Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) B.Pharma (Bachelor of Pharmacy) 2020 March 2nd Sem 46015 Advanced Math Previous Question Paper
1 | M- 46015 (S4)-2723
Roll No. Total No. of Pages : 03
Total No. of Questions : 10
B.Pharmacy (Sem.?2,4)
ADVANCED MATH
Subject Code : PHM-122
M.Code : 46015
Time : 3 Hrs. Max. Marks : 80
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of FIFTEEN 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 FOUR questions carrying TEN marks each and students
have to attempt any THREE questions.
SECTION-A
l. Do as Directed :
a) Find the differential equation of all circles touching the axis of y as the origin and
centres on the axis of x.
b) Solve the given differential equation (x + y) dx + (y ? x) dy = 0
c) Solve the given differential equation
6 4 3
3 2 1
dy x y
dx x y
? ?
?
? ?
.
d) Eliminate the arbitrary constants and obtain a differential equation from y = A + Bx
+Cx
2
.
e) Find Laplace Transform of t
n
, where n is a positive integer.
f) Find Laplace Transform of e
?2t
sin 4t.
g) Find inverse Laplace Transform of
2
2 6
4
s
s
?
?
.
h) Find inverse Laplace Transform of
1
log
1
s
s
?
?
.
i) Find Laplace Transform of tsin
2
3t.
j) Find inverse Laplace Transform of
2 2
5
3( 1)
2
s
s
?
.
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1 | M- 46015 (S4)-2723
Roll No. Total No. of Pages : 03
Total No. of Questions : 10
B.Pharmacy (Sem.?2,4)
ADVANCED MATH
Subject Code : PHM-122
M.Code : 46015
Time : 3 Hrs. Max. Marks : 80
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of FIFTEEN 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 FOUR questions carrying TEN marks each and students
have to attempt any THREE questions.
SECTION-A
l. Do as Directed :
a) Find the differential equation of all circles touching the axis of y as the origin and
centres on the axis of x.
b) Solve the given differential equation (x + y) dx + (y ? x) dy = 0
c) Solve the given differential equation
6 4 3
3 2 1
dy x y
dx x y
? ?
?
? ?
.
d) Eliminate the arbitrary constants and obtain a differential equation from y = A + Bx
+Cx
2
.
e) Find Laplace Transform of t
n
, where n is a positive integer.
f) Find Laplace Transform of e
?2t
sin 4t.
g) Find inverse Laplace Transform of
2
2 6
4
s
s
?
?
.
h) Find inverse Laplace Transform of
1
log
1
s
s
?
?
.
i) Find Laplace Transform of tsin
2
3t.
j) Find inverse Laplace Transform of
2 2
5
3( 1)
2
s
s
?
.
2 | M- 46015 (S4)-2723
k) The mean of 200 items was 50. Later on it was discovered that two items were
misread as 92 and 8 instead of 192 and 88 respectively. Find the correct mean.
l) Compute the arithmetic mean from the given data
Height (in cm) : 219 216 213 210 207 207 201 198
No. of Persons : 2 4 6 10 11 7 5 4
m) A bag contains 7 white, 6 red and 5 black balls. Two balls are drawn at random. Find
the probability that they will both be white.
n) If the variance of the Poisson distribution is 2, find the probabilities for r = 1, 2, 3, 4
from the recurrence relation of the Poisson distribution.
o) Define critical region.
SECTION-B
2. Solve
2
dy dy
y x a y
dx dx
? ?
? ? ?
? ?
? ?
.
3. State and prove First Shifting theorem for Laplace Transformation.
4. Using Laplace Transformation, solve
2
2
2 5 sin
t
d x dx
x e t
dt dt
?
? ? ? , where x (0) = 0 and x ?(0)
= 1.
5. Find mean and standard deviation of the following :
Series Frequency Series Frequency
15-20
20-25
25-30
30-35
35-40
40-45
2
5
8
11
15
20
45-50
50-55
55-60
60-65
65-70
70-75
20
17
16
13
11
5
6. The odds that a book will be favourably received by three independent critics are 5 to 2, 4
to 3 and 3 to 4, respectively. What is the probability that, of the three reviews, majority
will be favourable ?
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1 | M- 46015 (S4)-2723
Roll No. Total No. of Pages : 03
Total No. of Questions : 10
B.Pharmacy (Sem.?2,4)
ADVANCED MATH
Subject Code : PHM-122
M.Code : 46015
Time : 3 Hrs. Max. Marks : 80
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of FIFTEEN 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 FOUR questions carrying TEN marks each and students
have to attempt any THREE questions.
SECTION-A
l. Do as Directed :
a) Find the differential equation of all circles touching the axis of y as the origin and
centres on the axis of x.
b) Solve the given differential equation (x + y) dx + (y ? x) dy = 0
c) Solve the given differential equation
6 4 3
3 2 1
dy x y
dx x y
? ?
?
? ?
.
d) Eliminate the arbitrary constants and obtain a differential equation from y = A + Bx
+Cx
2
.
e) Find Laplace Transform of t
n
, where n is a positive integer.
f) Find Laplace Transform of e
?2t
sin 4t.
g) Find inverse Laplace Transform of
2
2 6
4
s
s
?
?
.
h) Find inverse Laplace Transform of
1
log
1
s
s
?
?
.
i) Find Laplace Transform of tsin
2
3t.
j) Find inverse Laplace Transform of
2 2
5
3( 1)
2
s
s
?
.
2 | M- 46015 (S4)-2723
k) The mean of 200 items was 50. Later on it was discovered that two items were
misread as 92 and 8 instead of 192 and 88 respectively. Find the correct mean.
l) Compute the arithmetic mean from the given data
Height (in cm) : 219 216 213 210 207 207 201 198
No. of Persons : 2 4 6 10 11 7 5 4
m) A bag contains 7 white, 6 red and 5 black balls. Two balls are drawn at random. Find
the probability that they will both be white.
n) If the variance of the Poisson distribution is 2, find the probabilities for r = 1, 2, 3, 4
from the recurrence relation of the Poisson distribution.
o) Define critical region.
SECTION-B
2. Solve
2
dy dy
y x a y
dx dx
? ?
? ? ?
? ?
? ?
.
3. State and prove First Shifting theorem for Laplace Transformation.
4. Using Laplace Transformation, solve
2
2
2 5 sin
t
d x dx
x e t
dt dt
?
? ? ? , where x (0) = 0 and x ?(0)
= 1.
5. Find mean and standard deviation of the following :
Series Frequency Series Frequency
15-20
20-25
25-30
30-35
35-40
40-45
2
5
8
11
15
20
45-50
50-55
55-60
60-65
65-70
70-75
20
17
16
13
11
5
6. The odds that a book will be favourably received by three independent critics are 5 to 2, 4
to 3 and 3 to 4, respectively. What is the probability that, of the three reviews, majority
will be favourable ?
3 | M- 46015 (S4)-2723
SECTION-C
7. a) Solve (3y + 2x + 4) dx ? (4x + 6y + 5) dy = 0.
b) Solve
3
3
dy y
x
dx x
? ? ? .
8. a) Find inverse Laplace Transform of
2
2 2
2 1
( 1)( 4)
s
s s
?
? ?
.
b) Using Laplace transform, solve the simultaneous equations
2 3 0,
dx
x y
dt
? ? ? 2 0,
dy
x y
dt
? ? ? where x (0) = 8, y (0) = 3.
9. a) Calculate the first four moments about mean for the following data :
Variate : 1 2 3 4 5 6 7 8 9
Frequency : 1 6 13 25 30 22 9 5 2
b) Goals scored by two teams A and B in a football season were as below :
No. of Goals Scored No. of Matches
A B
0
1
2
3
4
27
9
8
5
4
17
9
6
5
3
Find out which team is more consistent.
10. a) The mean height of 500 male students in a certain college is 151 cm and the standard
deviation is 15 cm. Assuming the heights are normally distributed, find how many students
have heights between 120 cm and 155 cm ?
b) A random sample of size 16 has 53 as mean. The sum of squares of the deviation from mean
is 135. Can this sample be regarded as taken from the population having 56 as mean.
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 22 March 2020