Download OU Pharm D Question Paper 1st Year 2014 7289 Remedial Mathematics

Download OU (Osmania University) Pharm D (Doctor of Pharmacy) 1st Year 2014 7289 Remedial Mathematics Previous Question Paper

Code No. 7289
FACULTY OF PHARMACY
Pharm. D. I Year (Instant) Examination, January 2014
Subject: Remedial Mathematics
Time: 3 Hours Max.Marks: 70
Note: Answer all questions from Part A. Answer any five questions from Part B.
PART  A (10 x 2 = 20 Marks)
1 If A =
? ?
? ?
? ?
i 0
0 -i
write A
2
.
2 If
? ? ? ?
? ? ? ?
? ?? ?
2
2 3 x y
= ,
3 0 3 0
Find the values of x and y.
3 Eliminate  ? from the equations x = a Sec
n
?, y = b tan
n
?.
4 Find the equation to the line passing through (2, 4) and parallel to x-axis.
5 Find the equation to the circle whose one end point is (2, 4) and mid point is (0,0).
6 Find the integral of
?
2
2
x
dx
1+ x
.
7 Define the order and degree of the differential equation and hence find the order
and degree from the d.e.
? ?
? ?
? ?
2
3 2
3 2
d y d y dy
+ + + y = 0
dx dx dx
8 Evaluate
?
2
x 2
x - 4
Lt
x - 2
.
9 Find the Laplace transform sinat.
10 If u = log (x
2
-y
2
) then find
u u
x y
x y
? ?
+
? ?
.
PART  B (5 x 10 = 50 Marks)
11 (a) If A =
? ?
? ?
? ?
1 -1
2 -1
and B =
? ?
? ?
? ?
x 1
y -1
and (A+B)
2
= A
2
+B
2
. Find x and y.
(b) If A =
a b
c d
? ?
? ?
? ?
and I =
? ?
? ?
? ?
1 0
0 1
then show that A
2
 (a+d) A = (bc  ad) I.
12 (a) If tan 20
?
= K, show that
o o 2
o o 2
Tan 250 +Tan 340 1-K
=
Tan 200 - Tan 110 1+K
.
(b) Prove that
o o
1 1 4
+ =
Cos 290 3 Sin 250 3
.
13 (a) Show that
? ? 0
tan a? a
Lt =
sin b? b
.
(b) If u = tan
-1
? ?
? ?
? ?
2 2
x + y
x + y
then prove that x
? ?
? ?
u u 1
+ y = sin2u.
x x 2
&&2
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Code No. 7289
FACULTY OF PHARMACY
Pharm. D. I Year (Instant) Examination, January 2014
Subject: Remedial Mathematics
Time: 3 Hours Max.Marks: 70
Note: Answer all questions from Part A. Answer any five questions from Part B.
PART  A (10 x 2 = 20 Marks)
1 If A =
? ?
? ?
? ?
i 0
0 -i
write A
2
.
2 If
? ? ? ?
? ? ? ?
? ?? ?
2
2 3 x y
= ,
3 0 3 0
Find the values of x and y.
3 Eliminate  ? from the equations x = a Sec
n
?, y = b tan
n
?.
4 Find the equation to the line passing through (2, 4) and parallel to x-axis.
5 Find the equation to the circle whose one end point is (2, 4) and mid point is (0,0).
6 Find the integral of
?
2
2
x
dx
1+ x
.
7 Define the order and degree of the differential equation and hence find the order
and degree from the d.e.
? ?
? ?
? ?
2
3 2
3 2
d y d y dy
+ + + y = 0
dx dx dx
8 Evaluate
?
2
x 2
x - 4
Lt
x - 2
.
9 Find the Laplace transform sinat.
10 If u = log (x
2
-y
2
) then find
u u
x y
x y
? ?
+
? ?
.
PART  B (5 x 10 = 50 Marks)
11 (a) If A =
? ?
? ?
? ?
1 -1
2 -1
and B =
? ?
? ?
? ?
x 1
y -1
and (A+B)
2
= A
2
+B
2
. Find x and y.
(b) If A =
a b
c d
? ?
? ?
? ?
and I =
? ?
? ?
? ?
1 0
0 1
then show that A
2
 (a+d) A = (bc  ad) I.
12 (a) If tan 20
?
= K, show that
o o 2
o o 2
Tan 250 +Tan 340 1-K
=
Tan 200 - Tan 110 1+K
.
(b) Prove that
o o
1 1 4
+ =
Cos 290 3 Sin 250 3
.
13 (a) Show that
? ? 0
tan a? a
Lt =
sin b? b
.
(b) If u = tan
-1
? ?
? ?
? ?
2 2
x + y
x + y
then prove that x
? ?
? ?
u u 1
+ y = sin2u.
x x 2
&&2
Code No. 7289
&.2&..
14 (a) Evaluate
?
a
o
dx
1+ x
(b) Evaluate
?
2 2
(a - x ) dx.
15 (a) Solve e
x
tan y dx + (1-e
x
) sec
2
y dy = 0.
(b) Solve (D
2
+1)y = e
x
+ sin x + x
2
.
16 (a) If L[F(t)] = F(s) then prove that L(e
at
F(t)] = F(s-a).
(b) Find the Laplace transform of e
2t
+ t
2
+ t sint.
17 (a) Verify
2 2
z z
x y x y
? ?
=
? ? ? ?
when z is equal to x
3
+ y
3
 3axy.
(b) Solve (xy
2
+ x) dx + (yx
2
+ y) dy = 0.
18 (a) Find the equation to the circle which passes through the point (4,1), (6,5) and
has the centre on the line 4x + y  16 = 0.
(b) Find the equation of the ellipse whose focus is (0,3), eccentricity is
3
5
and
directrix is 3y 25=0.
***
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