Download PTU M-Sc -Chemistry 1st Semester May 2019 75119 NUMERICAL METHODS FOR CHEMISTS Question Paper

Download PTU (I. K. Gujral Punjab Technical University) MSc -Chemistry 1st Semester May 2019 75119 NUMERICAL METHODS FOR CHEMISTS Question Paper.

1 | M-75119 (S44)-2493

Roll No. Total No. of Pages : 02
Total No. of Questions : 15
M.Sc.(Chemistry) (2018 Batch) (Sem.?1)
NUMERICAL METHODS FOR CHEMISTS
Subject Code : CHL406B-18
M.Code : 75119
Time : 3 Hrs. Max. Marks : 50
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of FIVE questions carrying TWO marks
each.
2. SECTION-B contains EIGHT questions carrying FOUR marks each and students
have to attempt any SIX questions.
3. SECTION-C will comprise of two compulsory questions with internal choice in both these
questions. Each question carries EIGHT marks.

SECTION-A
1. Illustrate the associative law of matrix multiplication using an example.
2. Prove that any square matrix can be expressed as a sum of symmetric and skew-
symmetric matrix.
3. Define Bohr?s radius.
4. How are differential equations applicable in chemical kinetics?
5. Explain conditional probability with example.

SECTION-B
6. Express A
2 2 4
1 3 4
1 2 3
? ? ? ?
? ?
? ?
? ?
? ? ? ?
? ?
as the sum of a symmetric and skew-symmetric matrix.
7. Obtain the inverse of the following matrix :
2 0 1
A 5 1 0
0 1 3
? ? ?
? ?
?
? ?
? ?
? ?

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1 | M-75119 (S44)-2493

Roll No. Total No. of Pages : 02
Total No. of Questions : 15
M.Sc.(Chemistry) (2018 Batch) (Sem.?1)
NUMERICAL METHODS FOR CHEMISTS
Subject Code : CHL406B-18
M.Code : 75119
Time : 3 Hrs. Max. Marks : 50
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of FIVE questions carrying TWO marks
each.
2. SECTION-B contains EIGHT questions carrying FOUR marks each and students
have to attempt any SIX questions.
3. SECTION-C will comprise of two compulsory questions with internal choice in both these
questions. Each question carries EIGHT marks.

SECTION-A
1. Illustrate the associative law of matrix multiplication using an example.
2. Prove that any square matrix can be expressed as a sum of symmetric and skew-
symmetric matrix.
3. Define Bohr?s radius.
4. How are differential equations applicable in chemical kinetics?
5. Explain conditional probability with example.

SECTION-B
6. Express A
2 2 4
1 3 4
1 2 3
? ? ? ?
? ?
? ?
? ?
? ? ? ?
? ?
as the sum of a symmetric and skew-symmetric matrix.
7. Obtain the inverse of the following matrix :
2 0 1
A 5 1 0
0 1 3
? ? ?
? ?
?
? ?
? ?
? ?

2 | M-75119 (S44)-2493

8. Prove that the function f (x) = 5x ? 3 is continuous at x = 0, at x = ?3 and at x = 5.
9. Find the derivative of f given by f (x) = sin
?1
x assuming it exists.
10. Find the general solution of the differential equation dy/dx ? y = cos x.
11. Show that the differential equation (x ? y) dy ? (x + y) dx = 0 is homogeneous and solve
it.
12. An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after
the other without replacement. What is the probability that both drawn balls are black?
13. A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a
six. Find the probability that it is actually a six.

SECTION-C
14. a) Show that 0.
1 1 1
x y y z z x
z x y
? ? ?
? ? ?
Or
b) Find the area of the region enclosed between the two circles x
2
+ y
2
= 4 and
(x ? 2)
2
+ y
2
= 4
15. a) Find the general solution of the differential equation dy/dx = (x + 1)/(2 ? y), (y ? 2).
Or
b) Use method of least squares to fit a straight line to the data
X: 2 4 6 8 10 12
Y: 7.32 8.24 9.20 10.19 11.01 12.05

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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