Download OU (Osmania University) B.Pharma 1st Year (Bachelor of Pharmacy) 2016 6035 Mathematics Previous Question Paper

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Code No. 6035
FACULTY
B. Pharmacy I Year (Main) Examination, April / May 2016
Subject : Mathematics
Time : 3 Hrs Max. Marks: 70
Note: Answer all questions. All questions carry equal marks.
1 (a) (i) Solve the equation for x
e
2x
? e
x
? 6 = 0.
(ii) In a trianle ABC, prove that sin2A + sin2B ? sin2C = 4cosAcosBcosC
OR
(b) (i) If x = 1 + lo a
bc
; y = 1 lob
ca
; and z = 1 + loc
ab
. Prove that xyz = xy + yz + zx.
(ii) If Tan 35
o
+ cot 37
o
+ tan 325
o
= xtan 53
o
+ tan 127
o
then find the value of x.
2 (a) (i) Find the derivative of secx usin first principle.
(ii) If
?
?
?
< < +
? <
=
2 1 ; 3 4
1 0 ; 4 5
) (
2
x bx x
x x
x f
Is continus at every point of its domain then fin d the value of b.
OR
(b) (i) Find the maximum and minimum values of the polynomial f(x) = x
3
? 3x
2
? 6x + 6.
(ii) If
x
y
e
y
x
e u
x y y x
cos sin
/ /
+
?
?
?
?
?
?
?
?
= then show that 0 =
?
?
+
?
?
y
u
y
x
u
x .
3 (a) (i) Evaluate dx e e
x x
?
+ 1 .
(ii) Evaluate dx
x
x x
?
+
+
2 sin 1
cos sin
.
OR
(b) (i) Evaluate dx
x
?
+ cos 5 4
1
.
(ii) Evaluate dx
x x
x
?
+
+
6 24 4
12 4
2
4 (a) (i) If
?
?
?
?
?
?
=
4 2
5 8
A satisfies the equation x
2
+ 4x ? p = 0 then find ?P?.
(ii) Solve the equation 2x + 4y + 5z = 18; 2x ? y + 8z = 13 and 5x ? 2y + 7z = 20 by
matrix inversion method.
OR
(b) (i) Find the rank of the matrix
?
?
?
?
?
?
?
?
?
?
=
8 6 4 2
4 3 2 0
4 3 2 1
A .
(ii) If
?
?
?
?
?
?
=
3 2
1 0
A ,
?
?
?
?
?
?
=
3 4
2 1
B and
?
?
?
?
?
?
=
5 6
1 2
C then prove that A(B + C) = AB + AC.
5 (a) (i) Explain linear and non linear raphs with examples.
(ii) Find the equation of circle whose centre is ( 1, 2) and the end of diameter is (4, 6).
OR
(b) (i) What are the basic mathematical principles are used in Bioloical Testin.
(ii) Find the equation of the line perpendicular to the line 2x + 3y ? 5 = 0 and passin
thrh (3, 4).
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