1

PAT 1 (.. 57) 12. 5 12

60 = = = (2 ) 1. 64 2. 109 3. 114 4. 124

PAT 1 (.. 57) 14. , + + = 0 , | + | = 5 , | + | = 3 || = 10 () 0 tan = 3 () = 12 1. () () 2. () () 3. () () 4. () ()

26. = + 2 + | | = 2 ||2 1. 5 2. 6 3. 7 4. 8

9 Apr 2015

2

PAT 1 (.. 57) 13. , () ( ) = ( ) () || = || , | | = | + | 1. () () 2. () () 3. () () 4. () ()

PAT 1 (.. 56) 15. () = + + , = + 2 + = + + + = 1 () = 2 + = + || = 3

5 = 3

60 1. () () 2. () () 3. () () 4. () ()

45. , = + 125

, = 6 + = 2 + | | = 5 , > 0

|5 + |2

3

PAT 1 (.. 55) 15. , + = 0 , = 8 = 2

arcsin 13

arcsin 23

||2 + ||2 1. 6 2. 10 3. 14 4. 18

32. A(3, 2) F L 4 3 + 14 = 0 L B(, ) > 0 AF FB

PAT 1 (.. 55) 12. A(1, 1), B(2, 5) C(2, 3) ABC L

A B CD L D AD 1. 7

25(3 4) 2. 7

25(3 4) 3. 7

25(3 + 4) 4. 7

25(3 + 4)

4

14. . | |2 < ||2 ||2 . | |2 = ||2 + ||2 1. . . 2. . . 3. . . 4. . .

PAT 1 (.. 54) 12. + + = 0

1. | | cosec35 = | | (1 + cot20cot35

) 2. | | cosec20 = | | (1 + cot35cot20

)

3. | | cosec35 = | | (1 + tan20tan35

) 4. | | cosec20 = | | (1 + tan35tan20

)

13. A, B, C P AC Q AB AQ : QB = 1 : 2 AB = 6 3 BC = 2 + 3 PQ 1. 2 2. 2 + 3. 2 4. + 2

X

Y

110 125

5

33. A(3, 0) , B(3 + 3 , 1) C(, ) C 4 AB AC 60 |AC | = 23 |AB | 2 + 2

PAT 1 (.. 54) 15. || = 1 , || = 3 60

|+||2|

1. 1319

2. 137

3. 1 4. 719

36. A(, ) , B(4, 6) C(1, 4) ABC P AB A 3

5 A B CP = + 2 +

6

PAT 1 (.. 53) 14. , , = + , = 4 3 = 2 + | |2 = ||2 + ||2 5 + 5 = 21 1. 5 2. 6 3. 10 4. 14

15. , 1. ( )2 ( )( ) 2. ( )2 = (||||)2 3. + + = 0 , || = 3 , || = 4 || = 7 = 12 4. | |2 = ||2 ||2

PAT 1 (.. 53) 16. = + 3 , || = 3 | | = 4 | + | 1. 6 2. 10 3. 13 4. 4

7

32. = 2 5 = + 2 = 11 = 8 5 + tan + sin 2

PAT 1 (.. 53) 14. = + 1

2 3 = 2 + 2 +

3 1. (3, 3

2 ) 2. ( 3

2 , 0) 3. (0, 3

2 ) 4. ( 3

2 , 3)

33. , = + 2 + 3 , = 2 + , = + + , , = 2 , ( + ) = 3 , + = + + , 2

3 +

1

2 +

1

3 + 4 + 2

8

PAT 1 (.. 52) 1 13. + . || = || . + 2 2 1. . . 2. . . 3. . . 4. . .

2 12. ABC D AC F BC AD = 1

4AC ,

BF =1

3BC DF = AB + BC

PAT 1 (.. 52) 24. 3 + + 3 5 1. 3 2. 32 3. 4 4. 42

9

25. | | |||| ( 2) + 3 = (2 + )

1. [0, 12) 2. [1

2, 1) 3. [1, 3

2) 4. [3

2, 2)

PAT 1 (.. 52) 24. ABCD M AD AM = 1

5AD

N AC AN = 16AC MN = AB + bAD +

1. 215

2. 15 3. 1

3 4. 1

25. + 2 2 + 1. 4

5 2. 0 3. 1

5 4. 3

5

10

A-NET 51

1 14. , || = 3, || = 2 || = 1 + + 4 = 0 + +

1. 52 2. 1 3. 0 4. 1

2

15. O(0, 0, 0), A(1, 5, 7), B(2, , 1) C(, 3, 2) OA B OC B OC

1. sin = 537

2. |B | |C | = 21

3. 532

4. 75 A-NET 50

1 10. = + + 2 = 2 3 , || = 3 cos = 1

3

1. 6 + 8 10 2. 6 8 + 10 3. 12 + 4 10 4. 12 4 + 10

11

11. P(8, 5), Q(15,19), R(1,7) = + (, ) QPR

1. 2 2. 2 3. 211

4. 211

A-NET 49

1 13. = + 3 = 2 + = 3 + , 1. 12 2. 8 3. 8 4. 16

2 4. = 3 + 4 = + || =10 +

12

PAT 1 (.. 57) 12. 4 PAT 1 (.. 57) 14. 1 26. 4 PAT 1 (.. 57) 13. 1 PAT 1 (.. 56) 15. 4 45. 200 PAT 1 (.. 55) 15. - 32. 3 PAT 1 (.. 55) 12. 3 14. 3 PAT 1 (.. 54) 12. 4 13. 3 33. 93 PAT 1 (.. 54) 15. 2 36. 3 PAT 1 (.. 53) 14. 2 15. 3 PAT 1 (.. 53) 16. 2 32. 2 PAT 1 (.. 53) 14. 2 33. 3 PAT 1 (.. 52) 1/13. 1 2/12. 9 PAT 1 (.. 52) 24. 4 25. 2 PAT 1 (.. 52) 24. 1 25. 1 A-NET 51 1/14. 1 1/15. 4 A-NET 50 1/10. 1 1/11. 4 A-NET 49 1/13. 4 2/4. 14