem.?1)
MATHEMATICS IN CHEMISTRY
Subject Code : MSCH-103
M.Code : 72262
Time : 3 Hrs. Max. Marks : 100
INSTRUCTIONS TO CANDIDATES :
1. Attempt FIVE questions in ALL including Question no.1 which is COMPULSORY
and selecting ONE EACH from Unit I to IV.
2. All questions carry EQUAL marks.

1. Write briefly :
a) Give the drawback of Gauss elimination method.
b) Give Newton?s backward difference formula.
c) Evaluate the first approximation from
2
1,
dy
x y
dx
? ? y(0) = 1 using Picard?s method.
d) Using Euler?s method, find an approximate value of y(0.2) from
, (0.1) 1.22.
dy
x y y
dx
? ? ?
e) Classify the following PDE
2 2
2 2
2 2
(1 ) 0
u u
x y
x y
? ?
? ? ?
? ?
.
f) Give regression line x on y and y on x.
g) Give four properties of normal distribution.
h) Define null hypothesis by giving suitable example.
i) Give four properties of F distribution.
j) Give four properties of ?
2
distribution.
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1 | M-72262 (S17)-2191

Roll No. Total No. of Pages : 03
Total No. of Questions : 09
M.Sc.(Chemistry) (2015 to 2017) (Sem.?1)
MATHEMATICS IN CHEMISTRY
Subject Code : MSCH-103
M.Code : 72262
Time : 3 Hrs. Max. Marks : 100
INSTRUCTIONS TO CANDIDATES :
1. Attempt FIVE questions in ALL including Question no.1 which is COMPULSORY
and selecting ONE EACH from Unit I to IV.
2. All questions carry EQUAL marks.

1. Write briefly :
a) Give the drawback of Gauss elimination method.
b) Give Newton?s backward difference formula.
c) Evaluate the first approximation from
2
1,
dy
x y
dx
? ? y(0) = 1 using Picard?s method.
d) Using Euler?s method, find an approximate value of y(0.2) from
, (0.1) 1.22.
dy
x y y
dx
? ? ?
e) Classify the following PDE
2 2
2 2
2 2
(1 ) 0
u u
x y
x y
? ?
? ? ?
? ?
.
f) Give regression line x on y and y on x.
g) Give four properties of normal distribution.
h) Define null hypothesis by giving suitable example.
i) Give four properties of F distribution.
j) Give four properties of ?
2
distribution.
2 | M-72262 (S17)-2191

UNIT-I
2. a) Solve using Gauss elimination method
2x + 2y + z = 12
3x + 2y + 2z = 8,
5x + 10y ? 8z = 10.
b) Solve by Jacobi?s method 20x + y ? 2z = 17, 3x + 20y ? z = ? 18, 2x ? 3y + 20z = 25.
3. a) Find
dy
dx
at x = 1.6 and
2
2
d y
dx
at x = 1.1 from the following data :
x 1.0 1.1 1.2 1.3 1.4 1.5 1.6
y 7.989 8.403 8.781 9.129 9.451 9.750 10.031
b) Evaluate
6
2
0
1
1
dx
x ?
?
using Simpson?s 1/3 rule.
UNIT?II
4. a) Using Taylor?s series method, find value of y (0.2) from 2 3 , (0) 0
x
dy
y e y
dx
? ? ?
b) Using modified Euler?s method, find value of y (0.3) from , (0) 1
dy
x y y
dx
? ? ? .
5. Using Runge-Kutta method, find value of y (0.2) and y (0.4) from , (0) 1
dy y x
y
dx y x
?
? ?
?
.
UNIT-III
6. a) Calculate the coefficient of correlation from the following data :
x 105 104 102 101 100 99 98 96 93 92
y 101 103 100 98 95 96 104 92 97 94
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1 | M-72262 (S17)-2191

Roll No. Total No. of Pages : 03
Total No. of Questions : 09
M.Sc.(Chemistry) (2015 to 2017) (Sem.?1)
MATHEMATICS IN CHEMISTRY
Subject Code : MSCH-103
M.Code : 72262
Time : 3 Hrs. Max. Marks : 100
INSTRUCTIONS TO CANDIDATES :
1. Attempt FIVE questions in ALL including Question no.1 which is COMPULSORY
and selecting ONE EACH from Unit I to IV.
2. All questions carry EQUAL marks.

1. Write briefly :
a) Give the drawback of Gauss elimination method.
b) Give Newton?s backward difference formula.
c) Evaluate the first approximation from
2
1,
dy
x y
dx
? ? y(0) = 1 using Picard?s method.
d) Using Euler?s method, find an approximate value of y(0.2) from
, (0.1) 1.22.
dy
x y y
dx
? ? ?
e) Classify the following PDE
2 2
2 2
2 2
(1 ) 0
u u
x y
x y
? ?
? ? ?
? ?
.
f) Give regression line x on y and y on x.
g) Give four properties of normal distribution.
h) Define null hypothesis by giving suitable example.
i) Give four properties of F distribution.
j) Give four properties of ?
2
distribution.
2 | M-72262 (S17)-2191

UNIT-I
2. a) Solve using Gauss elimination method
2x + 2y + z = 12
3x + 2y + 2z = 8,
5x + 10y ? 8z = 10.
b) Solve by Jacobi?s method 20x + y ? 2z = 17, 3x + 20y ? z = ? 18, 2x ? 3y + 20z = 25.
3. a) Find
dy
dx
at x = 1.6 and
2
2
d y
dx
at x = 1.1 from the following data :
x 1.0 1.1 1.2 1.3 1.4 1.5 1.6
y 7.989 8.403 8.781 9.129 9.451 9.750 10.031
b) Evaluate
6
2
0
1
1
dx
x ?
?
using Simpson?s 1/3 rule.
UNIT?II
4. a) Using Taylor?s series method, find value of y (0.2) from 2 3 , (0) 0
x
dy
y e y
dx
? ? ?
b) Using modified Euler?s method, find value of y (0.3) from , (0) 1
dy
x y y
dx
? ? ? .
5. Using Runge-Kutta method, find value of y (0.2) and y (0.4) from , (0) 1
dy y x
y
dx y x
?
? ?
?
.
UNIT-III
6. a) Calculate the coefficient of correlation from the following data :
x 105 104 102 101 100 99 98 96 93 92
y 101 103 100 98 95 96 104 92 97 94
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b) A has one share in a lottery in which there is 1 prize and 2 blanks; B has three shares
in a lottery in which there are 3 prizes and 6 blanks. Compare the probability of A?s
success to that of B?s success.
7. a) In sampling a large number of parts manufactured by a machine, the mean number of
defective in a sample of 20 is 2. Out of 1000 such samples, how many would be
expected to contain at least 3 defective parts.
b) Fit a Poisson distribution to the data:
x 0 1 2 3 4
f 122 60 15 2 1
UNIT ? IV
8. a) A die was thrown 9000 times and a throw of 5 or 6 was obtained 3240 times. On the
assumption of random throwing, do the data indicate an unbiased die?
(take z
0.05
= 1.96)
b) A sample height of 6400 soldiers has a mean of 67.85 inches and a standard deviation
of 2.56 inches while a simple sample of heights of 1600 sailors has a mean of 68.55
inches and a standard deviation of 2.52 inches. Do the data indicate that the sailors
are on the average taller than soldiers? (take z
0.05
= 1.96)
9. a) The nine items of a sample have the following values 45, 47, 50, 52, 48, 47, 49, 53,
51. Does the mean of these differ significantly from the assumed mean of 47.5?
(for v = 8, t
0.05
= 2.31)
b) A set of five similar coins is tossed 320 times and the result is :
No. of heads 0 1 2 3 4 5
Frequency 6 27 72 112 71 32
Test the hypothesis that the data follows a Binomial distribution.
(for v = 5,
2
0.05
? 11.07)

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page of Answer Sheet will lead to UMC against the Student.
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