Download OU B.Pharma 1st Year 2012 6504 Mathematics Question Paper

Download OU (Osmania University) B.Pharma 1st Year (Bachelor of Pharmacy) 2012 6504 Mathematics Previous Question Paper

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FACULTY OF PHARMACY
B.Pharmacy 1 Year (Main) Examination, June 2012
MATHEMATICS
Time : 3 Hours] [Max. Marks : 70
Note : Answer all questions. All questions carry equal marks.
1. a) 1) If ax = by = cz and y
2
= 2x, prove that Iog
b
a = log
c
b.
2) Prove that A + B = 45? <=? (1 + tan A) (1+ tan B) = 2. Hence show that
1
tan 22-
2
=
OR
S a

1 1
b) 1) If (3.4)x = (0.034)Y = 10000 find the value of
x

- ?
y
2) In a triangle ABC, prove that
Sin 2A + Sin 2B - Sin 2C = 4 Cos A Cos B Sin C.
2.
a) 1) Prove that It
x
3
; 8x
2
+ 45 7
x-?3 2x - 3x 9 3
dy .
2) Find
dx
x = a cost 0, y = b sine 0.
OR
b) 1) Using first principle find the derivative of sinx.
2) Find the maximum and minimum values of f(x) = x
3
- 6x
2
+ 9x + 15.
3. a) 1) Evaluate f
1

3 + 5x 2x
-
2
dx
2) Evaluate
r 2x + 3
dx
3x
2
+ 14x - 5
OR
b) 1) Evaluate f
1

5 + 4 cos x
dx
2) Evaluate f
1
dx
(2x + 3)-Nix + 2
(This paper contains 2 pages) 1 P.T.O.
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f
4 4.;
w? m
. 44

)0. ?
1,1
?;'
)
re
,
k
???.
4/1
1A
HO'
k
F
9
k__
1111111111111111 Code no.: 6504/M
FACULTY OF PHARMACY
B.Pharmacy 1 Year (Main) Examination, June 2012
MATHEMATICS
Time : 3 Hours] [Max. Marks : 70
Note : Answer all questions. All questions carry equal marks.
1. a) 1) If ax = by = cz and y
2
= 2x, prove that Iog
b
a = log
c
b.
2) Prove that A + B = 45? <=? (1 + tan A) (1+ tan B) = 2. Hence show that
1
tan 22-
2
=
OR
S a

1 1
b) 1) If (3.4)x = (0.034)Y = 10000 find the value of
x

- ?
y
2) In a triangle ABC, prove that
Sin 2A + Sin 2B - Sin 2C = 4 Cos A Cos B Sin C.
2.
a) 1) Prove that It
x
3
; 8x
2
+ 45 7
x-?3 2x - 3x 9 3
dy .
2) Find
dx
x = a cost 0, y = b sine 0.
OR
b) 1) Using first principle find the derivative of sinx.
2) Find the maximum and minimum values of f(x) = x
3
- 6x
2
+ 9x + 15.
3. a) 1) Evaluate f
1

3 + 5x 2x
-
2
dx
2) Evaluate
r 2x + 3
dx
3x
2
+ 14x - 5
OR
b) 1) Evaluate f
1

5 + 4 cos x
dx
2) Evaluate f
1
dx
(2x + 3)-Nix + 2
(This paper contains 2 pages) 1 P.T.O.
(0000E11 Code No. : 610/M

6 2 - 2
-

- 2 2 2 show that (A - 21) (A - 41) = 0.
2 2 2
4. a) 1) If A=

0 1 2
2) Find the rank of 1 2 3
3 2 1
OR
b) 1) Show that
b+c c+a a+b
a+b b+c c+a
a
= a
3
+ b
3
+ C
3
3abc

2) If A .
[2
3
0
5 show that A
2
+ 3A -101= 0.
5. a) 1) Find the equation of line passing through the point (2, -3) and having
intercepts whose ratio is 3 : 2.
2) Show that the points (- 6, 0) (-2, 2), (-2, - 8) and (1, 1) are concylic.
OR
b) 1) Find the equation of line dividing the line segment joining (2, 3), (4, - 5) in
the ratio 2 : 3 and having slope - 3.
2) Find the circle which passes through (-1, 2), (- 4, 5) and has its centre on
the line x 2y = 0.
2 2,300
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