Download OU B.Pharma 1st Year 2013 2654 Mathematics Question Paper

Download OU (Osmania University) B.Pharma 1st Year (Bachelor of Pharmacy) 2013 2654 Mathematics Previous Question Paper

,
Code No. 2654 / M
FACULTY OF PHARMACY
B. Pharmacy I Year (Main & Backlog) Examination, June 2013
Subject: Mathematics
Time: 3 Hours Max.Marks: 70
Note: Answer all questions. All questions carry equal marks.
1.(a) i) If (x-y) log
a
2= (y-z) log
b
2 = (z-x) log
c
2, then show that abc = 1.
ii) If tan 20
o
= ?, show that
o o 2
o o 2
tan250 + tan340 1- ?
=
tan200 - tan110 1+ ?
.
OR
(b) i) If a
x
= b
y
= c
z
and y
2
= xz then show that log
b
a = log
c
b.
ii) find the value of cos 5
o
+ cos 24
o
+ cos 175
o
+ cos 204
o
+ cos 300
o.
2.(a) i) Find the derivative of the function f(x) =
3
2 3
x +1
(x -1)(x -1)
.
ii) If f(x) = x sin(1/x) when x? 0 and f(0) = 0, show that f is continuous but not
derivable for x=0.
OR
(b) i) Find the maximum and minimum values of the polynomial function f is given by
f(x) = 8x
5
 15x
4
+ 10x
3
.
ii) if u = tan
-1
(y/x), then show that
2 2
2 2
y y
0
x y
? ?
+ =
? ?
.
3.(a) i) Evaluate
?
cosx
dx
a+b sinx
.
ii) Evaluate
? 2
3x +7
dx
3x + 14x -5
.
OR
(b) i) Evaluate
? 2
tan x
dx
1+cos x
ii) Evaluate
?
cos 4x + 1
dx
cos x - tan x
.
4.(a) i) Define symmetric and skew symmetric matrix.
If A =
? ?
? ?
? ?
? ?
? ?
1 -2 3
2 3 -1
-3 1 2
and B =
? ?
? ?
? ?
? ?
? ?
1 0 2
0 1 2
1 2 0
, find BA.
ii) Define determinant of a matrix. Find A
-1
if A =
? ?
? ?
? ?
? ?
? ?
2 0 3
6 2 1
3 1 4
.
OR
FirstRanker.com - FirstRanker's Choice
,
Code No. 2654 / M
FACULTY OF PHARMACY
B. Pharmacy I Year (Main & Backlog) Examination, June 2013
Subject: Mathematics
Time: 3 Hours Max.Marks: 70
Note: Answer all questions. All questions carry equal marks.
1.(a) i) If (x-y) log
a
2= (y-z) log
b
2 = (z-x) log
c
2, then show that abc = 1.
ii) If tan 20
o
= ?, show that
o o 2
o o 2
tan250 + tan340 1- ?
=
tan200 - tan110 1+ ?
.
OR
(b) i) If a
x
= b
y
= c
z
and y
2
= xz then show that log
b
a = log
c
b.
ii) find the value of cos 5
o
+ cos 24
o
+ cos 175
o
+ cos 204
o
+ cos 300
o.
2.(a) i) Find the derivative of the function f(x) =
3
2 3
x +1
(x -1)(x -1)
.
ii) If f(x) = x sin(1/x) when x? 0 and f(0) = 0, show that f is continuous but not
derivable for x=0.
OR
(b) i) Find the maximum and minimum values of the polynomial function f is given by
f(x) = 8x
5
 15x
4
+ 10x
3
.
ii) if u = tan
-1
(y/x), then show that
2 2
2 2
y y
0
x y
? ?
+ =
? ?
.
3.(a) i) Evaluate
?
cosx
dx
a+b sinx
.
ii) Evaluate
? 2
3x +7
dx
3x + 14x -5
.
OR
(b) i) Evaluate
? 2
tan x
dx
1+cos x
ii) Evaluate
?
cos 4x + 1
dx
cos x - tan x
.
4.(a) i) Define symmetric and skew symmetric matrix.
If A =
? ?
? ?
? ?
? ?
? ?
1 -2 3
2 3 -1
-3 1 2
and B =
? ?
? ?
? ?
? ?
? ?
1 0 2
0 1 2
1 2 0
, find BA.
ii) Define determinant of a matrix. Find A
-1
if A =
? ?
? ?
? ?
? ?
? ?
2 0 3
6 2 1
3 1 4
.
OR
,
Code No. 2654 / M
-2-
4.(b) i) Write the following equation in matrix form AX = B and solve for X by finding A
-1
.
The equations are x+y-2z = 3; 2x-y+z = 0; 3x+y-z = 8.
ii) Solve the system of equations x+2y+3z = 14; 4x+5y+7z = 35; 3x+3y+4z = 21 by
using the Gauss-elimination method.
5.(a) i) Derive the equation y = mx+c for a straight line and explain the importance of
m and c and how to determine the value of m.
ii) Find Latus sectum, eccentricity from the equation x
2
+y
2
-4x+4 = 0.
OR
(b) i) Find the centre and radius of the circle 3x
2
+3y
2
+6x-12y-1 = 0.
ii) Explain about linear and non-linear graphs and their importance in biological data
representation and comparison.
****
FirstRanker.com - FirstRanker's Choice