Download PTU B.Sc (Non-Medical) 2020 March 1st Sem 75744 Mathematical Physics Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) B.Sc (Non-Medical) 2020 March Previous Question Papers

1 | M-75744 (S105)-1147
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Sc. (Non Medical) (2018 & Onwards) (Sem.?1)
MATHEMATICAL PHYSICS
Subject Code : BSNM-103-18
M.Code : 75744
Time : 3 Hrs. Max. Marks : 50
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying ONE marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.

SECTION-A
1. Write briefly :
a) Find the Wronskian of {x
2
, ? 2x
2
, 3x
3
}
b) Solve y
3
dx + (xy + x
2
) dy = 0.
c) Find the integrating factor of the equation
(x
4
e
x
? 2mxy
2
) dx + 2mx
2
ydy = 0
d) Find the angle between the planes x + y + z = 1 and x + 2y + 3z = 0.
e) Prove that vector product is not associative, in general,
i.e., a ? (b ? c) ? (a ? b) ? c
f) Prove that
C S
dr dS ? ? ? ? ?
? ? ?
?
?
?

g) If the vector function ( ) f t
?
have constant magnitude then prove . 0
df
f
dt
?
?
? ?
.
h) Define dirac delta function.
i) Evaluate ?f, if f (r, ?) = r
2
? b
2
cos ? where b is a constant.
j) Show that f (r, ?, ?) = r sin ? cos ? satisfies Laplace?s equation.
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1 | M-75744 (S105)-1147
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Sc. (Non Medical) (2018 & Onwards) (Sem.?1)
MATHEMATICAL PHYSICS
Subject Code : BSNM-103-18
M.Code : 75744
Time : 3 Hrs. Max. Marks : 50
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying ONE marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.

SECTION-A
1. Write briefly :
a) Find the Wronskian of {x
2
, ? 2x
2
, 3x
3
}
b) Solve y
3
dx + (xy + x
2
) dy = 0.
c) Find the integrating factor of the equation
(x
4
e
x
? 2mxy
2
) dx + 2mx
2
ydy = 0
d) Find the angle between the planes x + y + z = 1 and x + 2y + 3z = 0.
e) Prove that vector product is not associative, in general,
i.e., a ? (b ? c) ? (a ? b) ? c
f) Prove that
C S
dr dS ? ? ? ? ?
? ? ?
?
?
?

g) If the vector function ( ) f t
?
have constant magnitude then prove . 0
df
f
dt
?
?
? ?
.
h) Define dirac delta function.
i) Evaluate ?f, if f (r, ?) = r
2
? b
2
cos ? where b is a constant.
j) Show that f (r, ?, ?) = r sin ? cos ? satisfies Laplace?s equation.
2 | M-75744 (S105)-1147
SECTION-B
2. Solve (3x + y ? z) p + (x + y ? z) q = 2 (z ? y).
3. Find the volume of the parallelepiped if the edge vectors are [4, 9, ?1], [2, 6, 0],
[5, -4, 21].
4. For the function
2 2
y
f
x y
?
?
, find the value of directional derivative making an angle 30?
with the positive x-axis at point (0, 1).
5. Apply Green?s theorem in the plane to evaluate
2 2 2 2
[(2 ) ( ) ]
C
x y dx x y dy ? ? ?
?
?
where C
is boundary of the surface enclosed by the x-axis and the semi-circle
2
1 y x ? ? .
6. Evaluate
2
0
2
( ) 1
2
2 2
( ) (2 )
x x
I e
? ?
? ?
?
? ?
? ? ??
?
sin x dx explicity and let ? ? 0 to show that
0
0
lim ( ) sin I x
? ?
? ? .

SECTION-C
7. Define scalar triple product and their interpretation in terms of volume.
8. State and prove Stoke?s theorem.
9. Use a CAS to evaluate div u and curl u if u (r, ?, z) = r
2
cos ? e
r
? rz
2
sin
2
? e
?
+ e
z
e
k
.




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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