Download OU B.Pharma 1st Year 2010 7004 Mathematics Question Paper

Download OU (Osmania University) B.Pharma 1st Year (Bachelor of Pharmacy) 2010 7004 Mathematics Previous Question Paper

Code No. 7004
FACULTY OF TECHNOLOGY
B. Pharmacy I - Year (Supplementary) Examination, March 2010
Subject : MATHEMATICS
Time : 3 Hours). (Max. Marks: 70
Note: Answer All questions. All questions carry equal marks.
1.(a) If x = log , y = log r and z = log then show that xyz = x + y + z + 2.
1
(b) If sin x + sin y = -
1
and cos x + cos y = - then show that
4 3
x ( + y 3 7
tan
2 4
and cot (x + y)
24
A B
(c) If A + B + C = 180
?
, prove that sin A + sin B + sin C = 4 cos --cos -cos --
2 2 2
OR
(d) If 8a is not an integral multiple of Tr, prove that
tan a + 2tan 2a + 4tan 4a + 8cot 8a = cota
B C
(e) If A + B + C = 180
?
, prove that, sin A + sin B - sin C = 4sin
f
sin-cos
2 2 2
Cosa sin a
(f) show that acos 2a + bsin 2a = a.
a b
au
2.(a) If u = x
3
+ y
3
- x
2
y + xy
2
, find
xP-
ax

I -'-j- +
ay ?
x -2
(b) Compute Lt .
x
-
+
2
X
3
8
(c) Find
c
i
f
when y = logx using first principle.
dx
OR
(d) Find the maximum value of 2x
4
- 3x
2
- 36x + 10.
0
2
0 0
2
9 0
2
0

(e) lf x = r cose, y = r sine, then find
ax
2
' ay
2
'axay
(f) Differentiate, \I
I+ x2
1- X
2

X
5

3.(a) Evaluate dx.
1+ X
12

(b) Evaluate fx2
2x +1
+x+idx
(c) Evaluate
f
dx
l+sin2x
OR
%
(d) Evaluate fxsinx dx.
0
Evaluate
dx
6
1
1+sinx
Find the area bounded between the curves y
2
?= 4ax, x
2
= 4by.
(e)
(f)
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Code No. 7004
FACULTY OF TECHNOLOGY
B. Pharmacy I - Year (Supplementary) Examination, March 2010
Subject : MATHEMATICS
Time : 3 Hours). (Max. Marks: 70
Note: Answer All questions. All questions carry equal marks.
1.(a) If x = log , y = log r and z = log then show that xyz = x + y + z + 2.
1
(b) If sin x + sin y = -
1
and cos x + cos y = - then show that
4 3
x ( + y 3 7
tan
2 4
and cot (x + y)
24
A B
(c) If A + B + C = 180
?
, prove that sin A + sin B + sin C = 4 cos --cos -cos --
2 2 2
OR
(d) If 8a is not an integral multiple of Tr, prove that
tan a + 2tan 2a + 4tan 4a + 8cot 8a = cota
B C
(e) If A + B + C = 180
?
, prove that, sin A + sin B - sin C = 4sin
f
sin-cos
2 2 2
Cosa sin a
(f) show that acos 2a + bsin 2a = a.
a b
au
2.(a) If u = x
3
+ y
3
- x
2
y + xy
2
, find
xP-
ax

I -'-j- +
ay ?
x -2
(b) Compute Lt .
x
-
+
2
X
3
8
(c) Find
c
i
f
when y = logx using first principle.
dx
OR
(d) Find the maximum value of 2x
4
- 3x
2
- 36x + 10.
0
2
0 0
2
9 0
2
0

(e) lf x = r cose, y = r sine, then find
ax
2
' ay
2
'axay
(f) Differentiate, \I
I+ x2
1- X
2

X
5

3.(a) Evaluate dx.
1+ X
12

(b) Evaluate fx2
2x +1
+x+idx
(c) Evaluate
f
dx
l+sin2x
OR
%
(d) Evaluate fxsinx dx.
0
Evaluate
dx
6
1
1+sinx
Find the area bounded between the curves y
2
?= 4ax, x
2
= 4by.
(e)
(f)
1 2 2
.. 2..
Code No. 7004
4.(a) If A = 2 1 2 , then show that A
2
? 4A 51 = 0
2 2 1
1 2 3
7

(b) Define raw matrix, column matrix. Find the rank of the matrix. A = 2 3 4
0 1 2
OR
Ogo
Solve the following equation by Gauss-Jordon method.
3x + 4y + 5z = 18
2x y + 8z = 13
5x ? 2y + 7z = 20
(d) If A =
3 ?2
-
[
1 6
B =
4 ?1
2 5
, then find AB and BA.
5.(a) Define Boolean algebra. Discuss the set of postulates defining Boolean algebra.
(b) Construct logic circuit for the following Boolean function using AND / OR / NOT
gates
f = (A + B) (A B)
OR
(c) Show that the points (-1, 7) (3, -5) (4, -8) are collinear.
(e) Show that the points 2i+ 31?K, 1 -27 + , 3i+4j- 2k
are coplanar.
? ?
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