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& ~ F U # S,t$ &amd d30d6, zbe3_edddo, doi-i&~& - 560 003 KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM,
BANGALORE - 560 003
azF.afl.ix9.b. dBe84, 2013 S.S.L.C. EXAMINATION, APRIL, 2013
Bnod : 08. 04. 2013
Date : 08. 04. 2013
&dB en)da39di-i%k MODEL ANSWJ3RS
SoBe$ do% : 81-K CODE NO. : 8 1-K
a ~ a h : d61 Subject : MATHEMATICS
[ sodr(Q : 100
[ Max. Marks : 100
( Kannada Version )
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11.
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13.
14.
15.
16.
17.
18.
19.
20.
11.
21.
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24.
25.
26.
27.
28.
29.
30.
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x 2 - 4 x + 1 = O
5
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, A ABC 1
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8 So.&?.
B = x 100 X
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A ' n B'
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1
-\lx+y
a x 2 + b x + c = O
m ~ a d
t = d d 2 - ( ~ + r ) '
QOW hoed ( 90" )
V = n r 2 h
a&&$ ~o~A@X
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36.
37.
.+5ad*ad zm'q&Zd
5 $ 0 3 a i D W . 5 803 &r($od 2 do$ aiDr(%Q SflilC333d mz&S = C
eruqd 2 aiDr+~$&~ 3 29$ &ii$od S 7 b h d r n ~ $ ~ S = C
:. LeJ3, m@&S
= 5 ~ 2 X 3c2
- 5 x p 2 X 3 x F -- - 1 7 x 1
= 10x3
= 30
H = ( a - 7 )
L = ( a 3 - 1 0 a 2 + 1 1 a + 7 0 )
A = ( a 2 - 1 2 a + 3 5 )
B = ?
A x B = H x L
H x L ... B = - - L - H X A A
L a 3 - 1 0 a 2 + 1 1 a + 7 0 - - A - a 2 - 1 2 a + 35
a + 2
a 2 - 1 2 a + 3 5 ) a 3 - 1 0 a 2 + 1 1 a + 7 0
a 3 - 12a2 + 35a
-1 (+I (-1
2a - 24a + 70
2a - 24a + 70 I (+I (-1
0 0 0
:. B = ( a - 7 ) ( a + 2 )
= a 2 - 5 a - 14.
1 - 2
1 - 2
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1 - 2
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1
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- - ( d 3 ) 2 + 2 X ~ X 4 3 + ( 1 r 2 ) 2 5 - 2
- - 5 + 2 m + 2 3
- - 7 + 2 m 3
eiw Z3d x -60.
&Bd 233 = dn. 18.75
ddd = e$e)3 dd - 3nBd 236
x -- x x = x - 18.75 100
x2 - - - x - 18.75
x2 = 1OOx- 1875
:. x 2 - lOOx+ 1875 = 0
( x - 7 5 ) ( x - 2 5 ) = 0
:. x = 75 @ @ ~ n x = 25
37bAa3 e5w 236 do. 75 dn. 25.
x 2 - 8 x + 1 = O
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a=l, b = -8 , c = l
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oow8aerl A AOB, L AOB = 90'
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A B ~ = A O ~ + B O ~
= [ k A c ) 2 + [ $ m ) 2
1 1 = - A C ~ + q ~ ~ 2
4
:. A B ~ = L ( A c ~ + 4 B D ~ )
:. I A C 2 + B ~ ' = 4 A B 2 1
T
Q
O P I P T
:. L OFT = 90"
L OPQ = xo
L Q P T = 9 0 ° - X "
be??&, L PQT = 90' - x0
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2
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A PQT @ham
L PTQ + L QPT+ L PQT= 180"
L P T Q + 9 0 ° - ~ 0 + 9 0 0 - ~ o = 180'
L PTQ + 180' - 2x0 = 180"
:. L PTQ = 2xo
:. L PTQ = 2 L OPQ.
z $ h m 20 ax. = 1 So.&?.
i) - - 160 - 8 So.&?. 20
120 - 6 So.&?. 1 5 -
loo - 5 5o.ae. ) -
60 iv) 20 = 3 So.ae.
40 V) = 2 So.ae.
80 vi) 20 = 4 So.&?.
D
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A
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1 - 2
1 3
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2
2
...... (i) ...... (ii)
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@md d ~ m d S q , &&d
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bD B C
qa- F = 5
v = 5
E = 8
F + V = 5 + 5 = 1 0
E + 2 = 8 + 2 = 1 0
(i) (ii) Bod
I F + v = E + 2I
&Be$fi 693 em, @Z&@F~% d o 4 = n ( U ) = 100
fir33 @do33dam eru+en~md eg6@~T(% do&& = n ( M ) = 82%
@ p a @d~hd&~ eru.!&eca~md e~.&@~fid 3oS6 = n ( S ) = 72%
ad& @d&fi%O- m+en~md @z$~@F~(% doSb = n ( M n S ) = 55%
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A x B :. L = - H
B A = A X H @@33 - X B . H
B x 3 - x 2 - l o x - 8 - - H - x 2 + 3x + 2
x - 4
x 2 + 3 x + 2
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B . - - " H - x - 4
B :. L = A X j=j
= ( x 3 - 2 x 2 - 13x- 1 0 ) ( x - 4 )
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A L = X B
H
A ~3 - zx2 - 13x- 10 - - H - x 2 + 3 x + 2
x - 5
x 2 + 3 x + 2 x 3 - 2 ~ ~ - 13x - 10
x 3 + 3 x 2 + 2 x
(-1 (-) (-1
- 5 x 2 - 1 5 x - 10
- 5x2 - 15x- 10
(+I (+I (+)
0 0 0
A . - .. = ( x - 5 )
. L = ( x - 5 ) ( . . x 3 - x 2 - l o x - 8 )
a ( b 2 c 2 - 1 ) b ( c 2 a 2 - 1 ) c ( a 2 b 2 - 1 ) a d p d = + + bc + 1 c a + 1 a b + 1
- - a ( b c - l ) ( b c + l ) + b ( c a - l ) ( c a + l ) + bc+ 1 c a + 1
c ( a b - l ) ( a b + 1 ) a b + 1
= a ( b c - l ) + b ( c a - l ) + c ( a b - 1 )
= a b c - a + a b c - b + a b c - c
= 3 a b c - a - b - c
= 3abc - abc . a + b + c = a b c ]
= 2abc.
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addo&& L APQ = 90" ...... (i)
L BPQ = 90' ...... (ii) L APQ + L BPQ = 180"
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rbaedd $d$u = do&@$ $$@u 4 1 - zr3 = - .r2 h
" 3 3 4 22 1 22 - x - x r 3 = - x - x 12x 1 2 x 6 ? 7 7 7
4 r 3 = 12x 1 2 x 6
1p3x 1 2 x 6 r3 =
9 :. r 3 = 216
:. r =
r F F z q r9ne%d + r a ~ &ad&& 84e$;ijw = 4 nr 2
2 2 = 4 x 7 ~ 6 ~ 6
I rlne4d d3r-a~ &dfib %e$;ijw = 452.57 zd.5o.at.
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A
B A C I;. F
6 : A A B C AS_ A DEF ii%O-,
L B A C = L EDF
L A B C = L DEF
&& i A C B = L DFE
L B C A C a'$)?& : - - - - - DE - EF - DF
dM : A X = DE &A_ AY = DF arbdoS, AB dJ&_ AC d% &?6 X &S& Y t30&d4&~ 3,Ti3d38b. X Y de8b.
m@:
adnw+dd~
A A X Y & & _ A h E F d % O - L A = L D
A X = DE, AY = DF
:. A AXY= A DEF
:. XY = EF &a_ L L = L DEF
L AXY = L DEF = L ABC
aodd , L AXY = L A B C
:. XY I 1 BC ... (il AB A C B C .
" A X - A Y - X Y
AB A C B C "soda, = @ =
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