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KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM,
BANGALORE - 560 003
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2012
S.S.L.C. EXAMINATION, APRIL, 2012
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MODEL ANSWERS
81-K
CODE NO. : 81-K
$033~:
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09.
: 04. 2012
Date : 09. 04. 2012
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Subject : MATHEMATICS
[ zidcbdQ wodr(%~: 100
I Max. Marks : 100
( Kannada Version )
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I. 1 .
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(AUB)nC=lAnc)U(Bnc)
1
2.
C
4n+ 1
1
3.
B
r
-nn PC=
k
r
1
4.
A
C.V. =
5.
B
3x1
1
6.
C
(a+3)
1
7.
D
HxL=AxB
1
8.
B
0
1
9.
A
a 3 +b 3 + c 3
1
10.
D
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1
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100
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K ~ = K
1
12.
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1
A = -2 x ( x + 4 )
1
13.
C
ab
1
14.
D
b
-
1
15.
A
120"
1
16.
A
8. 15, 17
1
17.
B
25o.a~.
1
18.
C
V = nr2h
1
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D
250 &.$o.ae.
1
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A
AC2
1
a
D F ~
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21.
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1
22.
G
1
23.
B'A'
1
a2
1
25.
b2-4ac
1
26.
x 2 - ( r n + n ) x +rnn=O
1
27.
1
1
28.
AE
-
1
24.
a.b.c
AB
29.
A = 4nr2 ( r = h e $ i d $i?Zb;,)
1
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31.
A={2,3,5,7)
1
-
B={3,6,9)
2
A n B={3)
( A ~ B ) =' { 1 , 2 , 4 , 5 , 6 , 7 , 9 )
1
-
(i)
2
A ' = & A = { 1,4,6 , 9 )
1
2
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= a+c
b = - 2ac = 2 0
a+c
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a
1
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2
b = HM = 20
=
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140 a t . = 7 So.&?.
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F =
SodA = 8
V = Zl,0r(rl% SO% = 6
1
E = eoe33rid $023, = 12
5
F + V = 8 + 6 = 14
E + 2 = 1 2 + 2 = 14
:.
49.
F +V = E
1
1
-
+ 2.
2
dddb rn&rtno& dod,d&- meXRn%3z
j $338e)m m d d eruQ33863w3,WJ&FssA%3 = 9
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Ax B
LCM = ---H
LCM =
1
2
( x 3 - 3 x 2 - lox+ 2 4 ) ( x 3 - 2 x 2 - 9 x + 18)
(x2+x- 6 )
x-4
x 2 + x - 6 ) x -3x2-10x+24
& + x 2 - 6x
(-1
(+I
(-)
1
-
2
(+I
(+I
(-)
0
:.
LCM = ( x - 4 ) [ x 3 - 2 x 2 - 9 x + 181
e$n
LCM= ( x 3 - 3 x 2 - 1 0 x + 2 4 ) ( x - 3 )
52.
2
1
$dm&9@z;d @$enF = 64x 2
1
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16<3 =
3
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x2
7
64<3 = <3 x 2
21
1
2
x
3@j3e;d
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=
a
x = 8 5o.ae.
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= 3x
21
= 3(8)
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= 24 5 0 . a ~ .
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L APQ
+ L BPQ =
180"
L A P B = 180'
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8~3U~d3i;?id3
ar
+ ar
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3
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2
I
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a r ( r 4 - 1 ) = 90
a r ( r 2 +l ) ( r 2 - 1 ) = 9 0
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r2-1 = 3
1
2
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-
r = +.$4
1
2
r = t 2
wdd, r > 1
[i)Bod
-
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a r ( l + r 2 ) = 30
a ( 2 )( 1
+22)
= 30
a(2)(5)=30
10a = 30
a = 3- 0
10
a
&rt
=
3.
-21
Tn= arn-
T,= 3 [ 2 ) ' - '
=
Z1
3(217
= 3(128)
1
2
= 384
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