Download OU (Osmania University) B.Pharma 1st Year (Bachelor of Pharmacy) 2010 4404 Mathematics Previous Question Paper

'!IIIIIIIEN 11111 1 1111
Code No. : 4404
FACULTY OF PHARMACY
B. Pharmacy I Year (Supplementary) Examination, Nov./Dec. 2010
MATHEMATICS
Time : 3 Hours] [Max. Marks : 70
Note : Answer all questions. All questions carry equal marks.
1. a) If log
y
[1+log
b
[ +log
c
x]] = 0, find x.
b) If sin a = 41.0
1
sin -
T
- _ and a , p are acute then find a +i3
v5
OR

/
1 .
+ A sin - - A = ---sin 3A . Hence show that
3
I
`
3 4
c) Prove that sin A sin

(
27t
` 9
l

(
37t

(
4e 3
9
J
1.6
sin
\
9
J

sin sin sin

d) If x = l+log
a
bc, y = l+log
b
ca, and z = l+log
c
ab, prove that xyz = xy+yz+zx
2. a) Show that Lt

2
x ? 1
1

x
-
>
1
2x.?,-7x +1 3 ?
b) Find the maximum and minimum values of f(x) = x
3
+-
3
x
OR
x y z
u
u
au
c) If u =
z x '
show that x + y + z? = 0.
y ax ay az,
d) Prove that x
3
-3x
2
+3x+7=0, has neither maximum nor minima.
(This paper contains 3 pages) 1 P.T.O.
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'!IIIIIIIEN 11111 1 1111
Code No. : 4404
FACULTY OF PHARMACY
B. Pharmacy I Year (Supplementary) Examination, Nov./Dec. 2010
MATHEMATICS
Time : 3 Hours] [Max. Marks : 70
Note : Answer all questions. All questions carry equal marks.
1. a) If log
y
[1+log
b
[ +log
c
x]] = 0, find x.
b) If sin a = 41.0
1
sin -
T
- _ and a , p are acute then find a +i3
v5
OR

/
1 .
+ A sin - - A = ---sin 3A . Hence show that
3
I
`
3 4
c) Prove that sin A sin

(
27t
` 9
l

(
37t

(
4e 3
9
J
1.6
sin
\
9
J

sin sin sin

d) If x = l+log
a
bc, y = l+log
b
ca, and z = l+log
c
ab, prove that xyz = xy+yz+zx
2. a) Show that Lt

2
x ? 1
1

x
-
>
1
2x.?,-7x +1 3 ?
b) Find the maximum and minimum values of f(x) = x
3
+-
3
x
OR
x y z
u
u
au
c) If u =
z x '
show that x + y + z? = 0.
y ax ay az,
d) Prove that x
3
-3x
2
+3x+7=0, has neither maximum nor minima.
(This paper contains 3 pages) 1 P.T.O.
111111111111 111111111111111
Code No. : 4404
3. a) Evaluate
1
J
.
dx
x(l+logx)
r
x xe
b) Evaluate
j (1+ x)
2 dx
OR
1 sin x
c) Evaluate
dx
x +cosx
sin x cos x
d) Evaluate 4
dx
1+ sin x
4. a) Define Rank of the matrix and hence find the rank of the matrix,
-
1 2 3 4
w

A= 2 4 6 8
3 6 9 12_
b) Solve the system of equations
2x ? y + 8z= L3; 3x + 4y +5z = l 8 and 5x 2y + 7z = 20 by Gaussian
elimination method.
OR
c) Solve the system of equations
x + 2y + 3z = 4, 2x + 3y + 5z = 5, 3x + 4y + 6z = 12 by matrix inversion method.
FirstRanker.com - FirstRanker's Choice
'!IIIIIIIEN 11111 1 1111
Code No. : 4404
FACULTY OF PHARMACY
B. Pharmacy I Year (Supplementary) Examination, Nov./Dec. 2010
MATHEMATICS
Time : 3 Hours] [Max. Marks : 70
Note : Answer all questions. All questions carry equal marks.
1. a) If log
y
[1+log
b
[ +log
c
x]] = 0, find x.
b) If sin a = 41.0
1
sin -
T
- _ and a , p are acute then find a +i3
v5
OR

/
1 .
+ A sin - - A = ---sin 3A . Hence show that
3
I
`
3 4
c) Prove that sin A sin

(
27t
` 9
l

(
37t

(
4e 3
9
J
1.6
sin
\
9
J

sin sin sin

d) If x = l+log
a
bc, y = l+log
b
ca, and z = l+log
c
ab, prove that xyz = xy+yz+zx
2. a) Show that Lt

2
x ? 1
1

x
-
>
1
2x.?,-7x +1 3 ?
b) Find the maximum and minimum values of f(x) = x
3
+-
3
x
OR
x y z
u
u
au
c) If u =
z x '
show that x + y + z? = 0.
y ax ay az,
d) Prove that x
3
-3x
2
+3x+7=0, has neither maximum nor minima.
(This paper contains 3 pages) 1 P.T.O.
111111111111 111111111111111
Code No. : 4404
3. a) Evaluate
1
J
.
dx
x(l+logx)
r
x xe
b) Evaluate
j (1+ x)
2 dx
OR
1 sin x
c) Evaluate
dx
x +cosx
sin x cos x
d) Evaluate 4
dx
1+ sin x
4. a) Define Rank of the matrix and hence find the rank of the matrix,
-
1 2 3 4
w

A= 2 4 6 8
3 6 9 12_
b) Solve the system of equations
2x ? y + 8z= L3; 3x + 4y +5z = l 8 and 5x 2y + 7z = 20 by Gaussian
elimination method.
OR
c) Solve the system of equations
x + 2y + 3z = 4, 2x + 3y + 5z = 5, 3x + 4y + 6z = 12 by matrix inversion method.
110111 11111.11111 11111 1111 1111
Code No. 4404

[
2
1 -4 2

d) If A
2 3

) Define linear and non-linear correlation.
b) From the data given below rmil the number of items tt,
3, xy=120,
i-4
,
8 it x
2
=90 where x y are deviations from arithmetic average.
c) mules
d t the coed

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