Download OU (Osmania University) B.Pharma 1st Year (Bachelor of Pharmacy) 2018 13030 Mathematics Previous Question Paper

.

Code No. 13030/Non CBCS
FACULTY
B. Pharmacy I Year (Non CBCS)(Backlo) Examination, December 2018
Subject : Mathematics
Time : 3 Hrs Max. Marks: 70
Note: Answer all questions. All questions carry equal marks.
1 (a) (i) Show that sin (45
o
+ A) sin (45
o
? A) =
2
1
cos 2A.
(ii) If A + B | C = 180
o
prove that
2
cos
2
cos 2
2
cos
2
sin
C B C B A
= ?
?
?
?
?
?
+ .
OR
(b) (i) If lo
a
abc = x +1, lo
b
abc=y+1 and lo
c
abc = z+1 show that xyz = x + y + z.
(ii) Prove that Tan9
o
? Tan27
o
? Tan 63
o
+ Tan 81
o
= 4.
2 (a) (i) Find the derivative of f(x, y) = x
2
+ y
2
+x, usin first principal.
(ii) Discuss the continuity of the function
?
?
?
?
?
=
?
+
=
) 0 , 0 ( ) , ( , 0
) 0 , 0 ( ) , ( ,
) (
2 2
y x
y x
xy
y x
x f at (0, 0)
OR
(b) (i) Find the maximum and minimum values of the function
f(x, y) = 4x
2
+ 9y
2
? 8x ? 12y + 4.
(ii) If
?
?
?
?
?
?
?
?
+
+
=

y x
y x
u
2 2
1
sin prove that u Tan
y
u
y
x
u
x =
?
?
+
?
?
.
3 (a) (i) Evaluate dx x x
?
.
(ii) Evaluate
?
+
dx
x
x
1
6
8
OR
(b) (i) Evaluate
?
+ +
+
dx
x x
x
3 2
4 3
2
(ii) Evaluate
?
+
dx
x sin 3 2
1
4 (a) (i) If
?
?
?
?
?
?

=
2 4
5 3
A prove that A
2
? 5A = 14 I, where I is the unit matrix of second
order.
(ii) Solve the equation x + 3y + 6z = 2, 3x ? y + 4z = 9, x ? 4y + 2z = 7 by matrix
Inversion method.
OR
..2
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.

Code No. 13030/Non CBCS
FACULTY
B. Pharmacy I Year (Non CBCS)(Backlo) Examination, December 2018
Subject : Mathematics
Time : 3 Hrs Max. Marks: 70
Note: Answer all questions. All questions carry equal marks.
1 (a) (i) Show that sin (45
o
+ A) sin (45
o
? A) =
2
1
cos 2A.
(ii) If A + B | C = 180
o
prove that
2
cos
2
cos 2
2
cos
2
sin
C B C B A
= ?
?
?
?
?
?
+ .
OR
(b) (i) If lo
a
abc = x +1, lo
b
abc=y+1 and lo
c
abc = z+1 show that xyz = x + y + z.
(ii) Prove that Tan9
o
? Tan27
o
? Tan 63
o
+ Tan 81
o
= 4.
2 (a) (i) Find the derivative of f(x, y) = x
2
+ y
2
+x, usin first principal.
(ii) Discuss the continuity of the function
?
?
?
?
?
=
?
+
=
) 0 , 0 ( ) , ( , 0
) 0 , 0 ( ) , ( ,
) (
2 2
y x
y x
xy
y x
x f at (0, 0)
OR
(b) (i) Find the maximum and minimum values of the function
f(x, y) = 4x
2
+ 9y
2
? 8x ? 12y + 4.
(ii) If
?
?
?
?
?
?
?
?
+
+
=

y x
y x
u
2 2
1
sin prove that u Tan
y
u
y
x
u
x =
?
?
+
?
?
.
3 (a) (i) Evaluate dx x x
?
.
(ii) Evaluate
?
+
dx
x
x
1
6
8
OR
(b) (i) Evaluate
?
+ +
+
dx
x x
x
3 2
4 3
2
(ii) Evaluate
?
+
dx
x sin 3 2
1
4 (a) (i) If
?
?
?
?
?
?

=
2 4
5 3
A prove that A
2
? 5A = 14 I, where I is the unit matrix of second
order.
(ii) Solve the equation x + 3y + 6z = 2, 3x ? y + 4z = 9, x ? 4y + 2z = 7 by matrix
Inversion method.
OR
..2
.

Code No. 13030/Non CBCS
..2..
(b) (i) Find the rank of the matrix
?
?
?
?
?
?
?
?
?
?

=
2 1 3
4 2 6
2 1 3
A
(ii) If
?
?
?
?
?
?
=
?
?
?
?
?
?

=
3 2
1 2
,
3 2
2 1
B A and
?
?
?
?
?
?
=
0 2
1 3
C verify that
A (B+C) = AB + AC.
5 (a) (i) Explain Linear and non Linear raphs with examples.
(ii) Find the equation of the circle passin thrh the points (1, 0), (2, 1) (5, 3).
OR
(b) (i) What are the basic mathematical principles are used in bioloical Testin.
(ii) Find the equation of the Line passin thrh ( 3, 2) with slope 2/3.
*****
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