Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) B.Pharma (Bachelor of Pharmacy) 2020 March 2nd Sem 46012 Remedial Mathematics Previous Question Paper
1 | M- 46012 (S4)-2710
Roll No. Total No. of Pages : 03
Total No. of Questions : 10
B.Pharmacy (Sem.?1,3)
REMEDIAL MATHEMATICS
Subject Code : PHM-112
M.Code : 46012
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. Write short notes on :
a) Solve the equation x
2
+ x + 7 = 0.
b) For what values of x and y the following pair of matrices A and B equal
A
3 7 5
1 2 3
x
y x
? ? ?
?
? ?
? ?
? ?
and B
0 2
8 4
y ? ? ?
?
? ?
? ?
c) Find the value of x so that the determinant
3 7 5
1 2 3
x
x
?
?
is zero.
d) If tan x = 3/5 find the value of sin 2x.
e) Show that
2
1 cos
cot
1 cos 2
x x
x
?
?
?
.
f) Find the x and y intercepts of the line 3x + 4y ? 7 = 0.
g) Find the angle between the line x + y + 1 = 0 and ?x + 2y + 5 = 0.
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1 | M- 46012 (S4)-2710
Roll No. Total No. of Pages : 03
Total No. of Questions : 10
B.Pharmacy (Sem.?1,3)
REMEDIAL MATHEMATICS
Subject Code : PHM-112
M.Code : 46012
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. Write short notes on :
a) Solve the equation x
2
+ x + 7 = 0.
b) For what values of x and y the following pair of matrices A and B equal
A
3 7 5
1 2 3
x
y x
? ? ?
?
? ?
? ?
? ?
and B
0 2
8 4
y ? ? ?
?
? ?
? ?
c) Find the value of x so that the determinant
3 7 5
1 2 3
x
x
?
?
is zero.
d) If tan x = 3/5 find the value of sin 2x.
e) Show that
2
1 cos
cot
1 cos 2
x x
x
?
?
?
.
f) Find the x and y intercepts of the line 3x + 4y ? 7 = 0.
g) Find the angle between the line x + y + 1 = 0 and ?x + 2y + 5 = 0.
2 | M- 46012 (S4)-2710
h) In a moderately skewed distribution, the median is 20 and the mean is 22.5. Using
these values, find the approximate value of the mode.
i) Define mean and median.
j) Differentiate the function f (x) = x
2
sin x with respect to x.
k) If x
2
+ sin xy = 7, find
dy
dx
.
l) Solve the integral
sin
cos
x
xe dx
?
.
m) Solve
x
xe dx
?
.
n) Find the derivative of f (x) = x
3/2
+ sin x with respect to x.
o) Find the value of tan 225
0
.
SECTION-B
2. Solve the following system of equations by using Cramer?s law
3x ? 2y + 3z = 8, 2x + y ? z =1, 4x ? 3y + 2z = 4.
3. Show that 2sin
2
? ? + 4 cos ( ? + ?) sin ? sin ? + cos 2 ( ? + ?) = cos 2 ?.
4. Find the foot of perpendicular of the point (2, 3) on the line x + y ? 11 = 0
5. Solve the integral
2
2 3
( 1) (2 3)
x
dx
x x
?
? ?
?
.
6. Differentiate
2
2
( 3)( 4)
3 4 5
x x
x x
? ?
? ?
with respect to x.
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1 | M- 46012 (S4)-2710
Roll No. Total No. of Pages : 03
Total No. of Questions : 10
B.Pharmacy (Sem.?1,3)
REMEDIAL MATHEMATICS
Subject Code : PHM-112
M.Code : 46012
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. Write short notes on :
a) Solve the equation x
2
+ x + 7 = 0.
b) For what values of x and y the following pair of matrices A and B equal
A
3 7 5
1 2 3
x
y x
? ? ?
?
? ?
? ?
? ?
and B
0 2
8 4
y ? ? ?
?
? ?
? ?
c) Find the value of x so that the determinant
3 7 5
1 2 3
x
x
?
?
is zero.
d) If tan x = 3/5 find the value of sin 2x.
e) Show that
2
1 cos
cot
1 cos 2
x x
x
?
?
?
.
f) Find the x and y intercepts of the line 3x + 4y ? 7 = 0.
g) Find the angle between the line x + y + 1 = 0 and ?x + 2y + 5 = 0.
2 | M- 46012 (S4)-2710
h) In a moderately skewed distribution, the median is 20 and the mean is 22.5. Using
these values, find the approximate value of the mode.
i) Define mean and median.
j) Differentiate the function f (x) = x
2
sin x with respect to x.
k) If x
2
+ sin xy = 7, find
dy
dx
.
l) Solve the integral
sin
cos
x
xe dx
?
.
m) Solve
x
xe dx
?
.
n) Find the derivative of f (x) = x
3/2
+ sin x with respect to x.
o) Find the value of tan 225
0
.
SECTION-B
2. Solve the following system of equations by using Cramer?s law
3x ? 2y + 3z = 8, 2x + y ? z =1, 4x ? 3y + 2z = 4.
3. Show that 2sin
2
? ? + 4 cos ( ? + ?) sin ? sin ? + cos 2 ( ? + ?) = cos 2 ?.
4. Find the foot of perpendicular of the point (2, 3) on the line x + y ? 11 = 0
5. Solve the integral
2
2 3
( 1) (2 3)
x
dx
x x
?
? ?
?
.
6. Differentiate
2
2
( 3)( 4)
3 4 5
x x
x x
? ?
? ?
with respect to x.
3 | M- 46012 (S4)-2710
SECTION-C
7. Find inverse of the matrix
1 1 1
A 1 2 3
2 1 3
? ?
? ?
? ?
? ?
? ? ?
? ?
.
8. The weight of coffee in 70 jars in shown in the following table :
Weight (in grams) 200-201 201-202 202-203 203-204 204-205 205-206
Frequency 13 27 18 10 1 1
Determine the mean, median, variance and standard deviation of the above distribution.
9. a) Find
dy
dx
if x = a ( ? ? sin ?), y = a (1 + cos ?).
b) Solve the integral
tan
sin cos
x
dx
x x
?
.
10. a) Find the equation the line perpendicular to the line 2x ? y + 7 = 0 and pass through the
point (1,1)
b) Show that sin 20? sin 40? sin 60? sin 80? =
3
16
.
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