Download OU (Osmania University) B.Pharma 1st Year (Bachelor of Pharmacy) 2011 Mathematics Previous Question Paper

FACULTY OF PHARMACY
B. Pharmacy I-Year (Main & Backtog) Examination, June 2011
MATHEMATICS
Time : Three Hours] [Maximum Marks : 70
Note Answer ALL questions. All questions carry equal marks.
1 1
A.
If sin a
10
, sin 13 and a, 13 are acute then show that a + i =
4
.
9
.1)
.
If tan A = 1
?
2
and tan B = 3
3 3
where A and B are acute angles then find A + B.
OR
AB) (if sin A - sin (60 + A) sin (60 ? A) =
?
4
sin 3A.
3
Prove that 4 sin 20
0
sin 40? sin 60
0
sin 80
0
.
2.
(A)/ Find the derivatives of the following function tan 2x using first principle.
(x
3
1
5u 8u
(ii) If U sec
-
'
then show that +
u
zcot u.
x + y
8x s
y

K
2
x?K if
(iii) If f, given by f(x) w{ 2
if x 1,
is a continuous function on R, then find
<
the value of K.
OR
( j(i) Prove that x' 3x
2
+ 3x + 7 ? 0, has neither maxima nor minima.
) Show that f(x) - ---- sin x (1 + cos x) has a maximum value at x = 3.
HVS--887 1 (Contd.)
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FACULTY OF PHARMACY
B. Pharmacy I-Year (Main & Backtog) Examination, June 2011
MATHEMATICS
Time : Three Hours] [Maximum Marks : 70
Note Answer ALL questions. All questions carry equal marks.
1 1
A.
If sin a
10
, sin 13 and a, 13 are acute then show that a + i =
4
.
9
.1)
.
If tan A = 1
?
2
and tan B = 3
3 3
where A and B are acute angles then find A + B.
OR
AB) (if sin A - sin (60 + A) sin (60 ? A) =
?
4
sin 3A.
3
Prove that 4 sin 20
0
sin 40? sin 60
0
sin 80
0
.
2.
(A)/ Find the derivatives of the following function tan 2x using first principle.
(x
3
1
5u 8u
(ii) If U sec
-
'
then show that +
u
zcot u.
x + y
8x s
y

K
2
x?K if
(iii) If f, given by f(x) w{ 2
if x 1,
is a continuous function on R, then find
<
the value of K.
OR
( j(i) Prove that x' 3x
2
+ 3x + 7 ? 0, has neither maxima nor minima.
) Show that f(x) - ---- sin x (1 + cos x) has a maximum value at x = 3.
HVS--887 1 (Contd.)
rosx?3sinx +7
dx.
3. (A) (i) Find the value of
cos x + sin x +1
(ii) Evaluate
(iii) Evaluate
/
2 sinx +3cosx +4
_ d
x

3sinx+4cosx?5
r
dx
4 ? cos x
OR
r 1 + sin x
94 ('t.)-- Evaluate j
dx
x+cosx *
j
- 2x+3
(i.) Evaluate
dx
. x
l
+ x
2
- 2 x
i) Evaluate isec
2
x cosec
2
x dx .
4. Show that
1 a
?
a
1

1 b
2
b
3

1 C
2
C'
? (a ? b) (b c) (c ? a) (ab + be +

) Show that
a+b+2c a b
c b+c+2a b
c a c+a+2b
2(a + b c)
3
.

OR
(B) (i) Solve the following equations by Gauss-Jordan method :
3x + 4y + 5z= 18, 2x ? y + 8z = 13, 5x ? 2y + 7z = 20.
1 2 1
If A = 0
1
?1 then find A' 3A
2
A ? 31.
3 ?1 1
FIVS-887 2
(Contd.)
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FACULTY OF PHARMACY
B. Pharmacy I-Year (Main & Backtog) Examination, June 2011
MATHEMATICS
Time : Three Hours] [Maximum Marks : 70
Note Answer ALL questions. All questions carry equal marks.
1 1
A.
If sin a
10
, sin 13 and a, 13 are acute then show that a + i =
4
.
9
.1)
.
If tan A = 1
?
2
and tan B = 3
3 3
where A and B are acute angles then find A + B.
OR
AB) (if sin A - sin (60 + A) sin (60 ? A) =
?
4
sin 3A.
3
Prove that 4 sin 20
0
sin 40? sin 60
0
sin 80
0
.
2.
(A)/ Find the derivatives of the following function tan 2x using first principle.
(x
3
1
5u 8u
(ii) If U sec
-
'
then show that +
u
zcot u.
x + y
8x s
y

K
2
x?K if
(iii) If f, given by f(x) w{ 2
if x 1,
is a continuous function on R, then find
<
the value of K.
OR
( j(i) Prove that x' 3x
2
+ 3x + 7 ? 0, has neither maxima nor minima.
) Show that f(x) - ---- sin x (1 + cos x) has a maximum value at x = 3.
HVS--887 1 (Contd.)
rosx?3sinx +7
dx.
3. (A) (i) Find the value of
cos x + sin x +1
(ii) Evaluate
(iii) Evaluate
/
2 sinx +3cosx +4
_ d
x

3sinx+4cosx?5
r
dx
4 ? cos x
OR
r 1 + sin x
94 ('t.)-- Evaluate j
dx
x+cosx *
j
- 2x+3
(i.) Evaluate
dx
. x
l
+ x
2
- 2 x
i) Evaluate isec
2
x cosec
2
x dx .
4. Show that
1 a
?
a
1

1 b
2
b
3

1 C
2
C'
? (a ? b) (b c) (c ? a) (ab + be +

) Show that
a+b+2c a b
c b+c+2a b
c a c+a+2b
2(a + b c)
3
.

OR
(B) (i) Solve the following equations by Gauss-Jordan method :
3x + 4y + 5z= 18, 2x ? y + 8z = 13, 5x ? 2y + 7z = 20.
1 2 1
If A = 0
1
?1 then find A' 3A
2
A ? 31.
3 ?1 1
FIVS-887 2
(Contd.)
5. (A) (0 Discuss the set of Postulates defining Boolean Algebra.
(ii) Find the eccentricity, co-ordinates of foci, length of latus rectum and equations of
directries of the ellipse.
9x
2
+ 16y' - 36x + 32y - 92 = O.
OR
(B) (i) Find the intercepts of the plane 4x + 3y ,L 2z + 2 - 0 on the co-ordinate axes.
(ii) Write Boolean function to realize the full adder and draw the corresponding logic
diagram.
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