Download PTU B.Sc-Agriculture 2020 March 2nd Sem 72360 Mathematics ? Ii Question Paper

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

1 | M-72360 (S2)-1908
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Sc.(Agriculture) (2014 to 2018) (Sem.?2)
MATHEMATICS ? II
Subject Code : BSAG-205A
M.Code : 72360
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO 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
Q1. Write briefly :
a) Evaluate
2
0
tan sin
lim
x
x x
x
?
?
.
b) Evaluate lim
x x
x x
x
e e
e e
?
?
? ?
?
?
.
c) Differentiate
1
1
x
y
x
?
?
?
with respect to x.
d) Show that y = a sin x ? is solution of
2
2
0
d y
y
dx
? ? ? .
e) If y = e
ax
, find y
n
.
f) If radius of a sphere is 5 cm and is increasing at 0.1 cm/sec, how fast is its volume
changing ?
g) Evaluate
2
cot
sin
x
dx
x
?
.
h) Show that ?xe
x
dx = e
x
(x ? 1) + c.
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1 | M-72360 (S2)-1908
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Sc.(Agriculture) (2014 to 2018) (Sem.?2)
MATHEMATICS ? II
Subject Code : BSAG-205A
M.Code : 72360
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO 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
Q1. Write briefly :
a) Evaluate
2
0
tan sin
lim
x
x x
x
?
?
.
b) Evaluate lim
x x
x x
x
e e
e e
?
?
? ?
?
?
.
c) Differentiate
1
1
x
y
x
?
?
?
with respect to x.
d) Show that y = a sin x ? is solution of
2
2
0
d y
y
dx
? ? ? .
e) If y = e
ax
, find y
n
.
f) If radius of a sphere is 5 cm and is increasing at 0.1 cm/sec, how fast is its volume
changing ?
g) Evaluate
2
cot
sin
x
dx
x
?
.
h) Show that ?xe
x
dx = e
x
(x ? 1) + c.
2 | M-72360 (S2)-1908
i) Prove that
2
log
( 1)( 2) 1
dx x
c
x x x
? ? ?
? ?
? ?
? ? ?
? ?
?
.
j) Evaluate
3
(2 3sin 5 ) x x x dx ? ?
?
.

SECTION-B
2. Show that
1 1
lim 1
x
x x e ? ?
? ?
? ?
? ?
? ?
.
3. Find
dy
dx
for y = x
sinx
.
4. Find the equation of the tangent and normal to the curve y = x
3
? 3x
2
? x + 5 at the point
(3, 2).
5. Evaluate ? e
ax
sin bx dx.
6. Prove that
1
2 2
sin
dx x
c
a
a x
?
? ?
?
?
.

SECTION-C
7. Evaluate
2 2
dx
x x ?
?
.
8. Evaluate
2
( 1)( 1)
dx
x x x ? ? ?
?
.
9. If y = tan
?1
x, show that (1 + x
2
) y
2
+ 2xy
1
= 0 and deduce that (1 + x
2
) y
n+2
+ 2 (n + 1)
xy
n + 1
+ n (n + 1) y
n
= 0. Hence determine y
n
when x = 0.


NOTE : Disclosure of identity by writing mobile number or making passing request on any
page of Answer sheet will lead to UMC case against the Student.

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