-
PR (D) - 7040 [ Turn over
— 560 003
KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE – 560 003
/ 2020 S.S.L.C. EXAMINATION, MARCH / APRIL, 2020
MODEL ANSWERS
: 07. 04. 2020 ] : 81-K
Date : 07. 04. 2020 ] CODE NO. : 81-K
Subject : MATHEMATICS
/ Old Syllabus
/ Private Repeater
/ Kannada Version
[ : 100
[ Max. Marks : 100
I. 1.
A B
(A) ( A B )l = A
l B
l
(B) ( A B )l = A
l B
l
(C) ( A B )l = A
l B
l
(D) ( A B )l = A B
(A) ( A B )l = A
l B
l 1
D CCE PR UNREVISED
-
81-K 2 CCE PR
PR (D) - 7040
2. a b ( G )
(A) G = 2
ba (B) G = ab
(C) G = 2
ba (D) G = ab
(B) G = ab 1
3. 8 12 24
(A) 4 (B) 24
(C) 8 (D) 12
(A) 4 1
4. P ( x ) = 4
2 x P ( 2 )
(A) 8 (B) 4
(C) 0 (D) 2
(C) 0 1
5. 0
2 cbxax
(A) acb 42 (B) acb 42
(C) acb 42 (D) acb 42
(B) acb 42 1
-
CCE PR 3 81-K
PR (D) - 7040 [ Turn over
6.
AB P
OPA
(A) 60º (B) 0º
(C) 180º (D) 90º
(D) 90º 1
7.
sin 30º
(A) 1 (B) 3
(C) 2
1 (D) 2
(C) 2
1
1
8.
(A) 6, 8, 9 (B) 3, 4, 6
(C) 7, 8, 9 (D) 6, 8, 10
(D) 6, 8, 10 1
-
81-K 4 CCE PR
PR (D) - 7040
II. 6 1 = 6
9 14
9. 52 nTn 10
nT = 2n – 5
10T = 2 ( 10 ) – 5
= 20 – 5
10T = 15
1
10. 00 CPnn
00CP nn = 1 + 1 = 2
1
11.
0
12.
= 100 C.V. = X
100
1
13. p ( x ) = 865423 xxx
3 1
14. 0562 xx
= 1
)6(
a
b = 6 ½ + ½
1
-
CCE PR 5 81-K
PR (D) - 7040 [ Turn over
III.
15. 50
42 24
= n ( A ) = 50
= n ( B ) = 42 ½
= n ( A B ) = 24
= n ( A B ) = ? ½
n ( A B ) = n ( A ) + n ( B ) – n ( A B )
= 50 + 42 – 24
= 92 – 24 ½
= 68
= 68. ½ 2
16. 6
1,
4
1,
2
1 , .... 20
2
1 ,
4
1 ,
6
1 , .....
2, 4, 6, .... ½
a = 2, d = 2 n = 20 n
T = ?
nT = a + ( n – 1 ) d
20T = 2 + ( 20 – 1 ) 2 ½
= 2 + ( 19 ) 2 ½
= 2 + 38
= 40
20 =40
1. ½
2
-
81-K 6 CCE PR
PR (D) - 7040
17. 32
2 + 3
2 + q
p3 , p, q z, q 0 ½
q
p3 – 2
q
qp 23
3 ½
q
qp 2
3 ½
32 ½ 2
18.
10 ½
n = 10
= 2
)3( nn ½
= 2
)310(10 ½
= 2
710 ½
= 35. 2
-
CCE PR 7 81-K
PR (D) - 7040 [ Turn over
10 ½
n = 10
= nCn 2
= 102
10 C ½
= 10!2!)210(
!10
½
= 10!2!8
!8910
= 1012
910
= 45 – 10 ½
= 35 2
19. ( n + 3 ) ! = 20 ( n + 1 ) ! n
( n + 3 ) ! = 20 ( n + 1 ) !
( n + 3 ) ( n + 2 ) ( n + 1 ) ! = 20 ( n + 1 ) ! ½
( n + 3 ) ( n + 2 ) = 20
2n + 5n + 6 – 20 = 0 ½
2n + 5n – 14 = 0
2n + 7n – 2n – 14 = 0
n ( n + 7 ) – 2 ( n + 7 ) = 0
( n + 7 ) ( n – 2 ) = 0 ½
n + 7 = 0 n – 2 = 0
n = – 7 n = 2
– 7 ½
n = 2 2
-
81-K 8 CCE PR
PR (D) - 7040
20. 1 6
a)
b)
S = { 1, 2, 3, 4, 5, 6 } ½ n ( S ) = 6
a) A =
A = { 2, 4, 6 } n ( A ) = 3
P ( A ) = 6
3
)(
)(
Sn
An
2
1 1½
b) B =
B = { 1, 4 }
n ( B ) = 2
P ( B ) = 6
2
)(
)(
Sn
Bn
3
1
2
21.
4 3 = 12 ½
= = ½
= = ½
= ½ 2
22. 183
1
2
13 .
3 183
1
2
1
= 293
1
2
13 ½
= 233
1
2
3
2
-
CCE PR 9 81-K
PR (D) - 7040 [ Turn over
= 22
2
2
3 ½
= 22
23 ½
= 2
2223
= 2
25 ½
23.
)3(5723 23 xxxx .
p ( x ) = 2x – 2x – 15
x – 3 = 0 x = 3
3 3 – 2 7 – 5
9 21 84 1
3 7 28 79
q ( x ) = 32x + 7x + 28 ½
r ( x ) = 79 ½ 2
2x – 2x – 15 = 2x – 5x + 3x – 15
= x ( x – 5 ) + 3 ( x – 5 ) 1
= ( x – 5 ) ( x + 3 )
2x – 2x – 15 = 0
( x – 5 ) ( x + 3 ) = 0 1
x – 5 = 0 x + 3 = 0
x = 5 x = – 3
x = 5 x = – 3. 2
-
81-K 10 CCE PR
PR (D) - 7040
24. 4 8
PA PB
— ½
— ½
2 — ½
— ½ 2
-
CCE PR 11 81-K
PR (D) - 7040 [ Turn over
25. 50
30º
½
AB = = 50
BC = ½
ABC A = 30°
tan 30° = AB
BC ½
503
1 BC
BC = 3
50
BC = 3
350 ½
= 3
350
2
-
81-K 12 CCE PR
PR (D) - 7040
26. XYZ P XY PQ XZ
XP = 4 XY = 16 XZ = 24 XQ
ABCD AB || CD AB = 3 CD AOB
COD
1
XYZ PQX
XYZ = PQX
= 90°
XYZ ~ PQX
-
CCE PR 13 81-K
PR (D) - 7040 [ Turn over
XP
XZ
XQ
XY
4
2416
XQ
XQ = 24
416
XQ = 3
8 ½
= 3
22 = 2.66 ½
2
AOB COD
AOB = COD
OAB = OCD
AOB ~ COD
2
2
CD
AB
= 1
99)3(
2
2
2
2
CD
CD
CD
CD ½
AOB : COD = 9 : 1 ½ 2
-
81-K 14 CCE PR
PR (D) - 7040
27. ( 2, 3 ) ( 4, 7 )
),(11
yx = ( 2, 3 ) ),(22
yx = ( 4, 7 )
=
2,
2
2121yyxx
½
=
2
73,
2
42 ½
=
2
10,
2
6 ½
= ( 3, 5 ) ½ 2
28. P ( 2, – 3 ) Q ( 10, y ) 10 y
),(11
yx = ( 2, – 3 ) ),(22
yx = ( 10, y )
d = 212
212
)()( yyxx ½
10 = 22 ])3([)210( y ½
10 = 22 )3()8( y
100 = ( 8 ) 2 + ( y + 3 ) 2
100 = 64 + ( y + 3 ) 2
100 – 64 = ( y + 3 ) 2 ½
36 = ( y + 3 ) 2
( y + 3 ) 2 = 36
-
CCE PR 15 81-K
PR (D) - 7040 [ Turn over
y + 3 = 36
y = – 3 6
y = – 3 + 6 y = – 3 – 6 ½
y = 3 y = – 9
y = 3 – 9 2
29. 20
7
r = 7 cm h = 20 cm = ?
TSA = 2r ( r + h ) ½
= 2 )207(77
22 ½
= 2 2777
22 ½
= 44 27
= 1188 cm2 . ½ 2 30.
2
20 = 1
D
160
100 C 80
E 100 60
40 B 60
A
20 m = 1 cm
160 m = 20
160 = 8 cm
100 m = 20
100 = 5 cm ½
-
81-K 16 CCE PR
PR (D) - 7040
60 m = 20
60 = 3 cm
40 m = 20
40 = 2 cm
80 m = 20
80 = 4 cm
1½ 2
31. 2
i) A B
ii) A \ B
i) A B
1
-
CCE PR 17 81-K
PR (D) - 7040 [ Turn over
ii) A \ B
1 2
32. 13 nT
n 26
nT n
13 nTn
½
26 = 3n – 1
26 + 1 = 3n ½
27 = 3n
n = ½
n = 3 ½ 2
33.
23
23
.
23 23 ½
23
23
23
23
23
23
½
=
222
23
23
½
=
23
2.3.22322
2
-
81-K 18 CCE PR
PR (D) - 7040
= 1
6223 ½
= 5 + 2 6
34.
2
14 6 2 18
14
40
14 360° = 126°
6
40
6 360° = 54°
2
40
2 360° = 18°
½
18
40
18 360° = 162°
40
1½ 2
35. ( x – a ) 223 xxax a
-
CCE PR 19 81-K
PR (D) - 7040 [ Turn over
p ( x ) = 223 xxax
p ( x ) = 2)(23 aaaa ½
0 = 233 aaa ½
0 = a + 2 ½
a = – 2 ½ 2
36. 2x + 3 = 2x 0
2 cbxax
a, b c
2x + 3 = 2x
2x – 2x + 3 = 0 ½
a = 1 b = – 2 c = 3 1½ 2
37. ABC AMP
MP
BC
PA
CA 2
ABC AMP 1
ABC = AMP = 90°
A
ABC ~ AMP 1 2
-
81-K 20 CCE PR
PR (D) - 7040
AM
AB
MP
BC
AP
AC
MP
BC
PA
AC
38.
5 12
½
ABC B = 90°
222 BCABAC
= 122 + 5 2 1½
= 144 + 25
2AC = 169
AC = 169
AC = 13 2
39. tan 2A = cot ( A – 18º ) 2A A
tan 2A = cot ( A – 18° ) ... (i)
tan 2A = cot ( 90° – 2A ) ... (ii) ½
(i) (ii) 2
-
CCE PR 21 81-K
PR (D) - 7040 [ Turn over
cot ( A – 18° ) = cot ( 90° – 2A )
A – 18° = 90° – 2A 1½
A + 2A = 90° + 18
3A = 108°
A = 3
108
A = 36°
40. ( 3, 4 ) ( 7, 8 )
),(11
yx = ( 3, 4 ) ),(22
yx = ( 7, 8 ) ½
= 12
12
xx
yy
= 37
48
1½
= 4
4
= 1 2
IV.
41. 3
( C-I ) ( f )
1 — 5 4
6 — 10 3
11 — 15 2
16 — 20 1
n = 10
-
81-K 22 CCE PR
PR (D) - 7040
C.I. f x f x d =
x – x
2d 2df
1 — 5 4 3 12 – 5 25 100
6 — 10 3 8 24 0 0 0
11 — 15 2 13 26 5 25 50
16 — 20 1 18 18 10 100 100
n = 10 fx = 80 2df = 250
10
80)(
n
fxx = 8 1½
= 2510
2502
n
df = 5 1½
3
C.I. f x d 2d f d
2df
1 — 5 4 3 – 1 1 – 4 4
6 — 10 3 8 0 0 0 0
11 — 15 2 13 1 1 2 2
16 — 20 1 18 2 4 2 4
n = 10 f d = 0 2df = 10
= A = 8 1½
= 510
0
10
10222
i
n
df
n
df 1½
= 51501
= 5 3
-
CCE PR 23 81-K
PR (D) - 7040 [ Turn over
C.I. f x d = A – x 2d f d
2df
1 — 5 4 3 – 5 25 – 20 100
6 — 10 3 8 0 0 0 0
11 — 15 2 13 5 25 10 50
16 — 20 1 18 10 100 10 100
n = 10 fd = 0 2df = 250
= A = 8 1½
= 02510
0
10
250222
n
df
n
df
1½
= 25
= 5 3
C.I. f x 2x f x
2xf
1 — 5 4 3 9 12 36
6 — 10 3 8 64 24 192
11 — 15 2 13 169 26 338
16 — 20 1 18 324 18 324
n = 10 fx = 80 2xf = 890
=
22
n
xf
n
xf
1½
=
2
10
80
10
890
1½
= 6489
= 25
= 5 3
-
81-K 24 CCE PR
PR (D) - 7040
42.
½
A B P ½
A, P B ½
XPY ½
APX = 90° ... (i)
BPX = 90° ... (ii)
BPXAPX = 90° + 90° (i) (ii)
APB = 180° APB
APB
A, P B
3
1
-
CCE PR 25 81-K
PR (D) - 7040 [ Turn over
½
½
43. 3
x ( x + 1 ) = 6x + 24.
m n 01272 xx
a) ( m + n ) mn
b) nm
11
x ( x + 1 ) = 6x + 24 2x + x = 6x + 24
2x + x – 6x – 24 = 0 1
2x – 5x – 24 = 0
a = 1 b = – 5 c = – 24
x = a
acbb
2
42
x = )1(2
)24()1(4)5()5( 2 ½
x =
2
115
5
1215
2
96255
x = 2
115 x =
2
115
x = 2
16 x =
2
6
x = 8 x = – 3. ½ 3
2x – 7x + 12 = 0
a = 1 b = – 7 c = 12
m + n = 1
7
1
)7(
a
b = 7 1
mn = 1
12
a
c = 12 1
a) ( m + n ) mn = 7 12 = 84
b) 12
711
mn
mn
nm. 1
3
-
81-K 26 CCE PR
PR (D) - 7040
44. BD =
3
1 BC ABC D BC
22 79 ABAD 3
ABC ABC = 90º, BD AC. AB = c BC = a
BD = p CA = b 222111
pca
½
ABC AB = BC = AC
AP BC
BP = PC = 2
1 BC ½
BD = 3
1 BC
APD P = 90° ½
2AD = 22 DPAP 3
-
CCE PR 27 81-K
PR (D) - 7040 [ Turn over
= 22 )( BDBPAP
= BDBPBDBPAP ..2222
= BCBCBCAB3
1
2
12)
3
1( 22
= 2223
1
9
1BCBCAB 1½
= 9
39 222 BCBCAB
2AD = 9
39 222 ABABAB AB = BC = AC
9 2AD = 7 2AB .
ABC B = 90°
2AB = AC . AD
ADACAB .
11
2 ... (i) ½
2BC = AC . CD
CDACBC .
11
2 ... (ii) ½
2BD = AD . CD
2P = AD . CD ... (iii) ½
(i) (ii)
CDACADACBCAB .
1
.
111
22
3
-
81-K 28 CCE PR
PR (D) - 7040
CDADACac
1111122
1½
=
CDAD
ADCD
AC .
1
= CDAD
AC
AC .
1
CDADac .
11122
222
111
pac .
ABC = 2
1 AC BD
= 2
1 b p
= 2
bp ... (i) ½
ABC = 2
1 BC AB
= 2
1 a c
= 2
ac ... (ii) ½
(i) (ii)
22
acbp ½
bp = ac
b = p
ac
222 ACBCAB
-
CCE PR 29 81-K
PR (D) - 7040 [ Turn over
2c + 2a = 2b 1
2c + 2a = 2
22
p
ca
22ca ½
222
22
22
2
22
2
pca
ca
ca
a
ca
c
222
111
pca .
3
45.
A
A
cos1
cos1
= cosec A + cot A 3
A
A
A
A
cos
sin1
sin1
cos
= 2 sec A
A
A
A
A
A
A
cos1
cos1
cos1
cos1
cos1
cos1
½
= )cos1()cos1(
)cos1( 2
AA
A
½
=
A
A
2
2
cos1
)cos1(
½
=
A
A
2
2
sin
)cos1( ½
= A
A
sin
cos1
= A
A
A sin
cos
sin
1 ½
= cosec A + cot A. ½ 3
-
81-K 30 CCE PR
PR (D) - 7040
)sin1(cos
)sin1(cos
cos
sin1
sin1
cos 22
AA
AA
A
A
A
A
½
= )sin1(cos
sin.1.2sin1cos 222
AA
AAA
½
= )sin1(cos
sin211
AA
A
[ 1cossin 22 AA ] ½
= )sin1(cos
sin22
AA
A
½
= )sin1(cos
)sin1(2
AA
A
½
= 2 Acos
1 ½
= 2 sec A. 3 46.
6 10
14
3
1·5
7 2
-
CCE PR 31 81-K
PR (D) - 7040 [ Turn over
= 10 cm, = 2
10 = 5 cm = R
= 6 m, = 2
6 = 3 cm = r ½
r = 2
14 = 7 cm h = ?
=
hrrR 2333
1)(
3
2 ½
h =
2
33
3
1
)(3
2
r
rR
½
= 2
33 )(2
r
rR
= 2
33
7
)35(2 1
= 49
)27125(2
= 49
982
= 2 2
h = 4 cm. ½
= 4 cm. 3
-
81-K 32 CCE PR
PR (D) - 7040
= 2)51(
7
22
3
1
3
1 22 hr
= 251517
22
3
1
= 4·71 cm3 .
= 53)51(
7
22 22 hr 1½
= 5351517
22
= 24·75 cm3 .
= 33 )51(
7
22
3
2
3
2r
= 5151517
22
3
2
= 7
5049
= 7·07 cm3
= + +
= 4·71 + 24·75 + 7·07 1½
= 36·53 cm3 . 3
V.
47. 4 8 24
6 10 44
4
4 24 8 384
10
84TT = 24
a + 3d + a + 7d = 24
2a + 10d = 24 ... (i)
-
CCE PR 33 81-K
PR (D) - 7040 [ Turn over
106TT = 44
a + 5d + a + 9d = 44
2a + 14d = 44 ... (ii)
(i) (ii)
2a + 10d = 24 ... (i)
2a + 14d = 44 ... (ii)
(–) (–) (–)
– 4d = – 20 1
d = – 20
– 4
d = 5
d = 5 (i)
2a + 10d = 24
2a + 10 (5) = 24
2a + 50 = 24
2a = 24 – 50
2a = – 26
a = 2
26
a = – 13
a = – 13
a + d = – 13 + 5 = – 8 1
a + d = – 13 + 2 (5) = – 3 4
-
81-K 34 CCE PR
PR (D) - 7040
4T = 24
3ar = 24 ... (i) ½
8T = 384
7ar = 384 ... (ii) ½
(i) (ii)
384
24
7
3
ar
ar 1
16
11
4
r
4r = 16
r =
r = 2
3ar = 24
a (2) 3 = 24 1
a (8) = 24
a = 8
24
a = 3
1
)1(
r
raS
n
n
102331
)11024(3
12
)12(3 10
10
S 1
10S = 3069
4
-
CCE PR 35 81-K
PR (D) - 7040 [ Turn over
48. 9 4 2
PQ RS
— 2
— 1
— 1 4
-
81-K 36 CCE PR
PR (D) - 7040
49.
ABC DE || BC ½
EC
AE
DB
AD ½
D, C B, E ½
EL AB DN AC ½
ELDB
ELAD
2121
A =
2
1 bh
DBAD
DNEC
DNAE
2121
A =
2
1 bh
ECAE
EC
AE
DB
AD BDE = CDE
1.
-
CCE PR 37 81-K
PR (D) - 7040 [ Turn over
50. 2x – x – 6 = 0.
2x – x – 6 = 0
y = 2x y = 6 + x
y = 2x
x 0 1 2 3 – 1 – 2 – 3
y 0 1 4 9 1 4 9
y = 6 + x
x 0 1 2
y 6 7 8
x- 1 = 1
y- 1 = 1
-
81-K 38 CCE PR
PR (D) - 7040
2x – x – 6 = 0
y = 2x – x – 6
x 0 1 2 3 4 – 1 2 – 3
y – 6 – 6 – 4 0 6 – 4 0 6
x- 1 = 1
y- 1 = 1
2
-
CCE PR 39 81-K
PR (D) - 7040 [ Turn over
4