Serial No. of Q. C. A. B.
Roll No.
: 58 ] Total No. of Questions : 58 ]
[ : 32 [ Total No. of Printed Pages : 32
81-K Code No. : 81-K
Subject : MATHEMATICS / Kannada Version )
: 09. 04. 2012 ] : 10-30 : 100 ]
1-45
[ Date : 09. 04. 2012 [ Time : 10-30 A.M. to 1-45 P.M. [ Max. Marks : 100
]
FOR OFFICE USE ONLY Q. No.
Marks
Q. No.
Marks
Q. No.
Marks
Q. No.
Marks
Q. No.
1.
13.
25.
37.
49.
2.
14.
26.
38.
50.
3.
15.
27.
39.
51.
4.
16.
28.
40.
52.
5.
17.
29.
41.
53.
6.
18.
30.
42.
54.
7.
19.
31.
43.
55.
8.
20.
32.
44.
56.
9.
21.
33.
45.
57.
10.
22.
34.
46.
58.
11.
23.
35.
47.
12.
24.
36.
48.
Marks
T ota l Ma rk s Total Marks in words
Grand Total
1. 2. Signature of Evaluators
3800000
Registration No.
Signature of the Deputy Chief
Signature of the Room Invigilator
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2
i)
58
ii)
iii)
iv) v)
vi) /
/
vii)
15
viii)
I. 20 1.
3800000
A, B
C
(A)
A
(B
C)=(A
B)
(A
C)
(B)
A
(B
C)=(A
B)
(A
C)
(C)
(A
B)
C=(A
C)
(B
C)
(D)
(A
B)
C=(A
C)
(B
C)
1 = 20
81-K
3 2.
T n + 1 = 4n + 5
Tn =
(A)
4n – 5
(B)
4n – 1
(C)
4n + 1
(D)
4n + 5
3. n
(A)
n n
(C)
n
Cr P
r
P
r
Cr
= r
(B)
= r
(D)
4.
5.
(
(A)
C.V. =
(C)
C.V. =
A
(
)
X
X
100
. X 100
2
3
n
P
n
Cr
n
Cr
n
P
r
=
r
=
r
r
)
( C.V. )
(B)
C.V. =
(D)
X =
B
X
100
C.V.
2
1
100
AX = B
X
3800000
(A)
1
2
(B)
3
1
(C)
2
1
(D)
1
3
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4 6.
7.
( a2 – 9 ) (A)
(a–9)
(B)
(a–3)
(C)
(a+3)
(D)
(a+9)
A
B
B=A
H
L
(B)
H+L=A+B
(C)
H+B=A+L
(D)
H
L=A
B
[ ( a + b )2 – c2 ]
a=0 a‚ b‚ c
3800000
H
(A)
8.
9.
( a 2 + 5a + 6 )
a‚ b‚ c
(A)
1
(B)
0
(C)
2
(D)
–2
(B)
a2 + b2 + c2
(D)
–
a+b+c=0 (A)
a3 + b3 + c3
(C)
–
3abc
( a2 + b2 + c2 )
( a3 + b3 + c3 )
L
81-K
5 a 2 – bc
10. a + b + c = 0 (A)
( ab + bc + ca )
(B)
( ab – bc – ca )
(C)
– ( ab – bc – ca )
(D)
– ( ab + bc + ca )
(A)
x2 + 2 = 6
(B)
2m 2 = 72
(C)
P2 =9
(D)
K2 = K
11.
12.
13.
( A )
( x )
(A)
A =
1 x(x–4) 2
(B)
A =
1 x(x+4) 2
(C)
A =
1 ( 4x ) 2
(D)
A =
1 ( x + 4x ) 2
n an
+1
. b
4
n –1
(A)
ab
n
b a
(B)
ab n ab
(C)
ab
n
a b
(D)
ab n a
14. ax 2 + bx + c = 0
3800000
(A)
b a
(B)
– c a
(C)
c a
(D)
– b a
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6 15.
TA
TB
O
ATB = 60°
AOB = A
O
60°
T
B (A)
120°
(A) (C)
(B)
90°
(C)
60°
8, 15, 17
(B)
5, 8, 17
5, 12, 17
(D)
3, 6, 9
16.
17. 5
3
?
B
A
3800000
(A)
8
(B)
2
(C)
5
(D)
3
(D)
240°
81-K
7 18.
( r ),
(A)
V =
(C)
V =
1 3
r2 h r2 h
19.
20.
( h ),
(B)
V = 2 rh
(D)
V =
50
125
(B)
2500
(C)
500
(D)
250
DEF,
A=
D
rh
10
(A)
ABC
( V )
B=
E
(A)
AC 2 DF 2
(B)
AB 2 DF 2
(C)
AC 2 EF 2
(D)
BC 2 DE 2
ABC DEF
II.
=
10 21.
a
d
1 = 10
n
………………………… .
22. A, G, H
( AM ), ( HM )
3800000
( GM )
AH = ………………………… .
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8 B
( AB ) l = ……………………… .
( a2 + b2 + c2 )
………………………………… .
23. A
24.
25. ax 2 + bx + c = 0
(
26.
) = ………………………………… .
x
m
n
………………… .
27. ( a + b )
28.
(a–b)
ABC =
………………… .
AD DE = = AC BC
AED = 90°
? ?
A
E D
B
29.
30.
3800000
C
…………………… .
………………… .
81-K
9 III.
31.
U=
{ 1, 2, 3, 4, 5, 6, 7, 9 }
A=
{ x : x 10
B =
{
x : x 10
} 3
}
( A
B )l
=
A
l
Bl 2
3800000
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10 32. n(U)=
n(K
= 1000
n(K)=
= 800
n(E)=
= 400
E)=
= 300.
2
3800000
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11 33.
1 1
3
34. 3 + 7 + 11 + ………
3800000
3
20 2
20
2
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12 3x 2
3800000
(n+1)
5
+ 3
36.
6x
1
35. If 2
P 3 = 120
0
6
5
9
= 2
7
n
x
2
2
81-K
13 37.
( a + b ) c 4s ( s – c )
38.
3800000
3
3
4
2
a+b+c = s 2
.
2
2
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14 39.
5 3+
2
40. x 2 – 5x + 3 = 0
3800000
2
2
81-K
15 41. m
n
2x 2 – 4x + 1 = 0
( m + n ) 2 + 4mn 2
42. S =
3800000
{ 2, 4, 6, 8 }
10
2
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16 43. 5
8 2
3800000
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17 44.
(a)
(b)
(c)
(d)
2
P Q
C
X
M
A
B Y
D
S R
3800000
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18 45.
r
r3 2
3800000
r 2
2
81-K
19 46.
2
[
20
]
= 1 C
D E
40 60
140 100 80 40
B
60
A
3800000
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20 47.
48.
3800000
2 2
1
1
1
2
1
1
1
2
2
81-K
21 IV.
49.
5
10
7
11 3
3800000
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22 50.
3800000
3
10 – 14
2
15 – 19
3
20 – 24
5
25 – 29
3
30 – 34
2
23 51. x 3 – 3x 2 – 10x + 24
81-K
x 3 – 2x 2 – 9x + 18 3
3800000
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24 52.
x
16 3 3
3800000
81-K
25 53.
3800000
ABC BC 2 = 2
(
AD A 2 2 AB – AC
)
BC
DB : CD = 3 : 1 3
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26 54. 3
3800000
81-K
27 V.
55.
2 90
4
30 1
6
2 8 4
3800000
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28 56. 4
3800000
81-K
29 57.
10
5
3 4
3800000
[ Turn over
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30 58. y = x 2
y = 2x + 3
x 2 – 2x – 3 = 0 4
3800000
31
3800000
81-K
[ Turn over
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3800000
32
