1. 76
14

2. A-NET
1:
25 # 3 #
1.

3. A = { x | x 2 − 6x − 16 0 }
B = { x | 2 − x 5}
A B = [a, b]
a + b !#$%#'$%#()
1. 15 2.16 3.17 4.18
2. -./)01
2 3#2(4
!5
.

4. $26-7 -%89 :2 (−2 , −1)
1
2 x[x 2x 3 0] 2 + − !# /).;$4
/).;
1.
.$7812;1
2 x[P(x)
[Q(x)
R(x)]
:2

5. x[P(x)
Q(x)
R(x)]
1
23#2(4
!51
2

6. B
1. . C 1.B 2. . B C 1. D. 3. .D. C 1.B 4. . C 1.D.
3.

7. $26-7 -%89$4
$E312;/
$3F 4)C-/
9

8. 3#2(4
!5 !# /).;$4
/).;
1.x[(x 0) (x 0)]
{x[x 0] x[x 0]}
2.{

9. x[x 0]

10. x[x 0]}

11. x[(x 0)
(x 0)]
3.x[(x 0)
(x 0)]
{

12. x[x 0]
x[x 0]}
4.x[(x 0)
(x 0)]
{x[x 0]
x[x 0]}
+
2x 1
4.

13. }
3x 4
r {(x , y) R R y
+
= × =
}
2
−
−
x 4
s {(x , y) R R y 2
9 x
= × =
$E3

14. 1
2

15. 3#2(4
!5$4
r s R R
1. )
2
,
9
3
4
( , 1) [
−
4
2
[
2
,
9
− − 2. , )
3
) (
3
−
2
−
2
,
9
3. , )
3
) (
3
4
( , 1) [
−
− − 4. , )
9
4
( − , − 1)
[
5.
h(x) = −4x + 13 C
g 1 (x) +
x 5
− =
g $4
OP;9Q
E;RS%

16. gof = h
f(1.3) !#$%#'1
2

17. 3#2(4
!5
2
1. 6.4 2. 6.8 3. 6.0 4. 6.2
−
0 2
6.

18. A C B $4
$ 3).E9 ERS; A =
1 a
, a $4
/
/).;'
BA = A-1 C det (4B - I) = 0
a !#$%#$%#'1
2

19. 3#2(4
!5
1. 1 2. 2 3. 3 4. 4
7.

20. P $4
-)[' y 2 − 2y − 8x − 7 = 0 ERS; ! l $4
$7
($)3).E9 7 ); E;RS !/]B
^9;2^#B% !S
/[O712; P C ! l $4
$7
7 D7:21
2

21. 3#2(4
!5
1. 2 2 14 0 x2 + y2 + x − y − = 2. 2 2 2 0 x2 + y2 + x − y − =
3. 2 2 2 0 x2 + y2 + x + y − = 4. 2 2 14 0 x2 + y2 + x + y − =

22. 77
18
(3, C ![O7)# '(_$-2)9[' 3x 2 − y 2 + 12y − 48 = 0 1
2

23. 3#2(4
!5D.
8.

24. ;)!D#
/ )
5
1. /^2/
RS;12;(_$-2)9['2^#B%!S (−2,6)
2. /^212;;)! C(_$-2)9[' (72;/%!S(
) #;
7
#^
3.
[%12;;)!^ 3
#^
4. ^12;
$2 C
[%12;;)!3#;
4
#^
9.

25. A = {x| 6x + 6x+1 = 2 x + 2 x+1 + 2 x+2 }
B = {x| log log log (2x 1) 0 7 2 3 − = }
DB012;7 Q.$E3 A '$E3 B :21
2

26. 3#2(4
!5
1. 0 2. 1 3. 2 4. 3
10. /; -:5
%!S12;7 $ !S^ %!S !/^22^B#%!S A(3, 5, 2) , B(1, -1, 6) C C(-2,1, 4)
1. 21 2. 3 21 3. 5 21 4. 7 21
v
= 3 i v
11.

27. u
4 j v
v
= i v
C v
+ j v
1
2

28. 1
2

29. 3#2(4
!5( #/).;
v
+ 2 v
1. $$32)9 u
v
% 30° '$$32)9 u
v
2 v
v
v
2 v
2. $$32)9%!S35;b'$$32)9 u
v
:2 6 i v
+ j v
v
+ v
3. $$32)9
RS;
#^%!S !%.]%;3);1
'$$32)9 u
v
:2
−4
5
i v
3
+
5
j v
v
v
4. | u
v
| | u
v
+ v
v
|
12.
f(x) = sin x C g(x) = arcsin 2x + 2 arcsin x
#12; (fog)(
1
) :21
2

30. 3#2(4
!5
3
1.
4
9
2.
2
(1 + 8 ) 3. 4 2 +
9
10
12
2
(7 + 2 10 )
4.
27
13.

31. ABC $4
7 $ !S^ ERS; !3);1
A ˆ
, B ˆ
, C ˆ
^ a, b,c
(sinA + sinB + sinC)(sinA + sinB − sinC) = 3sinAsinB
Cos C !#$%#()
1
1.
2
2.
3 3.
2
2
2
4. 1
14.

32. 7 )/4)C7;9 P = 3x + y
27 )1
2/:2 2x + 3y 120
x + y 10
y x 5
y 2 0
a $4
# %!S7 C b $4
#
2^%!S73 P
a b $%#'1
2

33. 3#2(4
!5
1. 158 2. 173 3. 89 4. 15
15.

34. Z 1 = -1 - 3 i C (z 2)3 =
1
+
2
3i
#12; Z1
2
6
+ (Z 2) 27 :21
2

36. 3#2(4
!5
1. 31 2. 26 3. 63 4. 127
16

37. z $4
/
$Q.;E
2
ERS; | iz −1 + az 4 | = 652 ;
5
|z| !#2^B#

38. Q#;

39. 3#2(4
!5
1
( 2. ]
1. , 1]
2
3
1
3. ]
(0 , 2
3
(
(1 , 4. , 2]
2
2

40. 78
17. !$1 8 /
$4
$1' 6 /
ERS;$4
$1B# 3 /
/
!S3 /
C !/
' 2 /
ERS;$4
/
B#
1 /
/
!S 1 /
7# 3$1;# 4 /
#/C$4
%!SDB012;$1%5;7!S/C !#
2^#
0 C$4
$1!S !#$%#'1
2

41. 14
1.
70
10
2.
70
28
3.
70
1
4.
70
18. #2;

42. '
RS; !B'27!1 3 B 7!; 4 B C7!
5$;.
5 B
^.'22 -)
2
2 B
#/C$4
%!S
/C(
B'2 2 B !7!$ :2
$%#'1
2

43. 1
1.
11
10
2.
66
19
3.
66
4.

44. 19. -./)01
2
. 1 2 + 2 3 + 3 4 + 4 5 + ... + 19 20 = 2,260
1.
n 2
+
+
n 1 n
−
2 2
=
a +
n 1 2
1
4
lim an
n
=
1
2

45. 3#2(4
!5B3
2;
1. . C 1. B 2. . B 3# 1. D. 3. . D. 3# 1. B 4. . C 1. D.
20.

46. a $4
/
/).;

47. f(x) =
#
!
−
3x a
−
, x 3
3x 3
−
2
ax 6a , x 3
f $4
OP;9Q
3#2$
:S2;
f$(a) !#$%#'1
2

48. 3#2(4
!5
1. 2 2. 4 3. 8 4. 10
21.

49. f(x) = 3x + 1
g $4
OP;9Q
ERS; ( ) 1 f o g x = x2 + % x R
f$(1) + g$(1)
!#$%#'1
2

50. 3#2(4
!5
41
1.
12
35
2.
12
33
3.
4
39
4.
4
22.
a :2/
/).;%!S%

51. -5:
%!S4j2
^$7
[
; y = a 2 x 2 + 4ax + 10 / x = 0 R; x = 1 !#
2^%!S
7
-:5
%!S%!S
2^%!S7$4
$%#()
1. 5 2. 7 3. 9 4. 11
23. /3);)//; !S3#2(4
!5
Q#;C
!S
96 105
86 95
76 85
66 75
56 65
46 55
3
7
10
y
x
4
1
2 BQ
!5 ! Q 65.5 1 = C ! 8^k
$%#' 75.5
7#
$'!S^;$'
2(%912;1
2 B !#$%#'1
2

52. 1. 5 2. 10 3. 15 4. 20

53. 79
24.

54. Xi $4
C
72'.Q7.3.12;
$)!^
%!S i $ :S2 i = 1, 2, 3, ..., 99, 100 %!S !C
$3F $%#' 100 C
#$b!S^$10.3 #k
.^ C# 8^k
12;C
$%#' 70, 40 C 60 3 ' 1
2

55. 3#2(4
!5/).;
100
1. % −
=
i 1
100
Xi 60 # % −
=
i 1
Xi 70
100
2. %( − )
=
i 1
100
Xi 70 2
#%( − )
=
i 1
2
Xi 40
3. )//;12;C
;#$4
$7
[
;$'
(4%;1
4.
)B3
2;)

56. $)!^
72'(
60
/R;37.
#
$)!^
DB

57. 72'(
C
35;3#
60 C
1R5
(4$4
DB
72'(
25.
3);7;-:5
%!S

58. 3
[
;43. 3)k
%!S2^B#)C #; 0 R; z ;
!5
Z 0.35 0.71 1.00 2.00
A 0.136 0.261 0.341 0.477
)^(
12;
;
2 # :2 #
;
m.;C#
;
Q^ 3#C# !)//;43. C-'# #
;
m.; !#$b!S^$10.3 60 '% 7#
$'!S^;$'
3)k
12 '% #
;
Q^ !#$b!S^$10.3 70 '% 7#
$'!S^;$'
3)k
7 '%
$42)9$EF
3912;)^(
12;
;
m.;)C #; 36 '% R; k
.^ $%#' $42)9$EF
3912;
)^(
12;
;
Q^ )C #; 63 R; X '%
X !#$%#

59. 1. 63.45 2. 72.45 3. 68.45 4. 78.45
2:
% 10 1 ' 5 # 2 #
6 ' 10 # 3 #
1.
x $4
/
$3F '%!S
2^%!S7ERS; 9, 12 C 15 ) x ;33# 11 ) x $ :2$]n 7
x !#$%#'$%#

60. 1. 1400 2. 1600 3. 1800 4. 2000
2.
$7
'12;(_$-2)9[' 16x 2 - 9y 2 + 32x +36y =164 3
x %!S/ x1 , x 2
)C^C)C #; x1 , x 2 ^
!S
#^
1. 0.5 2. 1 3. 2 4. 3
3.
log 2 3 = 159
#12; x ERS;722
;7 ) 2 2x+1 · 3 2x+2 = 12 2x
1. 2.09 2. 2.25 3. 2.75 4. 3.00
4.

61. A =
*
( ( ( )
-
+ + +
,
x 1 1
3 1 1
x 0 − 1
C12 (A) = 4
det (2A) !#$%#

62. 1. 15 2. 16 3. 17 4. 18
5.
lim
x
1
*
()
-
+,
1
− +
−
1
− 2 3x x 2
1 x
!#$%#

63. 1. 0.25 2. 0.55 3. 1 1. 25
6.

64. I $4
$E312;/
$3F
S = {x I 2x 2 − 9x − 26 0 C 1 − 2x 3}
D'12;7 Q.12; S $%#'$%#

65. 1. 14 2. 15 3. 16 4. 17

66. 80
7.

67. h(x) = 1 − x 5 C g(x) = x 5
f $4
OP;9Q
ERS; f(g(x)) = h(x)
f(5)
!#$%#

68. 1. 1 2. 2 3. 3 4. 4
8.

69. (x 1 + i) C(x + 2) $4
34)C2'12;OP;9Q
f(x) = x 3 + ax 2 + bx + c(x -3) ) f(x) $ :2$]n$%#

70. 1. 17 2. 20 3. 23 4. 25
9.
1
2 BQ
RS; !7 4)C7.%8.q12;7#
$'!S^;$'
$b!S^ 0.12 7#
$'!S^;$'
$b!S^$%#' 6 C7#
$'!S^;$'
3)k
$%#
' 10
7 4)C7.%8.q12;)4)D
!#$%#'$%#

71. 1. 1.05 2. 0.05 3. 0.20 4. 0.25
10.
7 -
89$Q.;OP;9Q
12;1
2 BQ
RS;)C #;34) x C y !)O$4
$7
3);
8
[^%!S i 1
=
%8
=
x = 32 , i i 1
%8
=
y = 16 i i 1
%8
=
x y = 65 i i 1
%2
1
i
8
x =140 1
=
%2
i
i y = 34,
x = 8
/C4)C 0# y (
$%#

72. 1. 1.33 2. 2.33 3. 1.75 4. 2.75

73. 81
)* 14

74. A-NET
7
E H c = c
+ +
(x 0)2 (y 6)
2
A F$ B C (0 , 6) D F E
H a
1
1. 32' 1
2 1 1
2
!5:2#;#^ r ;#
2; r ;/C%
(
C)'
B$E3 A
x2 − 6x −16 0 $E3 B | 2 x | 5
(x 8) (x + 2) 0 | x 2 | 5
5 x 2 5
2 8 3 x 7
;
5
$E3 A = [2, 8] ;
5
$E3 B = (3, 7)
A B = [7, 8] = [a, b]
;
5
a + b = 7 + 8 = 1
2. 32'1
2 4
3. 32'1
2 4
4. 32'1
2 3
5. 32'1
2 1
6. 32'1
2 3
7. 32'1
2 4
8. 32'1
2 3 %)/7 )(_$42)9 $-:S2 )^C$2!^-)
2 $1!^
)B4 ^'r [^;(47B#;)! /R;/C$).S
-./)03$:2(
/7 )(_$42)9['# 3x2 − y2 + 12y − 48 = 0
3(x2 ) − (y2 − 12y + 62 ) = 48 − 36
) 12 1
12
4
=
−
−
−
$%!^'' 3)k
(_$42)9 !]B
^9; = (h , k) = (0 , 6) , a = 2 , b = 12 , c = 4
(
(_$42)9['#%!S !
3 1;1
x $1!^
)B4(
;
!5
-)
2 ';)!3 $;:S2
(1%!S[/%^9
$).S 3)/72'(
|a b| = |b a|
3
2 8 A
B
A B
7 8

75. 82
1
2 1 B
/^2(_$42)9['#3
2;2^B#%;
E
^'112;]B
^9;
^)C^C%; 2
#^
./^2 B , D = (0 ± 2 , 6) = (2 , 6) ' (−2 , 6)
1
2 2-4 E b #2
/7 );)! ERS;$4
;)!%!S !
$21
x !]B
^9;
= (h , k) = (0 , 6) ! c c 4 , a b c b2 16
E
2
E
2
E
2
E H E = = = + = + 7 ):2
1
(y k)
b
(x h)
a
2
2
2
2
=
−
+
−
1
( 6)
y
16 2
2
2
2
=
−
+
+ E E b
b
x
18
;)!D#
/ )
(3 , /C(
5
1
b
6)
18
(
5
9
b 16
2
E
2
2
E
=
−
+
+
---------------------(2)
R;3);
!5
2;rF-^^
7 ) E b (
# 3#
2; !( -).'
^)

76. Q
1
2 3 $1
Q#^F/C$)F1R5
C)' 3)/$^#
3
bE = ):2( # (
[%^ 2b ) %
;

77. (2)
2
1
12
(
)
5
9
4
16
9
4
9
2
=
−
+
+
36
+ = $4
$%F/ .1
2 3 D.
144
(
9
) 1
25
4
13
3
2;))B
3#2 %[^
3#
%
b 3 E =
#^;

78. (1) /C$4
/).;
S
:2 ^
[% 2b 6 E = =
#^
^
$2 2a 2( 9 16 ) 10 E = = + =
#^
;
5
^
$2^#
[% = 10 − 6 = 4
#^
/^2;)!'/^2(_$42)9 (/%!S(
) = AD ):2 BE
= AC + CD
E h = a + a
= 5 + 2 = 7
9. 32'1
2 4
10. 32'1
2 2 .8!% AB = -2 i
v
+ 4 k
v
- 6 j
v
v
- 4 j
AC = -5 i
v
+ 2 k
v
AB × AC =
v v v
i j k
− −
− −
2 6 4
5 4 2
v
- (-4 + 20) j
= (-12 16) i
v
+ (8 30) k
v
v
- 16 j
= 4 i
v
- 22 k
v

79. 83
| AB × AC | = 16 + 256 + 484 = 756 = 6 21
-.%. 0 ABC = 3 21
v
= 3 i v
11. 32'1
2 1 .8!%
u
4 j v
v
= i v
C v
+ j v
v
+ v
1. ( #/).; Q 2 u
v
= 2(3 i v
4 j v
) + ( i v
+ j v
) = 7 i v
7 j v
v
u
+ 2 v
v
= (3 i v
4 j v
) + 2( i v
+ j v
) = 5 i v
2 j v
v
+ v
2 u
v
v
+ 2 v
' u
v
% 1
;
!5
cos 1 =
v v v v
− −
(7 i 7 j ) (5 i 2 j )
v v v v
− −
| 7 i 7 j || 5 i 2 j |
=
× + −
7 5 ( 7)(2)
+ +
2 2 2 2 7 7 5 2
=
49
7 2 29
=
7
58
3# cos 30° =
3
2
. cos 1 2 cos 30°
. 1 2 30°
v
+ v
S
:2 $$32)9 2 u
v
% ' 30° ' u
v
+ 2 v
v
/R;( #/).;
;
5
1
2 1 $4
32'
v
2 v
2. /).; u
v
= (3 i v
4 j v
) 2( i v
j v
) = i v
6 j v
v
2 v
( u
v
)(6 i v
j v
) = ( i v
6 j v
)(6 i v
j v
)
= 6 × 1 + 1(-6) = 0
7;#$$32)9 u
v
2 v
v
35;b' 6 i v + j v
/).;
v
+ v
3. /).; u
v
= 3 i v
+ 4 j v
+ i v
+ j v
= 4 i v
3 j v
v
+ v
$$32)9
RS;
#^%!S !%.]3);1
' u
v
:2
v v
+
(u v )
v v
+
| u v |
.
v v
+
(u v )
v v
+
| u v |
=
v v
−
(4 i 3 j )
v v
−
| 4 i 3 j |
=
v v
−
(4 i 3 j )
+
2 2 4 3
=
−4
5
i v
3
+
5
j v
/).;
v
v
4. /).; u
v
= (3 i v
4 j v
) ( i v
+ j v
) = 2 i v
5 j v
v
v
| u
v
| = | 2 i v
+ 5 j v
| = 2 2 2 + 5 = 29
v
+ v
| u
v
| = | 4 i v
3 j v
| = 2 2 4 + 3 = 25
v
v
. | u
v
| | u
v
+ v
v
|

80. 84
12. 32'1
2 4 .8!% (fog) (
1
) = f(g(
3
1
))
3
= f(arcsin
2
+ 2 arcsin
3
1
)
3
= sin(arcsin
2
+ 2 arcsin
3
1
)
3

81. arcsin
2
3
= A
. sin A =
2
3

82. arcsin
1
3
= B
. sin B =
1
3
. sin(arcsin
2
+ 2 arcsin
3
1
) = sin(A + 2B)
3
= sin A cos 2B + cos A sin 2B
= sin A(1 2 sin2 B) + cos A × 2 sin B cos B
2
= (
)(1 2(
3
1
)2) + 1 sin A − 2 2 sin B × 1 sin B − 2
3
= (
2
)(1 -
3
2
) +
9
2
−- 2
×
1 ()
3
*
+,
2
×
3
2
1
−-
1 ()
3
*
+,
= (
2
)(
3
7
) +
9
4
1− ×
9
2
×
3
1
9
1−
= (
2
)(
3
7
) +
9
5
×
3
2
×
3
8
3
=
14
+
27
2 40
27
=
14+ 4 10
27
=
2
(7 + 2 10 )
27
13. 32'1
2 1 .8!% /x12; sine

83. a
sinA
b
=
sin B
c
=
sinC
= k
. a = k sin A , b = k sin B , c = k sinC
sinA =
a
, sin B =
k
b
, sinC =
k
c
k
/[/%^9 (sinA + sin B + sinC)(sinA +sin B −sinC) = 3sinAsin B

84. 85
a
( + + + − c
=
)
k
b
k
a
)(
k
k
c
b
k
k
b
k
a
3
k
1
(a + b + c )(a + b − c )
= (3ab)
2 k
1
2
k
. (a + b + c )(a + b − c ) = 3ab
. C = 60°
Cos C =
1
2
14. 32'1
2 3 1
2 1($):S2;
!522 4yC 1 1
2 32
C)')
)B4 / ! 4 /
/ A $4
/3 2x + 3y = 100 ---------(1)
y x = 5 ----------(2)
ERS;
7 )(
x = 21 , y = 26
. A (21, 26)
/ B $4
/3 x + y = 10 zzz.. (1) / C x + y = 10 3# y = 2
y x = 5 zzz.. (2) . C(8, 2)
( 5 {.$2;
.
R;
C / D 2x + 3y = 120 3 # y = 2
, 15
2
ERS; B = )
2
. D = (57, 2)
4 / %
; P
P = 3x + y
(21, 26) P = 89
( 5 , 15
)
P = 15
min
2
2
(8, 2) P = 26
(57, 2) P = 173
max
A
D
B
C
y = 2
(10,0) (60,0)
(0,10)
(0,40)
x + y = 10
2x + 3y = 120
x − y = 5
a = max = 173
b = min = 15
a b = 173 15 = 158
32'1
2 3

85. 86
15. 32'1
2 3
.
1
2
!5

86. Q
%.'.$2 )9 $):S2;/
$Q.;E
2
)'
Z 1 = -1 - 3 i
*
3
1
-
− − i
= 2 ()
+,
2
2
= 2 (cos 240°+ i sin 240°)
Z1
6
= 2
6
(cos 1440°+ i sin 1440°)
= 64 (cos 0°+ i sin 0°)
= 64
(z 2 )3 =
1
+
2
3i
2
= cos 60° + i sin 60°
(z3 )9 = cos (9 x 60°) + i sin (9 x 60°)
2
z2
27 = cos 540° + i sin 540°
z2
27 = cos (360° x 180°) + i sin (360° x 180°)
z27 = -1
2
Z1
6
+ (Z 2) 27 = 64 -1 = 63 32'
16. 32'1
2 1 4iz −1 + 9z = 6 2
4i
+ 9z
= 6 2
z
4i + 9z z
z
= 6 2
4i + 9z z
z
= 6 2
2 4i + 9 z = 6 2 z
4 2 + (9 z 2 )2 = 6 2 z
1
z −1 = 2
4 16 + 81 z = 2 72 z ^; 2 72;1
;
81 z 72 z 16 4 2 − + = 0
2 2 (9 z − 4) = 0
9 z 4 2 − = 0
2 z = 0
z =
2
3
*
-
4
17. 32'1
2 4
. $:2$1 4 3/ 8 3 %(
( ()
+ +,
8
= 70 .8!
$ 3)%!SDB012;$1 4 3 B0
2^# 0
C$4
/
!S :2 ^.'(
$1!S%5; 4 3 ERS; ! 1 .8!
1
.
#/C$4
=
70
(;#^$
2C)
, z 0
z
z z = z
2 2 z = ((

87. )-*.) +((

88. )*+, ')

89. 87
18. 32'1
2 3 (
32'1
2 4
C)
'2(
#2
#[/%^9 ^.'12;$
!S^ 22%4y$^!
. P ((
7!$!^
) = P((
7!1 2) + P((
7!; 2) + P((
7!
5$;.
2)
=
*
*
( ()
-
+
-
+ +,
+ +,
( ()
*
*
( ()
-
+
-
+ +,
+ +,
( ()
*
*
( ()
-
-
+ +,
+ +,
( ()
5
2
12
2
4
2
12
2
3
2
12
2
=
10
66
3
6
+ +
66
66
=
19
66
19. 32'1
2 1
20. 32'1
2 3
lim ( )
3
f x
x
+
lim ( )
3
f ax
x
−
f(3)
*
( ()
-
+ +,
−
3x 9
−
lim
x 3
+ 3x 3
%
(
0
. DIFF
0
3 x = 3
3 6
2 3x
= lim (ax 2 6a)
x 3
−
−
= 9a − 6a
= 3a
= a(3)2 − 69
= 9a − 6a
= 3a
OP;9Q
3#2$
:S2; 3 )2' 32'3
2;$%#
€
f(x) 6 = 3a = 3a
a = 2
%
# f(x) = 2x 2 −12 , x 3
f$(x) = 4x , x 3
f$(a) = f$(2) = 8
21. 32'1
2 1 ^$ 3 1
272' Calculus 4P//'
/C
.^ 22D7 'OP;9Q
f o g, g o f 4)C/$^
C
. / f(x) = 3x + 1
f o g(x) = x 2 + 1
/C(
g(x) =
(x 2 + 1)2 − 1
3
=
1
3
1 2 2 + −
(x 1)
3
3 2
+ 2 +
+
f$(x) + g$(x) = (x 1)(2x)
3
2 3x 1
f$(1) + g$(1) =
3
8
+ =
3
4
41
12

90. 88
22. 32'1
2 2
.
y = a 2 x 2 + 4ax + 10
1
0
-5:
% !S A = 3 + +
(a 2 x 2 4ax 10)dx
x
= 1
0
2
3
2 2ax 10x)
3
(a + +
a 2
+ +
= 2a 10
3
a 2
+ +
. 7 ) A = 2a 10
3
2a
+ = 0
#
2^7 A$ = 2
3
2a = 6
a = 3
. -:5
%!S
2^7 ./ a = 3
(3)2
ERS;:2 A = 2(3) 10
3
+ + = 7
23. 32'1
2 2
4)'3);

91. $^#2
C
Q#; f !S7C7
46 55
56 65
66 75
76 85
86 95
96 105
4
x
y
10
7
3
4
4 + x
4 + x + y
14 + x + y
21 + x + y
24 + x + y
24 + x + y
1
Q1 3);'3
#;% !S (n)
4
1
= (24 x y)
4
+ +
1
Med 3);'3
#;%!S (n)
2
1
= (24 x y)
2
+ +
Q1 = 65.5 ';$2.5
';$2.m 3);'12''
12;Q5
56 65
1
. !S7C7 4 + x = (24 x y)
4
+ + zzzz..()
16 + 4x = 24 + x + y
3x y = 8 zzzzzzzz (1)
Med = 75.5 ';$2.m3);12''
Q5
66 75 (
)

92. 89
1
. !S7C7 4 + x + y = (24 x y)
2
+ +
8 + 2x + 2y = 24 + x + y
x + y = 16 zzzzzzzz(2)
(1) C (2) (
x = 6, y = 10 . N = 40 /
3
3#2(4 Q3 ERS;3);'3
;# (40) 30
4
3
(N)
4
= =
ERS;2^B#

93. Q5
%!S 4 (3
#;7%
^12;Q5
2!
)
. Q3 3);12''
:2 Q3 = 85.5
[/%^9 7#
$'!S^;$'
2(%9
. Q.D. =
Q Q3 1 −
2
=
35.5 − 65.5
2
= 10
24. 32'1
2 3 .8!% X = 70 , Mo = k
.^ = 40
Med = 8^k
= 60
N
1. ( #/).; Q % −
=
i 1
N
X % −
=
i 1
X a $ :S2 a $4
/
/).;

94. r
100
8^k
= 60 . % −
=
i 1
100
Xi 60 % −
=
i 1
Xi 70
N
2. ( #/).; Q %( − )
=
i 1
N
2 X X %( − )
=
i 1
2 X a $ 2:S a $4
/
/).;

95. r
100
X = 70 . %( − )
=
i 1
100
Xi 70 2
%( − )
=
i 1
2
Xi 40
3. /).; Mo Med X
. )//;$4
$7
[
;$'
1
4. ( #/).; $-)C# # 8^k
= 60 C
7;# !
(
C
# ):2$%#' 60 C
! 50
( #

96. Q# 60
Mo
40
Med
40
x
70
25. 32'1
2 3

97. Q
-:5
%!S

98. 3
[
;43.Q#^ERS;-:5
%!S

99. 3
[
;43.F:2 $42)9$EF
39)^(
S
$2;[^
m.;
i 36 60 x
z
2
−
36 60 = −
12
0
3
#; x Ck
.^ 2^B#%!S$!^

100. Q#(
=
1^ S.D. = 7
63 x
i x
z
x 70
1
−
63 70 = −
7
0

101. 90
;
) $42)9$EF
39)^(
12;# m.;#2
P(36 x 60) i = P(−2 z 0)
= P(0 z 2) ($4j3); z -.%.) = 0.477
ERS;[/%^9
P(36 x 60) i = P(−2 z 0)
= P(0 z 2) ($4j3); z -.%.) = 0.477
ERS;[/%^9
P(36 x 60) i 12; m;. P(36 x x) i = 12;Q^ E;RS%)'
# !#$%#' 0.477 $-!^;3##3
#; x
#/C
2^#B3);(
2^#B3);(
2^#BE
^ ):2112; x !
2;r3
2; -5:
%!S12; P(36 x x) i #2
# !#
2^# ):2 # 0.477
(
-:5
%!S
2^# 7;# x 2^B#%;1 :212; x %
2;$!^
#
5
#0.477
(
-:5
%!S
2^# 7;# x 2^B#%;1 :212; x
%
2;$!^
#
5
# 0.477 7;# x 2^B#%;E
^ :212; x
P(63 x x) P( 1 z 0) i = −
= P(0 z1) =0.341
7;# x 3
2;2^B#%;1 :212; x x (
^
P(63 x x) i Q^ P(36 x 60) i = m.;
P(63 x x) P(x x x) 0.477 i i + =
0.341 P(0 z z ) 0.477 i + =
P(0 z 0.35) =0.477 −0.341=0.136
(4$4j3); z
.3
#; x
0 z (
0.35 ;
5
z i −
=
x x
SD
x 70
7
0.35
−
=
x =70 + 2.45=72.45
2
1. 32'1
2 3. 1800
2. 32'1
2 4. 3
3. 32'1
2 1. 2.09
4. 32'1
2 2. 16
5. 32'1
2 3. 1
6. 32'1
2 4. 17
7. 32'1
2 3. 4
8. 32'1
2 1. 25
9. 32'1
2 3. 0.2
10. 32'1
2 2. 2.33