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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