Download OU B.Pharma 1st Year 2013 7204 Mathematics Question Paper

Download OU (Osmania University) B.Pharma 1st Year (Bachelor of Pharmacy) 2013 7204 Mathematics Previous Question Paper

PHARMACY,,HYD
Code No. 7204
FACULTY OF PHARMACY
B. Pharmacy I Year (Suppl.) Examination, November 2013
Subject: Mathematics
Time: 3 Hours Max.Marks: 70
Note: Answer all questions. All questions carry equal marks.
1.(a) Prove that
a b c
1 1 1
+ + =1.
1+log bc 1+log ca 1+log ab
(b) If sin ? =
1
10
; sin ? =
1
5
and ? , ? are acute angles then show that ? +? =
?
4
.
OR
(c) Find the value of xyz if
log x logy logz
= =
y - z z - x x - y
.
(d) Prove that
o o
1 1 4
+ = .
cos290 3.sin 250 3
2.(a) Find the maximum and minimum values of f(x) = x
3
+
3
x
.
(b) If xy = ae
x
+ bc
-x
then prove that ?? ? xy +2y - xy = 0.
OR
(c) If z = log
? ?
? ?
? ?
2 2
x + y
xy
, verify that
2 2
z z
.
xy yx
? ?
=
?? ??
(d) Prove that x
3
 3x
2
+ 3x + 7 has neither maximum nor minima.
3.(a) Evaluate
? 3
x
dx
1+ x
(b) Evaluate
?
-1
2
x sin x
dx.
1- x
OR
(c) Evaluate
? 4
sin x cos x
dx
1+sin x
(d) Evaluate
?
2
x +2x +5
dx.
(x +2)(x -1)(3x -1)
..2.
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PHARMACY,,HYD
Code No. 7204
FACULTY OF PHARMACY
B. Pharmacy I Year (Suppl.) Examination, November 2013
Subject: Mathematics
Time: 3 Hours Max.Marks: 70
Note: Answer all questions. All questions carry equal marks.
1.(a) Prove that
a b c
1 1 1
+ + =1.
1+log bc 1+log ca 1+log ab
(b) If sin ? =
1
10
; sin ? =
1
5
and ? , ? are acute angles then show that ? +? =
?
4
.
OR
(c) Find the value of xyz if
log x logy logz
= =
y - z z - x x - y
.
(d) Prove that
o o
1 1 4
+ = .
cos290 3.sin 250 3
2.(a) Find the maximum and minimum values of f(x) = x
3
+
3
x
.
(b) If xy = ae
x
+ bc
-x
then prove that ?? ? xy +2y - xy = 0.
OR
(c) If z = log
? ?
? ?
? ?
2 2
x + y
xy
, verify that
2 2
z z
.
xy yx
? ?
=
?? ??
(d) Prove that x
3
 3x
2
+ 3x + 7 has neither maximum nor minima.
3.(a) Evaluate
? 3
x
dx
1+ x
(b) Evaluate
?
-1
2
x sin x
dx.
1- x
OR
(c) Evaluate
? 4
sin x cos x
dx
1+sin x
(d) Evaluate
?
2
x +2x +5
dx.
(x +2)(x -1)(3x -1)
..2.
PHARMACY,,HYD
Code No. 7204
-2-
4.(a) Define rank of a matrix and hence find the rank of the matrix A =
? ?
? ?
? ?
? ?
? ?
? ?
1 2 3 4
2 4 6 8
2 3 4 5
3 4 5 6
.
(b) Solve the system of equations. 2x-y+8z=13; 3x+4y+5z = 18 and 5x-2y+7z = 20
by matrix inversion method.
OR
4.(c) Solve the system of equations x+2y+3z = 4; 2x+3y+5z = 5; 3x+4y+6z = 12 by
Gaussian elimination method.
(d) If A =
? ?
? ?
? ?
? ?
? ?
1 2 3
3 4 2
3 4 5
and B =
? ?
? ?
? ?
? ?
? ?
1 2 0
2 3 2
1 -1 2
then find (AB)
-1
.
5.(a) Define linear and non-linear graphs with an example.
(b) Find foci, latus rectum eccentricity, from y
2
+2y+3x+4 = 0.
OR
(c) Derive the equation y = mx + c and explain the importance m and c.
(d) Find the radius and centre of the circle x
2
+y
2
-4x+6y+4 = 0.
****
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