2. n(A) = a n(B) = b 3 −i
n[(A-B) (B-A)] = 7 n(A × B) = 40 n( {C C A B
n(C) ≤ 2})
x 2 − 3x < 0
−2 < log < −1
x [P(x) Q(x)]
x [Q(x) P(x)]
x[ P(x) Q(x)]
x [P(x) Q(x)]
π 4 4
1+ cos + arccos − arctan 2545 2546
2 5 3
100 105
125 130
1 0 2 115 125
A= 0 3 0
4 0 a
a>0 det(adj A) = 225
x+1
(gof)(x) = 2 [ f(x)] + 2f(x) − 4
2
g -1 (x)=
3
{1, 2,3, 4,5, 6, 7}
gof
f(100) + g(100) =300
y=f(x) y 2 -2y-8x-7=0
2
x 2 - 2x + 5 ∫
0
f(x)d(x) = 4
y=f(x)
7 7 x 2 +y 2 -2x-2y-14=0 x 2 +y 2 -2x-2y-2=0
−
4 4
9 9 x 2 +y 2 +2x+2y-14=0 x 2 +y 2 +2x+2y-2=0
−
4 4

3. 1 1
-
3 3
1. (p q) (r s)
2. r s
p q
p q p q
2
log 4 log 3 log 2 (x +2x) ≤ 0
5
6 3
z = i9 +i10 +...+i126 i 2 = -1
4
2z -1
1+ i −1 − i
1− i −1 + i
1
2
3
2
z = -2 + 2 3 i i 2 = −1 z17 y=8-0.5x
x+3
log
x-1
≥1 {
T = log 3 x x S }
x(cot 2x - cotx = 0)
f (x)=2x+1
1
x= -1
2

4. u v
u v u +v
u − 2v u + 2v 2u - v
2 1 u = 2
f(x) = 4 − x g(x) =
9 - x2 −
1
R gof 10
10
1 1 −1 10
2 4
28.  X  23x-1 6 x 255x-1 = 75x
1 1
8 15
 x  
1
1. 1 2. 2
3. 1 4. 2
4
5!5! y = mx x 2 + y 2 − 10 x + 16 = 0
3 1
−
4 2
5!5! 3 1
4
x1
x1 + 2x 2 + x 3 = 0
3x1 + x 2 - 2x 3 = 5
Z 0.97 1.58
2x1 - 3x 2 - 3x 3 = 9
A 0.334 0.443
x1 + y 2x1
A=
3 y
x -2 x4
10
1
x4 −
a 2x 2
b
2 2
3 5
3 3 cosec x sec x
sin x = tan x = - det 2 2 2
5 4 1 cos x −
7 7
1 1
−
3 3
2 4
− −
3 3

5. P(x)
x3
{
A = (x,y) 4x 2 + 9y 2 - 16x + 54y + 61 = 0 } x-2 P(x) (1 + 3i )
P(x) P(x)
1 3
4 4
7 11
4 4
3+3 27
log 3
( 3 +5
3
3 +6 )
2
x -9 1
34.     1
4
3 3
f(x) = − log 3 1 − log 3 3 2 + 2
x-3 4 4
3 +2
4
1. lim f(x) = 0
x -3
lim f(x)
x
  
3
1
− log 3 23
1
− 3log 3
23
4 4 4
2. lim f(x) = 0 lim f(x) = 6
x -3 x 3
a1, a 2, a 3, ...
3. lim f(x) = 0
x -3
lim f(x) = -6
x 3
4. lim f(x)    lim f(x) = 0 20
x −3 x 3
∑ (a i + 2i )
2 cos 2θ i=1
A = sin θ tan θ (1-sinθ) =
cosθ
-2 4 v v v v v v
3 3 u = i + 3j, v = 2i + j
v v v v
-11 2 (u + v) (u − v)
3 3 1 1
4 12
arccos + arcsin + X = π
3 5
5 13 2 1 2
tan X 5 5
2
3
−
6 f(x) = ( x + 1) g(x) = x + 1
63 63
16 16 Dfog R gof
−
63 63 [1, ∞ ) [0,1)
[ 2, ∞ ) [0, 4 )
20% 20% 30% 30%
92 84 63 OC OD
f(x) = x 2 - c c≥4
y = f(x) x = -2 x=1

6. X s2
X − 0.51s
p q
z=0 z = 0.51 (p q) r
p ( r q)
(q r) p
x2 x-4
-x x-1
x {0,1, 2,3, 4}
A = {a, b, c, d, e, f } B = {a, b}
1 2
5 5 B X A
4 3
5 7
P y = x2 L
x-y-2=0 ( 3,1) ( 5,1)
P L ( 0,1)
2 7 2 ( −2,1)
8 8
11 2 21 2
8 8 x 2 + 2y 2 + 2x - 2y - 16 = 0
x 2 + y 2 + 4x - 2y = 0
x 2 + y 2 + 4x - 2y - 15 = 0
θ = ABO x 2 + 2y 2 + 4x - 2y - 4 = 0
sec 2θ 16x 2 - 64x - 9y 2 - 80 = 0
1 7
9 13
9 10
25 9 16x 2 − 64x + 25 y 2 − 336 = 0
uuuv v v
OA = 3i + 4 j 16x 2 + 64x + 25 y 2 − 336 = 0
uuu
v v v
OB = 5i − 2 j OB 16x 2 − 64x + 25 y 2 − 400 = 0
uuuv
OD 16x 2 − 64x + 25 y 2 + 400 = 0
3 v v 4 v v
29
(
2i − 2 j ) 29
( )
3i − 2 j
A = {1, 2, 3, 4, 5, 6}
v v v v
7
(
5i − 2 j ) 7
(
3i − 2 j ) B= {{1} , {1,2} , {1,2,3} , {1,2,3,4}}
29 29
F = {f : B A f(x) x x B}
a<b