Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) B.Sc Hons (Bachelor of Science Honours) 2020 March Previous Question Papers
1 | M-77226 (S111)-2529
Roll No. Total No. of Pages : 02
Total No. of Questions : 11
B.Sc. (Honours) Chemistry (2019 Batch) (Sem.-1)
MATHS-I (CALCULUS-I)
Subject Code : UC-BSHM-104-19
M.Code : 77226
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of EIGHT 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 TEN marks.
SECTION-A
1. Attempt the following :
a) Determine the value of k for which the following function is continuous at x = 3.
2
9
; 3
( )
3
; 3
x
x
f x
x
k x
?
?
? ?
?
? ?
?
?
?
b) State Lagrange?s Mean Value Theorem.
c) Evaluate
2x
xe dx
?
.
d) Find the value of the integral
/2
7
/2
sin x dx
?
? ?
?
.
e) If u = x
m
y
n
, find the total derivative of u.
f) If Z = f (x + ct) + ? (x ? ct), prove that
2 2
2
2 2
z z
c
t x
? ?
?
? ?
g) Evaluate
3 1
2 2
0 0
( 3 ) x y dydx ?
? ?
.
h) If x = r cos ? and y = r sin ?, find the value of
( , )
( , )
x y
r
?
? ?
.
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1 | M-77226 (S111)-2529
Roll No. Total No. of Pages : 02
Total No. of Questions : 11
B.Sc. (Honours) Chemistry (2019 Batch) (Sem.-1)
MATHS-I (CALCULUS-I)
Subject Code : UC-BSHM-104-19
M.Code : 77226
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of EIGHT 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 TEN marks.
SECTION-A
1. Attempt the following :
a) Determine the value of k for which the following function is continuous at x = 3.
2
9
; 3
( )
3
; 3
x
x
f x
x
k x
?
?
? ?
?
? ?
?
?
?
b) State Lagrange?s Mean Value Theorem.
c) Evaluate
2x
xe dx
?
.
d) Find the value of the integral
/2
7
/2
sin x dx
?
? ?
?
.
e) If u = x
m
y
n
, find the total derivative of u.
f) If Z = f (x + ct) + ? (x ? ct), prove that
2 2
2
2 2
z z
c
t x
? ?
?
? ?
g) Evaluate
3 1
2 2
0 0
( 3 ) x y dydx ?
? ?
.
h) If x = r cos ? and y = r sin ?, find the value of
( , )
( , )
x y
r
?
? ?
.
2 | M-77226 (S111)-2529
SECTION-B
2. Find the derivative of the function x
sin x
.
3. Find the interval in which the function f (x) = 2x
3
+ 9x
2
+ 12x + 20 is increasing.
4. Evaluate the integral
2 1
( 1)( 2)
x
dx
x x
?
? ?
?
.
5. Evaluate :
1/ 2
1
2 3/2
0
sin
(1 )
x
dx
x
?
?
?
.
6. Let be a f (x, y) function defined as
2 2
; ( , ) (0,0)
( , )
0 ; ( , ) (0,0)
xy
x y
f x y x y
x y
?
?
?
? ?
?
?
?
?
. Show that
f (x, y) is discontinuous at (0, 0).
7. If
3 3
3 3
x y
T
x y
?
?
, prove that 3
u u
x y T
x y
? ?
? ?
? ?
.
8. Evaluate
0
y
x
e
dydx
y
? ?
?
? ?
by changing the order of integration.
9. Find the area bounded by the circle x
2
+ y
2
= p
2
using polar coordinates.
SECTION-C
10. Show that the surface area of a closed cuboid with square base and given volume is
minimum, when it is a cube.
Or
Using definite integrals, find the area bounded by the curves y
2
= 4ax and x
2
= 4ay.
11. Find the dimensions of the rectangular box, open at the top, of maximum capacity whose
surface is 432 cm
2
.
Or
Using triple integration, find the volume of the sphere x
2
+ y
2
+ z
2
= a
2
.
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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This post was last modified on 02 April 2020