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+6
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− 3' = +
6
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)=
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= *6
6
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' = 6 −*
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= − *6 −4
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6
= − *6 −4
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6*
= +=6 −3
= +=6 −3
( 6 ) + ( −* 6 ) − 3 ( 6 ) = +
6* =
*
3
4
*
3=+
*
=3
= ±*
∴
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L
6*
G
4=
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6 + *' + I= 3
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6 − ' + I=
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}
= /Hσ*4 = σ
*
4
=+
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42
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= +, σ** = *+,
σ44 = − +Hσ
∴ σ
*
− σ** ) + = σ** + σ*4
+ σ*4
*
σ
τ' =
L
4
=
= +1 E8
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+
12 × +/
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+ +3 × +/
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3 4A1 × +/
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=+3
=+=
α= +
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9
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=
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=
56 ()
C = /+
+
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= /++
3+
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H =+*
= + /2/
β
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4/
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3
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7
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8 = + 1+1
τ
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A A4
$ **
=
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8 = + 1+1 × + × 4+ × A3 =
8=
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A A43 E
33
7
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() $
3/
σ66 = 3+E8 Hσ'' = ++E8
E
τ6' = 3+E8
P
&
3+
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=+
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56 () σ66 = 3+ E8 H σ'' =
#
E
3=
&
++ E8 , τ6' = 3+E8
P
σ66 − σ''
9
*
*
+ τ*6' =
4+* + 3+* = /+ E8
7(
C
( )=
( )=
−
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)=
(
( )=
+
−
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−
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6
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+
−
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+
$
/
*
/
()
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− λ% = +
56 ()
4
4−λ
λ* − 2λ + / − 4 = +
(
=+
(/ − λ ) ( 4 − λ ) = 4 = +
λ* − 2λ + * = +
λ = *, λ = =
− *%) × - = +
, λ=*
4 4
6
6*
=
6 + 6* = +
+
H
+
6 = 6*
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G
L
*
−
&
*
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3
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56 ( )
7
C
P
,
7
7
=
=
+/
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4/
7 = + 2A=/7 H7 = + 14* 7
7
∴
6
+ 2A=/7
= ++E8
++
3A
% 7=
=
7
7=
7
= ++E8
/3 32
,
/B
&
&
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+ =4
+ 4*
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*=
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3=
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# =7
&
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2++ 8
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&
&
L
+*
0 8
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8( 8
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(
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+ A/
4
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+ 4/3
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4
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8( 8
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3
8
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6
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3* A
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0
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3=
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()
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=
6
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3
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= + * ( *41 − A/ /) = *2 4
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"
L
= /+ − +L
H
∴
*
L*
<+
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6
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5
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#
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+ *22
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+ /1= + + *22
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2
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6
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3
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56 () ' = *6 − + 6*
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written permission.
'
= * − + *6
6
*
'
<+∴'
6
6*
6= +
∴ ' = *+ − + = +
* − + *6 = +
© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the
written permission.