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

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Answer any five questions
All questions carry equal marks
- - -

1.a) Find AB and BA where A=

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1 2 1
2 4 1
111
?
?

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?
?
?
?
and B=

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1 1 1
3 2 3
1 4 6
?
?

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?
?
? ?
?

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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

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cot( 15) tan( 15)
1 2sin 2
A
AA
A

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? ? ? ?
?

b) Prove that Cos
9

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?
Cos
2
9
?

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Cos
3
9
?
Cos

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4
9
?
=
4

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1
2
[7+7]

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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

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x
y xe x x ?


b) Find the derivation of

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2
log
x
xe
x

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[7+7]

5.a) If,
2 2 2 1/2
() u x y z

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?
? ? ? , then show that
222
2 2 2
0

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uuu
x y z
?
? ? ?
? ? ?

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b) If
22
sin
xy

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u
xy
?
?
then prove that 3tan

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uu
x y u
xy
?
?

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?
[7+7]

6.a) Evaluate
2 x

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x e dx
?

b) Evaluate
2

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0
sin
(sin cos )
xdx
xx

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?
?
?
[7+7]

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

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b)
dy
dx
=

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xy
x
?
[7+7]

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

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