Download PTU M-Sc -Chemistry 1st Semester May 2019 51207 MATHEMATICS Question Paper

Download PTU (I. K. Gujral Punjab Technical University) MSc -Chemistry 1st Semester May 2019 51207 MATHEMATICS Question Paper.

1 | M-51207 (S39)-2483

Roll No. Total No. of Pages : 02
Total No. of Questions : 19
M.Sc. (Chemistry) (Campus) (2015 to 2017) (Sem.-1)
MATHEMATICS
Subject Code : CHL-405M
M.Code : 51207
Time : 3 Hrs. Max. Marks : 70
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains SIX questions carrying FIVE marks each and students
have to attempt ALL questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.

SECTION-A
Answer briefly :
1. Let u = 2i ? j + k and w = i + 2k are two vectors? find the cross product v ? w and dot
product u.w.
2. Find the gradient of scalar point function ? (x, y, z) = x
2
yz at the point (1, ?1, 2)
3. Find X and Y if X + Y =
1 3
2 4
? ?
? ?
?
? ?
and X ? Y =
10 3
.
5 4
? ? ?
? ?
? ?

4. Define a Hermitian matrix.
5. Find
dy
dx
where y = 2 cos x .
6. Evaluate the integral ?(x
5
+ 1)
7
x
4
dx.
7. Solve the differential equation
2
(1 ) ( 1).
dy
x y
dx
? ? ?
8. Write down the differential equation of a harmonic oscillator.
9. Find the probability of outcome 10 from two throws of a dice.
10. In how many ways a committee consisting of 3 men and 2 men can be chosen from 7
men and 5 women?
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1 | M-51207 (S39)-2483

Roll No. Total No. of Pages : 02
Total No. of Questions : 19
M.Sc. (Chemistry) (Campus) (2015 to 2017) (Sem.-1)
MATHEMATICS
Subject Code : CHL-405M
M.Code : 51207
Time : 3 Hrs. Max. Marks : 70
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains SIX questions carrying FIVE marks each and students
have to attempt ALL questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.

SECTION-A
Answer briefly :
1. Let u = 2i ? j + k and w = i + 2k are two vectors? find the cross product v ? w and dot
product u.w.
2. Find the gradient of scalar point function ? (x, y, z) = x
2
yz at the point (1, ?1, 2)
3. Find X and Y if X + Y =
1 3
2 4
? ?
? ?
?
? ?
and X ? Y =
10 3
.
5 4
? ? ?
? ?
? ?

4. Define a Hermitian matrix.
5. Find
dy
dx
where y = 2 cos x .
6. Evaluate the integral ?(x
5
+ 1)
7
x
4
dx.
7. Solve the differential equation
2
(1 ) ( 1).
dy
x y
dx
? ? ?
8. Write down the differential equation of a harmonic oscillator.
9. Find the probability of outcome 10 from two throws of a dice.
10. In how many ways a committee consisting of 3 men and 2 men can be chosen from 7
men and 5 women?
2 | M-51207 (S39)-2483

SECTION-B
11. If i + j + k, 2i + 5j, 3i + 2j ? 3k and i ? 6j ? k are the position vectors of points A, B, C and
D respectively, then find the angle between and AB CD
? ? ? ? ? ? ? ?
.
12. Solve the following system of equations using matrix method.
2x ? 3y + 4z = 8, y ? 3z = ? 7, x + 2y + 2z = 11
13. Find local maximum and minimum values of the function f (x) = 3x
4
+ 4x
3
? 12 x
2
+ 12.
14. Find the general solution of the following differential equation :
(x
2
+ y
2
+ x) dx + 2xydy = 0
15. Fit least square straight line to the following data points :
X : 1 2 3 4 5 6
Y : 6 4 3 5 4 2
16. Find the product of AB where A =
1 0 1
2 4 2
10 1 3
? ?
? ?
? ?
? ?
? ?
and B =
2 0 1
0 1 2
1 2 3
? ? ?
? ?
? ?
? ?
? ?


SECTION-C
17. Solve the Huckel Molecular ? orbital problem for the allyl radical
CH
2
CHCH
2
in terms of the Huckel parameters ? and ? :
( ? ? E) c
1
+ ?c
2
= 0
?c
1
+ ( ? ? E) c
2
+ ?c
3
= 0
?c
2
+ ( ? ? E)c
3
= 0
18. Find the Fourier series for f (x) = x + x
2
, ? ? ? x ? ?.
19. Evaluate the integral
2
( 1) ( 2)
dx
x x ? ?
?
by resolving into partial fractions.

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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