Download JNTUH Pharm D 1st Year PH106 Remedial Mathematics Question Paper

Download JNTUH (Jawaharlal Nehru Technological University Hyderabad) Pharm-D (Doctor of Pharmacy) 1st Year PH106 Remedial Mathematics Previous Question Paper

Code No: PH106
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
Pharm.D I Year Supplementary Examinations, October/November - 2019
REMEDIAL MATHEMATICS
Time: 3hours Max.Marks:70
Answer any five questions
All questions carry equal marks
- - -

1.a) Find AB and BA where A=
1 2 1
2 4 1
111
???
??
?
??
??
??
and B=
1 1 1
3 2 3
1 4 6
??
??
?
??
?? ?
??

b) Solve the following equations by using cramer?s Rule.
x - 2y + 3z =2; 3x + 2y- z =12; 2x - y +3 z = 7 [7+7]

2.a) Prove that
4cos 2
cot( 15) tan( 15)
1 2sin 2
A
AA
A
? ? ? ?
?

b) Prove that Cos
9
?
Cos
2
9
?
Cos
3
9
?
Cos
4
9
?
=
4
1
2
[7+7]


3.a) Find the equation of the line passing through the point (1, 1) and perpendicular to the line
passing through the points (3, 5) and (-6, -2).
b) Find the equation of the circle whose centre is (5, 7) and radius 4. [7+7]

4.a) Find the differential coefficient of sin log
x
y xe x x ??


b) Find the derivation of
2
log
x
xe
x
[7+7]

5.a) If,
2 2 2 1/2
() u x y z
?
? ? ? , then show that
222
2 2 2
0
uuu
x y z
???
? ? ?
? ? ?

b) If
22
sin
xy
u
xy
?
?
then prove that 3tan
uu
x y u
xy
??
??
??
[7+7]

6.a) Evaluate
2 x
x e dx
?

b) Evaluate
2
0
sin
(sin cos )
xdx
xx
?
?
?
[7+7]


7. Solve the following differential equations
a)
22
( ) ( ) 0 xy x dx yx y dy ? ? ? ?

b)
dy
dx
=
xy
x
?
[7+7]


8.a) Find ? ? 5sin 2sin3 L t t ?
b) Find ? ? t Sin e L
t 2 ?
[7+7]

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