X – Maths 1

LIST OF MEMBERS WHO PREPAREDQUESTION BANK FOR MATHEMATICS FOR CLASS X

TEAM MEMBERS

Sl. No. Name Designation

1. S.B. Tripathis SBV Jheel Khuranja(Vice-Principal) Delhi-110031

2. Ms. Ritu Tiwari R.P.V.V.,TGT (Maths) Suraj Mal Vihar,

Delhi.

3. Mrs. Amita Taneja R.P.V.V.TGT (Maths) Rohini

New Delhi.

2 X – Maths

S.A. - I

1. 3

2. 9

3. 16

4. 26

5. 39

6. 48

59

68

X – Maths 3

1

1. ‘a’ ‘b’

q r

a = bq + r, 0 r < b.

2. a b, (a > b)

1 q r

a = bq + r . 0 r < b.

2 r = 0 (a, b) = r

3 r 0 b r

(a, b)

3.

4. x , 0p

x qq

q

2m5n m n x

4 X – Maths

5.

px

q q

2m5n m, n x

6. p p

, 0p

qq

1. 5 × 11 × 13 + 7

(a) (b)

(c) (d)

2. 6

(a) 4n (b) 2n

(c) 6n (d) 8n

n

3. a b a b a b a b

(a) (b)

(c) 2

a b (d) 0

4. p 3 p

(a) (b)

(c) (d)

X – Maths 5

5.

(a) (b)

(c) (d)

6. a = bq + r, a, b

(a) 0 < r b (b) 0 r < b

(c) 0 < r < b (d) 0 r b

7.

(a) 3.131131113... (b) 4.46363636...

(c) 2.35 (d) b c

8.

421

7 2 .5

(a) 8 (b) 4

(c) 5 (d)

9.

(a) (b)

(c) (d) a c

10.

(a) (b)

(c) (d)

11. 0 1

(a) 0.11011011... (b) 0.90990999...

(c) 1.010110111... (d) 0.3030303...

6 X – Maths

12. pn = (a × 5)n pn a n

(a) (b)

(c) (d)

13.

(a) 2m3n, m, n > 0 (b) 3m5n, m, n > 0

(c) 5n7m, m, n > 0 (d) 2m5n, m, n > 0

14. 0.3 0.4

15. 73 3 711

16. (135, 225) = 45 (135, 225)

17. 18 50.

18.

19. a = 4q + r a q r

20. 5 3

21. 96

22. 3 5

X – Maths 7

23. 16 28

24. 120

25.

12 5

26. 2

5 37

27. 2 7

28. 56 112

29. 17 + 11 × 13 × 17 × 19

30. 5 × 6 × 2 × 3 + 3

31. 14n n

32. 210 55 210 × 5 + 55 y y

33. 56, 96 324

34. 3m 3m + 1

m

35. q 6q + 1,

6q + 5

36. q

5q, 5q + 1, 5q + 4

8 X – Maths

37. 6

38. n, n + 2, n + 4 3

39. 398 436

7

11

1. b 2. c

3. a 4. c5. c 6. b7. a 8. b9. b 10. a

11. b 12. b

13. d 14.79

15. 3 16. 675

17. 30, 18. 2

19. 0 r < 4 20. 5 3 , 2

21. = 1, = 9 23. 4

24. 2 × 2 × 2 × 3 × 5

29. HCF = 28, LCM = 336 30.

31.

32. HCF (210, 55) = 55 = 210 × 5 + 55 y y = –19

33. 4 34. a = 3q + r35. a = 6q + r 38. n = 3q + r39. 17

X – Maths 9

2

1. 1, 2 3

2. ax2 + bx + c a, b c

a 0

3. x y = p(x), x –

x = a p(x) p(a) = 0

4.

5. ax2 + bx + c a 0)

ba

.ca

6. p(x) g(x) q(x)

r(x)

p(x) = g(x).q(x) + r(x), g(x) 0

r(x) = 0 r(x) < g(x)

10 X – Maths

1. f(x) x

(a) f(x) > 0 (b) f(x) = 0

(c) f(x) < 0 (d)

2. f(x) y = f(x) ..........

(a) x- (b) y-

(c) (d) (x, y)

3. f(x) f(x)

(a) (x – ) (b) x – 2

(c) (x + ) (d) (2x – )

4. f(x) (y – a) f(x)

(a) y (b) a

(c) 2a (d) 2y

5.

(a) (b)

(c) (d)

6. x = f(y), y-

(a) (b)

(c) (d)

X – Maths 11

7. x2 + 1

(a) (b)

(c)

(d)

8. f(x) = x2 + x + 1 1 1

................

1 1................

(a) 1 (b) –1

(c) 0 (d)

9. g(x) = (x2 + 4)x2 + 13x + 4k

k =

(a) 2 (b) –2

(c) 1 (d) –1

10. 3x2 + ax – 14 2x – b 2 a – 2b

(a) –2 (b) 7

(c) –8 (d) –7

11. ax2 + bx + c

(a) a = c (b) a = b

(c) b = c (d) a = – c

12. f(x) = (x – 5) (x2 – x – 6)

(a) –2, +3, 5 (b) –2, –3, –5

(c) 2, –3, –5 (d) 2, 3, 5

12 X – Maths

13. y = ax2 + bx + c x-

(a) b2 –4ac > 0 (b) b2 – 4ac < 0

(c) b2 –4ac = 0 (d)

14. 2x2 + 7x – 3

15. p(x) = x2 – a (x + 1) – f (x + 1) ( + 1) = 0

f

16. x2 – (k + 6) x + 2 (2k – 1) k

1

.2

17. (x + a), 2x2 + 2ax + 5x + 10 a

18. 5 3 2 5 3 2

19.15 – 2

20. 23 8 4 3x x

21. (x + k), x2 – 2x – 15 x3 + a k a

22. 2 54

23. kx2 + 3k + 2x k

X – Maths 13

24. 4x2 – 9 – 8kx k

25. 6x2 – 3 – 7x

26. (a2 + a) x2 + 13x + 6a

a

27. (2x2 + px) – 15 (–5) p(x2 + x) + k

k

28. k 3x2 + 2kx + x – 5

29. f(x) = 2x4 – 5x3 + x2 + 3x – 2 g(x) q(x) = 2x2 – 5x

+ 3 r(x) = – 2x + 1 g(x)

30. (x–2), x3 – 3x2 – 4x + 12

31. , x2 – 5x + k – = 1 k

32. 2x2 + 5x + k k

( + )2 – = 24.

33. x4 – x3 –7x2 + x + 6 3

1

34. 4x4 – 20x3 + 23x2 + 5x – 6 2 3

14 X – Maths

35. 2 3 2 – 3 x4 – 4x3 – 8x2 + 36x – 9

36. 8x4 + 14x3 – 4x2 + 7x – 8 4x2 + 3x – 2x

37. 4x4 + 2x3 – 2x2 + x – 1 p(x) (x2 + 2x – 3)

p(x)

38. a b x4 + x3 + 8x2 + ax + b (x2 + 1)

39. 6x4 + 8x3 + 17x2 + 21x + 7 3x2 + 1 + 4x

r(x) = ax + b a b

40. 2x4 – 2x3 – 7x2 + 3x + 6

32

x

41. x4 – 3x3 – x2 + 9x – 6 – 3 3

42. (x3 – 3x + 1) x5 – 4x3 + x2 + 3x + 1

43. ax2 + bx + c

(i) a > 0 (ii) a < 0 ? a = 0

1. b 2. a

3. a 4. b

5. a 6. c

X – Maths 15

7. b 8. b

9. a 10. d

11. a 12. a

13. a 14.

1 1 73

15. 1 16. k = 7

17. p = 2 18. x2 – 10x + 7

19. 2 1

25

x x 20.2

2 3, 33

21. k = – 5, 3 and a = 125, 27 22. x2 – 4x – 1

23.3

2

24. 0

25. 1 3

,3 2 26. 5

27.7

7,4

p k 28. k = 1

29. g(x) = x2 – 1 30. –2, 3

31. k = 6 32. k = 2

33. –2, –1 34. 1 1

,2 2

35. ± 3 36. 14x – 10

37. 61x – 65

38. 0 1 7 0 1 and 7 r x a x f a f

39. r (x) = x + 2 = ax + b a = 1 and b = 2

40.3

2, 1,2

41. 3, 1, 2 42. (x – 1), (x + 1)

43. (i) (ii)

16 X – Maths

3

1.

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

a1, a2, b1, b2, c1 c2

a12 + b1

2 0, a22 + b2

2 0.

2.

3. a1x + b1y + c1 = 0 a2x + b2y + c2 = 0

1 1

2 2

a ba b

X – Maths 17

1 1 1

2 2 2

a b ca b c

1 1 1

2 2 2

a b ca b c

1.

(a) (b)

(c) (d)

2. 1 1 1

2 2 2

a b ca b c

(a) (b)

(c) (d)

3.

(a) (b)

(c) (d)

4.

(a) (b)

(c) (d)

5.

18 X – Maths

(a) (b)

(c) (d)

6. x = y x + y = 0

(a) (b)

(c) (d)

7. ax + by = c y-

(a)

0,cb

(b)

0,bc

(c)

, 0cb

(d)

0,

cb

8. 2x – 8y = 12 x 2 y

(a) –1 (b) +1

(c) 0 (d) 2

9.

(a) (b)

(c) (d) a c

10. x = a y = b

(a) (b)

(c) (a, b)

(d) (b, a)

11. ABC C = 3B, C = 2 (A + B) A, B, C = __

(a) 30°, 60°, 90° (b) 20°, 40°, 120°

(c) 45°, 45°, 90° (d) 110°, 40°, 50°

X – Maths 19

12. 2x + 3y = 4 x y

(a)

4 2

3x

y (b)

4 3

2x

y

(c)

4 32

yx (d)

4 23

xy

13. x = 2 x = 5

(a) (b)

(c) (d)

14. 4

12 3x x-

(a) (0, 3) (b) (3, 0)

(c) (2, 0) (d) (0, 2)

15. x – 2 = 0

(a) x- 2

(b) y- 2

(c) x- y- 2

(d) y- x- 2

16. ax + by = c lx + my = n

(a) am lb (b) am = lb

(c) ab = lm (d) ab lm

20 X – Maths

17.

70

95

18. 9000

20 160

19. 2x + 3y – 4 = 0

20. a (3, a) 2x – 3y = 5

21. 25 7

22. (1, 4) (0, 6)

(3, 4) (1, 0)

23.

x – y = 2 x + y = 2 p = 2x + 3

24. 3x + 5y = 15,

x – y = 5

25. p

(p + 2) x – (2p + 1) y = 3 (2p – 1)

2x – 3y = 7

26. k

(3 K + 1) x + 3y – 2 = 0

(K2 + 1) x + (k–2)y – 5 = 0

X – Maths 21

27. x + 3y = 4,

(i)

(ii)

(iii)

28. x – y = 4 x + y = 10 p y = 3 x –p.

29. k

Kx + 3y = K – 3

12x + Ky = K

30.

2x + 3y = 7

2x + ( + )y = 28.

31. x y

1 11 18; 9

2 3 3 2y yx x

32. x y

2x + 3y = 17

2x + 2 – 3y+1 = 5

33. x y

139x + 56y = 641

56x + 139y = 724

22 X – Maths

34. x y

5 12

x y x y

15 52, 0, 0.x y x y

x y x y

35.

3x – 5y = 19, 3y – 7x + 1 = 0

(4, 9)

36. 3x + 2y – 4 = 0 2x – y – 2 = 0

y-

37. x y

1 12 122 2 3 7 3 2x y x y

7 42

2 3 3 2x y x y2x + 3y 0 and 3x – 2y 0

38. p q

2, 6, 0, 0.

p q p qp q

pq pq

39. x y

2 3 173 2 3 2 5x y x y

5 12

3 2 3 2x y x y x + y 0, x – y 0

X – Maths 23

40. x y

2 3 4 92, 1, 0, 0x y

x y x y

41. 20

5

42.

39 132

43. 8 1

13 2

44. 1

1/4 120 90

45. 35 55

12 10 30 44

50 77

46. 10 A B

20 B A

A B

47. 21

20

1

24 X – Maths

48. 100

370 433 300 398

400

1. d 2. c

3. c 4. b

5. a 6. c

7. a 8. a

9. b 10. c

11. b 12. d

13. a 14. c

15. b 16. a

17. = x = y

2 702 95x y

x y

18. = x,

201 1 4

225

y xy

x y

19. 4x + 6y – 8 = 0 20.13

21. 16, 9 22. (2, 2)

23. (2, 0) p = 7 24.

25. p 4 26. 19

1,2

k k

X – Maths 25

28. (7, 3), 18

29. k = 6 30. (4, 8)

31. (7, 13) 32. (3, 2)

33. (3, 4) 34. (3, 2)

35. (–2, – 5), 3y – 7x + 1 = 0 36.

37. (2, 1) 38.

1 1,

2 4

39. (1, 1) 40. (4, 9)

41. 15, 10 42. 27, 12

43. 41 14 (2) 44. 96

45. 3 / , 5 / 46. 100, 80

47. Rs. 101, 5 48. 448 298, 12

26 X – Maths

4

1.

2.

ABC DEF

: ABC ~ DEF

A = D, B = E C = F

ABC ~ DEF

AB BCDE EF

B = E

: ABC ~ DEF

AB AC BCDE DF EF

3.

X – Maths 27

1. ABC ~ DEF. DE = 2 AB BC = 3 EF = _______.

(a) 1.5 (b) 3

(c) 6 (d) 9

2. DEW , AB || EW AD = 4 , DE = 12 DW = 24

DB

(a) 4 (b) 8

(c) 12 (d) 16

3.

A

B Ca

bc

FEd

ef

D

O

O

cd

(a) ae (b) af

(c) bf (d) be

28 X – Maths

4. ABC AB = 6 BC = 12 6 3CA A

(a) 30° (b) 45°

(c) 60° (d) 90°

5. 16 : 25

(a) 5 : 4 (b) 3 : 2

(c) 4 : 5 (d) 5 : 7

6. ABC

B A

C

D

53°

53°16

24

36

(a) BDC (b) DBC

(c) CDB (d) CBD

7. AMB ~ CMD 2 (AMB) = (CMD) MD

(a) 2 MB (b) 2 MD

(c) 2MB

(d) 2MD

X – Maths 29

8. AE

E

DCB

A

8

6 3

4

(a) 10 (b) 9

(c) 5 5 (d) 5

9. D E ABC AB AC

DE || BC AD : DB = 3 : 1, EA = 3.3 AC =

(a) 1.1 (b) 4.4

(c) 4 (d) 5.5

10. ABC BDE D BC

BDE BDE

(a) 2 : 1 (b) 1 : 2

(c) 4 : 1 (d) 1 : 4

11. ABC DE || BC x A

ED

B C

x – 5

x – 3x

x – 1

30 X – Maths

(a) 1 (b) –1

(c) 3 (d) –3

12. ABC B = 90° BE AC

...............BEC

ABC

(a) 12

(b) 21

(c) 41

(d) 14

13. 12

(a) 12 (b) 6 2

(c) 6 (d) 6 3

14. A B

A

B

1

1

1

2

2

2

(a) 3 5 (b) 5 3

(c) 5 (d) 5 2

15. 10

(a) 5 2 (b) 2 5

(c) 10 2 1 (d) 10 2 1

X – Maths 31

16. ACB ~ APQ, BC = 8 PQ = 4 BA = 6.5

AP = 2.8 CA AQ

B

P

Q

C

A

17. AE DE || BC.

3

4 2

A

ED

x

CB

18.

15 10

12

A

QP

CB

18

47°

47°

32 X – Maths

19. ABC, PQR AC = AB = 4

RQ = 10 BC = 6 PR PQR

20. ABC ~ PQR : x

A

54

CB6

R

7.26

QP x

21. PQR DE || QR 1

.4

DE QR

ar PQRar PDE

P

ED

RQ

22. ABC PQR B = Q 12

AB BCPQ QR

PRQR

23. , 10a a 3a

24. DE || BC. DE

X – Maths 33

10

2

A

ED

CB3

25. SR QPR = PSR. PR = 6

QR = 9

6

9

P

RQ S

26. PQR ,RS PQ QRS = P, PS = 5 SR = 8 PQ

27. ABC PBC BC

AB = BP.

28. ABCD B = 90°, AD2 = AB2 + BC2 + CD2. ACD =

90°.

34 X – Maths

BA

C

D

29. DE || BC, DE = 3 BC = 9 (ADE) = 30 2

BCED) A

ED

CB9

3

30. 8

17 10

31. ABC B 3BCAB

|ABAC

32. PRO PR 6

8 Q P R PQ = 24

RQ = 26 PQR

33. ABC AB = AC. P BC

PM AB PN AC

MP = NP

X – Maths 35

A

B CP

NM

34. SQ PQRS PQ RS

E F EF, SQ G

SG × QE = QG × SF.

35. a b

aba b

D

O

C A

B

L

a b

36.

37.

38.

39.

36 X – Maths

40.

41. ABCD

42. A

50

60 5

AB

C

43.

44. AD BC ,BD DADA DC ABC

A

B CD

X – Maths 37

45. DE || BC AD : DB = 5 : 4

ar DEFar CFB

A

B C

D

F

E

1. c 2. b

3. a 4. d

5. c 6. d

7. a 8. c

9. b 10. c

11. d 12. d

13. d 14. a

15. c 16. AC = 5.6 AQ = 3.25

17. 1.5 18. APQ ~ ABC

19.203 20. 4.8

21. 16 : 1 22.12

23. 90° 24. 2.5

38 X – Maths

25. 4 26. 17.8

29. 240 2 30. 9 , 6

31.12 32. 90°

41. 4 : 1 42. 50 61

43. 5 10 45.2581

X – Maths 39

5

1. ABC, B = 90° ‘A’

sin A

cos A

tan A

cot A

sec A

cosec A

2

1 1sin , cosec

cosec sin

1 1cos , sec

sec cos

A B

C

40 X – Maths

1 1tan , cot

cot tan

3.

sin costan , cot

cos sin ´

4.

sin2 + cos2 = 1 sin2 = 1 – cos2 cos2 = 1 – sin2

1 + tan2 = sec2 tan2 = sec2 – 1 sec2 – tan2 = 1

1 + cot2 = cosec2 cot2 = cosec2 – 1 cosec2 – cot2 = 1

5.

A 0° 30° 45° 60° 90°

sin A 012

12

32

1

cos A 13

2

12

12 0

tan A 013 1 3

cosec A 2 223 1

sec A 123 2 2

cot A 3 113 0

X – Maths 41

6.

sin (90° – ) = cos

cos (90° – ) = sin

tan (90° – ) = cot

cot (90° – ) = tan

sec (90° – ) = cosec

cosec (90° – ) = sec

0° 90°

1. x = a sin y = a cos x2 + y2

(a) a (b) a2

(c) 1 (d)1a

2. cosec 70° – sec 20°

(a) 0 (b) 1

(c) 70° (d) 20°

3. 3 sec – 5 = 0 cot =

(a)53 (b)

45

(c)34 (d)

35

4. = 45° sec cot – cosec tan

(a) 0 (b) 1

(c) 2 (d) 2 2

42 X – Maths

5. sin (90° – ) cos = 1 =

(a) 90° (b) 60°

(c) 30° (d) 0°

6. (1 + cos ) (1 – cos ) cosec2

(a) 0 (b) 1

(c) cos2 (d) sin2

7. TRY cos T + cos R + cos Y =

(a) 2 (b) 2 2

(c) 1 2 (d) 1

12

8. sec + tan = x, sec =

(a) 2 1xx

(b) 2 12

xx

(c) 2 12

xx

(d) 2 1xx

9.

cot sin 2 cos

2 2

(a) cot cos2 (b) cot2

(c) cos2 (d) tan2

10. sin – cos = 0, 0 90°

(a) cos (b) 45°

(c) 90° (d) sin

X – Maths 43

11.

2

sin

1 sin= .............

(a) cot (b) sin

(c)

sincos (d) tan

12.

1 sin.............

1 sin

(a) sec2 + tan2 (b) sec – tan

(c) sec2 – tan2 (d) sec + tan

13. ABC B = 90° 2 sin A cos A

(a) 1 (b)12

(c)12 (d) 2

14.

2 2

2 2

sin 20 sin 70 sec 60

2 cos 69 cos 21 K k

(a) 1 (b) 2

(c) 3 (d) 4

15. 1

tan7

2 2

2 2cosec sec

................cosec sec

(a)34 (b)

57

(c)37 (d)

112

44 X – Maths

16. PQR Q = 90° 3

sin5

R cos P

17. A B sin A = cos B A + B

18. 4 cot = 3 tan + cot

19. cot2 30° + sec2 45°

20. 16 cot A = 12,

sin cossin cos

A AA A

21. = 30° sin + cos2 = _______

22. 2 2

1 tan3

23. 3 tan 2 3 = 0

24. cosec sec – cot tan

25. tan (3x – 15) = 1 x

26. sin 5 = cos 4 5 4

27.

tan2 60° + 4 cos2 45° + 3 (sec2 30° + cos2 90°)

28.

cos 58 cos 38 cosec 522 3

sin 32 tan 15 tan 60 tan 75

X – Maths 45

29.

cosec4 – cosec2 = cot2 + cot4 .

30. sin + sin2 = 1 cos2 + cos4

31. sin 2 = cos ( – 36°), 2 – 36°

32. sin (3x + 2y) = 1 3

cos 3 2 ,2

x y 0 (3x + 2y) 90° x

y

33. sin (A + B) = sin A cos B + cos A sin B

(a) sin 75°

(b) cos 15°

34.

cos coscos 45 .

1 tan 1 cotA A

A AA A

35.

sec 1 sec 12cosec

sec 1 sec 1

36.

sin2 5° + sin2 10° + sin2 15° + .... + sin2 85°

37.

tan sec 1 cos.

tan sec 1 1 sin

38. 2sin 3 – 15 = 3x 2 2sin 2 10 tan 5x x

39. sin 60°

46 X – Maths

40. p = tan + sec 1

pp

41.

2 2tan cot 90 sec cosec 90 sin 35 sin 55tan 10 tan 20 tan 30 tan 70 tan 80

42.

coscos

m

cossin

n (m2 + n2) cos2 = n2

43. cos 1° cos 2° cos 3° ....... cos 180° = 0

44.

2

2sin cos sin cos 2 secsin cos sin cos tan 1

45. A, B C ABC

sin cos cos sin 1.

2 2 2 2B C A B C A

1. b 2. a

3. c 4. a

5. d 6. b

7. a 8. b

9. a 10. b

11. d 12. d

13. a 14. d

15. a 16. 3

cos5

P

X – Maths 47

17. 90° 18.2512

19. 5 20. 7

21.54 22. 30°

23. 30° 24. 1

25. x = 20. 26. 10°

27. 9 28. 1

31. 42° 32. x = 20, y = 15

33. 3 1 3 1

,2 2 2 2

take A = 45°, B = 30°

36.172 38.

1312

40. 2 sec 41. 2 3

43. 60°

44. A = 67.5°, B = 37.5°, C = 75°

48 X – Maths

6

1.

(i)

.i i

i

f xX

f

(ii)

,i i

i

f dX a

f di = xi – a.

(iii)

i i ii

i

f u x aX a h u

hf

2.

1 0

1 0 22f f

l hf f f

f1 =

f0 =

f2 =

h =

X – Maths 49

3.

2n Cfl hf

n =

Cf =

f =

h =

4. = – 2

5.

x-

x-

x-

x-

50 X – Maths

1. 10

(a) 5 (b) 6

(c) 5.5 (d) 6.5

2. 4, 6, 8, 10, x, 14 16 10 ‘x’

(a) 11 (b) 12

(c) 13 (d) 9

3. x, x + 1, x + 2, x + 3, x + 4, x + 5 x + 6

(a) x (b) x + 3

(c) x + 4 (d) 3

4. 2, 3, 2, 5, 6, 9, 10, 12, 16, 18 20

(a) 9 (b) 20

(c) 10 (d) 9.5

5. 2, 3, 6, 0, 1, 4, 8, 2, 5

(a) 1 (b) 3

(c) 4 (d) 92

6. 1, 0, 2, 2, 3, 1, 4, 5, 1, 0

(a) 5 (b) 0

(c) 1 (d) 2

7. 2, 3, 5, 4, 2, 6, 3, 5, 5, 2 x 2 ‘x’

(a) 2 (b) 3

(c) 4 (d) 5

X – Maths 51

8.

10–15 15–20 20–25 25–30 30–35

4 7 12 8 2

(a) 30–35 (b) 20–25

(c) 25–30 (d) 15–20

9.

(a) (b)

(c) (d)

10.

(a) 3 = + 2

(b) 3 = + 2

(c) 3 = + 2

(d) = 3 – 2

11. 19.5 – 29.5

(a) 10 (b) 49

(c) 24.5 (d) 25

12.

(a) (b)

(c) (d)

52 X – Maths

13.

0–10 10–20 20–30 30–40 40–50 50–60 60–70

4 4 8 10 12 8 4

(a) 20–30 (b) 40–50

(c) 30–40 (d) 50–60

14. 20 17 3

(a) 20 (b) 21

(c) 22 (d) 24

15. 5 18 16

(a) 23 (b) 24

(c) 25 (d) 26

16. 5

(a) 5.5 (b) 5.6

(c) 5.7 (d) 5

17. 3, 4, 6, 8, 14

(a) 0 (b) 1

(c) 2 (d) 3

18. = 15 = 16

(a) 10 (b) 11

(c) 12 (d) 13

X – Maths 53

19. 11 50 49

52

(a) 56 (b) 55

(c) 54 (d) 53

20. 2.6 ‘x’

1 2 3 4 5

4 5 x 1 2

(a) 24 (b) 3

(c) 8 (d) 13

21. 40 160 165 125

22. 24, 25, 26, x + 2, x + 3, 30, 31, 34

27.5 ‘x’

23.

x : 10 12 14 16 18 20

f : 3 5 6 4 4 3

24. 7.5 ‘p’

3 5 7 9 11 13

6 8 15 8 4

54 X – Maths

25.

x : 12 16 20 24 28 32

f : 5 7 8 5 3 2

26. 53 P

0–20 20–40 40–60 60–80 80–100

12 15 32 P 13

27. 20-30

10 1

20 14

30 36

40 59

50 60

28. 40

X – Maths 55

29. 40

30. 62.8 50 x

y

0–20 20–40 40–60 60–80 80–100 100–120

5 x 10 y 7 8

31.

300 0

250 12

200 21

150 44

100 53

50 59

0 60

56 X – Maths

32. 28.5 60

x y

0–10 10–20 20–30 30–40 40–50 50–60

5 x 20 15 y 5

33.

0–10 10–20 20–30 30–40 40–50 50–60 60–70

6 8 10 15 5 4 2

34. 100

10 10

20 15

30 30

40 50

50 72

60 85

70 90

80 95

90 100

35.

0–10 10–20 20–30 30–40 40–50 50–60 60–70 70–80 80–90 90–100

5 6 8 10 15 9 8 7 7 5

X – Maths 57

36. 10 50

120–130 130–140 140–150 150–160 160–170 Total

2 8 12 20 8 50

37. 65 50 x y

0–20 20–40 40–60 60–80 80–100 100–120 120–140

6 8 x 12 6 y 3

38. X 35

38–40 40–42 42–44 44–46 46–48 48–50 50–52

3 2 4 5 14 4 3

39. 2008-2009

140–150 150–160 160–170 170–180 180–190 190–200

5 10 20 9 6 2 52

40.

0–5 5–10 10–15 15–20 20–25 25–30 30-35 35-40 40–45

20 24 32 28 20 16 34 10 8

58 X – Maths

1. c 2. b

3. b 4. a

5. b 6. c

7. a 8. b

9. a 10. b

11. c 12. b

13. c 14. a

15. d 16. b

17. a 18. d

19. a 20. c

21. 161 22. x = 25

23. 14.8 24. p = 3

25. 20 26. 28

29. 147.5 30. x = 8, y = 12

31. 182.50 32. x = 8, y = 7

33. = 30, = 30.67, = 33.33

34. 41.32 35. 47.3

36. = 149.8 , = 151.5 , = 154

37. x = 10, y = 5.

38. = 45.8, = 46.5, = 47.9

39. 166.3 40. 13.33

X – Maths 59

SA - 1

1 10 10

- I 2 8 16

- II 3 10 30

4 6 24

34 80

SA - I

MCQ SA (I) SA (II) LA Total

2 (2) 1 (2) 2 (6) – 5 (10)

2 (2) 2 (4) 2 (6) 2 (8) 8 (20)

1 (1) 2 (4) 2 (6) 1 (4) 6 (15)

4 (4) 1 (2) 2 (6) 2 (8) 9 (20)

1 (1) 2 (4) 2 (6) 1 (4) 6 (15)

10 (10) 8 (16) 10 (30) 6 (24) 34 (80)

60 X – Maths

X (SA - 1)

Time Allowed : 3½ hours Maximum Marks : 80

1.

2. 34 A, B, C D

A 10 1 B 8

2 C 10 3 D 6

4

3. A 1 10 1

4. 2 3

4

5.

SECTION A

1 10

1. ABC A = 90° tan B . tan C

(a) tan B (b) tan C

(c) 0 (d) 1

X – Maths 61

2. x = yq + r, x y

(a) 0 r < y (b) 0 r y

(c) 0 < r < y (d) 0 r y

3. 2, 4, 6, 8, 10, x, 14, 16 a x

(a) 10 (b) 11

(c) 12 (d) 13

4. y = ax2 + bx + c x-

(a) b2 – 4ac = 0 (b) b2 – 4ac > 0

(c) b2 – 4ac < 0 (d) b2 – 4ac 0

5. 5 tan – 4 = 0

5 sin 4 cos5 sin 4 cos

(a)53 (b)

56

(c) 0 (d)16

6.

10–20 20–30 30–40 40–50 50–60 60–70 70–80

3 5 8 10 9 4 3

(a) 70–80 (b) 40–50

(c) 50–60 (d) 30–40

7. 5 –2

(a) x2 – 5x – 2 (b) x2 + 5x – 2

(c) x2 + 2x – 5 (d) x2 + 2x + 5

62 X – Maths

8.

(a) = 2 – 3

(b) = 2 –

(c) = 3 + 2

(d) = 3 – 2

9. y- 12 3x y

(a) (0, 2) (b) (2, 0)

(c) (0, 3) (d) (3, 0)

10. x = tan 2° × tan 36° × tan 54° × tan 88° x

(a) 45° (b) 1

(c) 2 (d) 90°

SECTION B

11 18 2

11. 90 144

12.

x : 12 16 20 24 28 32

f : 5 7 8 5 3 2

13. ABC D AB DE || BC AC E

1

.2

AE AC

X – Maths 63

ABC ~ DEF, BC = 5 , EF = 4 (ABC) = 75 2

(DEF)

14. f(x) = x2 – px + q

3 31 1

15.

0–10 10–20 20–30 30–40 40–50 50–60

5 8 12 10 7 4

16.

2sin 543 2 tan 14 tan 30 tan 76 .

cos 36

17. p

y – 2x – 5 = 0

px = 2y

18.

1tan 2,

tan2

21

tantan

.

SECTION C

19 28 3

19 x – y + 1 = 0 3x + 2y – 12 = 0 x-

20.

15 2 3

64 X – Maths

5 2

21. ABC, C = 90° CA CB P Q

AQ2 + BP2 = AB2 + PQ2

22. DE || BC. x

A

ED

CB

48

x – 43x

– 1

9

D C

BA

O

3 x – 5

x – 33x – 19

ABCD x

23. x y

1 12 122 2 3 7 3 2x y x y

7 42, 2 3 0, 3 2 0

2 3 3 2

x y x y

x y x y

X – Maths 65

24. 2x4 – 3x3 – 3x2 + 6x – 2 2 2x x

25.

cot cosec 1 1 coscot cosec 1 sin

A A AA A A

2 sec2 – sec4 – 2 cosec2 + cosec4 = cot4 – tan4

26. 1

sin10

M

1/3 b

AB

C

Q

b

27. sin 30°

28. ABC AB, AC AD PQR

PQ, PR PM ABC ~

PQR

SECTION D

29 34 4

29. 5q, 5q + 1, 5q + 4

q

66 X – Maths

30.

15

396

3

2

5100

300

2

31. ABC tan (A + B – C) = 1 sec (B + C

– A) = 2 A, B C

32. 28.5 x y

0–10 10–20 20–30 30–40 40–50 50–60 Total

5 x 20 15 y 5 60

33.

100-110 110–120 120–130 130–140 140–150 150–160 160-170

4 6 20 32 33 8 2

34.

1. d 2. a

3. c 4. b

5. c 6. b

X – Maths 67

7. d 8. d

9. c 10. b

11. = 18, = 720 12. 20

13. 48 2 14. 3

33 abc b

a

16. 2

33

17. p 4

18. 2

19. (2, 3), (–1, 0), (4, 0)

22. x = 11 x = 8, x = 9

23. x = 2, y = 1

24. (2x – 1) (x – 1)

30. 672 [ 800, 900] 1800

31. A = 60°, B = 52.5°, C = 67.5°

32. x = 8, y = 7

33. 140.9

68 X – Maths

X (SA - 1)

Time Allowed : 3½ hours Maximum Marks : 80

1.

2. 34 A, B, C D

A 10 1 B 8

2 C 10 3 D 6

4

3. 1 10

4. 1 2

3 3 2 4

5.

6. 15

SECTION A

1 10

1. a = bq + r, a, b

X – Maths 69

(a) 0 < r < b (b) 0 r < b

(c) 0 < r b (d) 0 r b

2. 1

px( )

x x

y

y

1

(a) 1 (b) 2

(c) 3 (d) 4

3. 2 DE || BC x

D E

A

B C

3

2

4 2

x

(a) 3 (b) 2

(c) 4 (d)203

70 X – Maths

4. sin ( + 36°) = cos , + 36°

(a) 36° (b) 54°

(c) 27° (d) 90°

5. 3 cos = 2 sin

4 sin 3 cos2 sin 6 cos

(a)18 (b)

13

(c)12 (d)

14

6. 3 ABC, B 4

tan3

A AC = 15

BC

BA

C

3

(a) 4 (b) 3

(c) 12 (d) 9

7.2124

(a) 1 (b) 2

(c) 3 (d) 4

X – Maths 71

8. x – 2y = 5 2x – 4y = 10

(a) (b)

(c) (d)

9. 15

tan cot7

A B A + B

(a) (b) 90°

(c) < 90° (d) > 90°

10. 50

(38.5, 34)

(a) 38.5 (b) 34

(c) 50 (d) 4.5

SECTION B

11 18 2

11. 7 × 11 × 12 + 11

12. p(x) (2x – 5) (x + 2)

13. 4 ABCD x y

D C

BA

x y–

x + y

16

22

4

72 X – Maths

14. sin (A + B) = 1 cos (A – B) = 1, 0° A + B 90°, A B

7

cot8

1 sin 1 sin1 cos 1 cos

15. ABCD AB || DC

:AO COBO DO

16. 5 S = 90°, PQ = 10 QS = 6 RQ = 9

P

SR Q

5

17. 50

150-155 155-160 160-165 165-170 170-175 175-180

8 14 20 4 3 1

18.

30-40 40-50 50-60 60-70 70-80

4 3 8 11 8

X – Maths 73

SECTION C

19 28 3

19. 3q 3q + 1

q

20.2 2

5

5 3

21.

4500

5400

22. , 3x2 + 5x – 2

2 2

23.

cot cos cosec 1:

cot cos cosec 1A A AA A A

24. cos sin 2 sin cos sin 2 cos

25. AD BC AB2 + CD2 = BD2 + AC2

74 X – Maths

D

B A

C

6

26.

27.

25-30 30-35 35-40 40-45 45-50

7 14 22 16 11

47 p

0-20 20-30 40-60 60-80 80-100

8 15 20 p 5

28.

40-45 45-50 50-55 55-60 60-65 65-70

2 3 8 6 6 5

SECTION D

29 34 4

29. 2x4 + 7x3 – 19x2 – 14x + 30

2 2

X – Maths 75

30.

31. cos8 – sin8 = (cos2 – sin2) (1 – 2 sin2 cos2) :

2 2

tan 90 cot sec 90 cosec

2 cot 27 sec 63cot 26 cot 41 cot 45 cot 49 cot 64

32.

cos sinsin cos

1 tan 1 cotA A

A AA A

33. 4x – y = 4; 4x + y = 12

(a)

(b) x-

34. 100

120-130 130-140 140-150 150-160 160-170 170-180

12 16 30 20 14 8

76 X – Maths

1. b 2. a

3. d 4. c

5. b 6. c

7. c 8. a

9. b 10. a

11. 12.

13. x = 19, y = 3 4964 14. A = 45°, B = 45°

16. 17 18. 65

21. Rs. 3900, Rs. 150 40 10

22. 3x2 + 10x – 8 27. 38.3 p = 12

28. 58.8 29. 3

2, 2, 5,2

33. x = 2, y = 4

X – Maths 77

S.A. - 2

1. 79

2. 87

3. 95

4. 103

5. 111

6. 126

7. 129

8. 147

156

78 X – Maths

X – Maths 79

1

1. ax2 + bx + c = 0, a 0,

a, b , c

2. , ax2 + bx + c = 0, a 0

a2 + b + c = 0 ax2 + bx + c

3. ax2 + bx + c = 0, a 0,

4. ax2 + bx + c = 0, a 0

2 4,

2b b ac

xa

b2 – 4ac 0.

5. ax2 + bx + c = 0, a 0, ___

(a) b2 – 4ac 0.

(b) b2 – 4ac 0.

(c) b2 – 4ac 0.

6. ax2 + bx + c = 0, a

(i) a2 + 2ab + b2 = (a + b)2 (ii) a2 – 2ab + b2 = (a – b)2

80 X – Maths

7. ax2 + bx + c = 0, a 0, D = b2 – 4ac

1.

(a) ax2 + bx + c (b) ax2 + bx + c = 0

(c) ax + b (d) ax + b = 0

2.

(a) 0 (b) 1

(c) 2 (d) 3

3. x2 – (2 + m) x + (m2– 4m – 4) = 0

(a) m = 0, m = 1 (b) m = 2, m = 2

(c) m = – 2, m = – 2 (d) m = 6, m = 1

4. ax2 + bx + c = 0 a

(a) 2 4b ac (b)

2 4b ac

(c) b2 – 4ac (d) b2 + 4ac

5.

(a) 1

2xx

(b) x2 + 1 = (x + 3)2

(c) x (x + 2) (d) 1

.xx

6. 2 3 ,

(a) x2 + 5x + 6 = 0 (b) x2 + 5x – 6 = 0

(c) x2 – 5x – 6 = 0 (d) x2 – 5x + 6 = 0

X – Maths 81

7. x2 – 3x + 2 = 0

(a) 1, –2 (b) –1, 2

(c) –1, –2 (d) 1, 2

8.

(a) 1 (b) 0

(c) 0 (d) 0

9. 2x2 + kx + 1 = 0 1

– ,2

‘k’

(a) 3 (b) –3

(c) 5 (d) –5

10. 5x2 – 6x + 1 = 0

(a)65 (b)

15

(c) 56 (d)

15

11. 2x2 + 5x – 7 = 0

(a) 52

(b) 72

(c) 52

(d) 72

12. 2x2 + kx + 2 = 0 ‘k’

(a) 4 (b) –4

(c) 4 (d) 16

82 X – Maths

13. 4x2 + 3px + 9 = 0 ‘p’

(a) p – 4 p 4 (b) p – 4 p 4

(c) p – 4 p 4 (d) p – 4 p 4

14. 7 52 2

(a) 2x2 + 7x + 5 = 0 (b) 2x2 – 7x + 5 = 0

(c) 2x2 – 7x – 5 = 0 (d) 2x2 + 7x – 5 = 0

15. 2 39 2 0

4 x x

(a)18 (b)

164

(c)1

16 (d)

16. x2 + 7x + k = 0 –2 k

17. ‘k’ 2x2 + kx + 3 = 0

18. ‘p’ 3x2 + px + 3 = 0

19. 63

20. 1 1

4 , 0.4

x xx

X – Maths 83

21. 22 7 5 2 0.x x

22. 51 278

23. ‘k’ (k – 12) x2 + 2 (k – 12) x + 2 = 0,

k 12,

24. –5 2x2 + px – 15 = 0 p(x2 + x) + k =

0 p k

25.

1 13, 2, 0.

2x x

x x

26. 5

10

27. (b – c)x2 + (c – a) x + (a – b) = 0

2b = a + c.

28.

(a) 5x2 – 3x + 2 = 0

(b) 2x2 – 9x + 9 = 0

29. 15 3

.10

30.

2 3 3 32 25 5, 3,

3 2 3 2x x

x xx x

31. a2x2 + (a2 – b2) x – b2 = 0.

84 X – Maths

32. 24 3 5 2 3 0.x x

33. 2x2 + kx + 3 = 0

34.

1 3 10, 2, 4.

2 4 3x x

x xx x

35.

1 1 11, 4, 7.

4 7 30x x

x x

36. 23 2 5 5 0.x x

37.

1 1 1 1,

a b x a b x a 0, b 0, x 0, x – (a + b).

38. 35 18

39.

46

40. 9 12

3

41. 360

5

42. 6

2

43. 2 224 2

44. 9000 20

160

X – Maths 85

45. 600

3 10

46.

160

47.

48.

15

49. A B 10 A B

12 B

50.8

211

1

1. b 2. c

3. a 4. c

5. a 6. d

7. d 8. b

9. a 10. a

11. b 12. c

13. b 14. a

86 X – Maths

15. a 16. k = 10, = – 5

17. 2 6 18. p 6 p – 6

19. x2 + 2x – 63 = 0 20.1

4,4

21. 5

, – 22

22. 9, 42

23. k = 14 24.7

7,4

25. 3 3 3 3, .

3 326. 10, 5

27. D = 0.

28. (a) (b) 33, .

229. 5, 10 30. 6, 1

31.

2

21,

b

a32.

3 2,

4 3

33. ,c bb a

34.5

5,2

35. 1, 2 36.5

, – 53

37. –a, –b. 38. 57

39. 4, 5, 6 40. 3

41. 40 42. 26 24 10,

43. 16 44. 50

45. 40, 50

46. 6 , 12 47. 29 , 5

48. 5 , 3

49. 30 50. 5, 6 min.

X – Maths 87

2

1.

2. (Pattern)

3.

a, a + d, a + 2d, ..... (a : d :

)

4. ‘a’ ‘d’ n

( an = a + (n – 1) d .

5. n ‘a’

‘d’ n

2 12nn

S a n d ‘l’

.2nn

S a l

6. (i) an d = an – an–1.

(ii) sn n an = sn–1 – sn–1

(iii) a, b, c 2b = a + c.

88 X – Maths

(iv) n r =

(n – r + 1)

1. 24 .............

(a) 6 (b) 8

(c) 3 (d) 2

2. n 2n + 7,

(a) 15 (b) 21

(c) 28 (d) 25

3. n

25 32 2n n 10

(a) 250 (b) 230

(c) 225 (d) 265

4. 4, 7, 10, ............. n 82 n

(a) 29 (b) 27

(c) 30 (d) 26

5. a, b c

(a)

2b c

a (b)

2a c

b

(c)

2

a bc (d) b = a + c

6. x – 7, x – 2, x + 3 12 .............

(a) x + 62 (b) x – 48

(c) x + 48 (d) x – 62

X – Maths 89

7. 1 2 3

8 , 8 , 8 ,8 8 8

.............

(a) 18

(b) 11

8

(c) 18

8(d) 1

8. –5, –2, 1, ............. n

(a) 3n + 5 (b) 8 – 3n

(c) 8n – 5 (d) 3n – 8

9. n 5n – 3n

(a) 2 (b) –3

(c) –2 (d) 3

10. 5, 2k – 3, 9 ‘k’

(a) 4 (b) 5

(c) 6 (d) –5

11. 10

(a) 50 (b) 55

(c) 60 (d) 65

12. 7, 11, 15, ............. 147, 9

(a) 135 (b) 125

(c) 115 (d) 110

13. n n2, n

(a) 2n – 1 (b) 2n + 1

(c) n2 – 1 (d) 2n – 3

90 X – Maths

14. 30 13

(a) 4 (b) 3

(c) 2 (d) 5

15. 39 3

(a) 2 (b) –3

(c) 4 (d) 3

16. 2, 8, 18, 32, ..........

17. 10 12

18. 41, 38, 35 ..........

19. 2 4 6

2011

20. –

12 120

21. 6 102 6

22. n sn = 3n2 – 4n, n

23. 24

44

X – Maths 91

24. 1 199

25. 22, 20, 18, .............

26. 4k + 8, 2k2 + 3k + 6 3k2 + 4k + 4

k

27. 11 11 17 17 28

28. 8 12

17.

6

29.

1

30. 20, 16, 12, ............., – 176

31. 31 1 13

,4 2 2

32. 57, 54, 51, ............. 570

33. 24 440

34. 40 n 3 – 2n

35. 2 29

155

36. n 4 2 –14

92 X – Maths

37. 5

3

38. 6 42 10 30

1 : 3 11

39. n 3n + 8 : 7n + 15 12

40.

a15

41. 8 140 24 996

42. 15

594

43.

3 12

375

44. 20 20

1 30

45. 16 528 16

1552

46. 200

40 30

47. –150

–550

X – Maths 93

48. 4 81

7

49. 8 15

28

50. 165

15 14 13

10 12

14

1. b 2. b

3. d 4. b

5. b 6. c

7. a 8. d

9. b 10. b

11. b 12. c

13. a 14. b

15. d 16. 50, 72

17. 4, 10, 16, ............. 18. 15 , –1

19. 812 20. 12

21. 15 22. 6n – 7, = 6

23. 23 24. 9800

25. 23 26. 0, 2

94 X – Maths

27. 0 28.1 5 7

, , , ...............2 6 6

29. = 3, = 2 30. –70, –80

31. 59 32. 19 or 20, {20 }

33. 5, 8, 11 34. –1520

35. 3

36. = – 8, = 7

37. 99090 38. = 2, 11 = 22

39. 7 : 16 40. 3

41. 7, 10, 13, 16, ........ 42. 852

43. 25 44. 450

45. = 3, = 4 46. 1360

47. 3, –1, –5, ........ 48. 12, 510

49.

1217, 7

2d 50. 6

X – Maths 95

3

1. A (x1, y1) B (x2, y2)

AB {(x2 – x1)2 + (y2 – y1)

2}.

2. P(x, y) (0,0) (x2 + y2) x-

y- y- x-

3. A(x1, y1) B(x2, y2) P(x,y), m1 :

m2

1 2 2 1 1 2 2 1

1 2 1 2,

m x m x m y m ym m m m

m1 : m2 k : 1

4. P(x1, y1) Q(x2, y2)

1 2 1 2,2 2

x x y y

5. (x1, y1), (x2, y2) (x3, y3)

1 2 3 2 3 1 3 1 21

.2 x y y x y y x y y

96 X – Maths

6.

x1(y2 – y3) + x2 (y3 – y1) + x2(y1 – y2) = 0

1. x ‘p’ y 3 p

(a) (3, 0) (b) (0, 3)

(c) (–3, 0) (d) (0, –3)

2. p (3, –2) y-

(a) 3 (b) 2

(c) –2 (d) 13

3. (6, 0) (0, –8)

(a) (3, 4) (b) (3, –4)

(c) (0, 0) (d) (–4, 3)

4. (4, 0) (0, x) 5 x

(a) 2 (b) 3

(c) 4 (d) 5

5. 7x ya b

y-

(a) (a, 0) (b) (0, b)

(c) (0, 2b) (d) (2a, 0)

X – Maths 97

6. 0AB, A (4, 0) B (0, –7) 0

(a) 11 (b) 18

(c) 28 (d) 14

7.

11 2, 5 , 5

3 3P Q

(a) 6 (b) 4

(c) 3 (d) 2

8. 12 4x y P Q, PQ

(a) (1, 2) (b) (2, 0)

(c) (0, 4) (d) (2, 1)

9. ABC A (–4, 2) D(2, 5), BC

ABC

(a) (0, 4) (b)

71,

2

(c)

72,

3(d) (0, 2)

10. 2x + 4 = 0 x – 5 = 0

(a) 9 (b) 1

(c) 5 (d) 7

11. (5 cos 35°, 0) (0, 5 cos 55°)

(a) 10 (b) 5

(c) 1 (d) 2

98 X – Maths

12. (–4, 0), (4, 0) (0, 3)

(a) (b)

(c) (d)

13. (0, 0), (2, 0) (0, 2)

(a) 4 (b) 6

(c) 6 2 (d) 4 2 2

14. AOBC A (0, 3), O (0, 0), B (5, 0)

(a) 5 (b) 3

(c) 34 (d) 4

15. (9, a), (b, –4) (7, 8) (6, 8)

(a, b)

(a) (4, 5) (b) (5, 4)

(c) (5, 2) (d) (3, 2)

16. (3, a) 2x – 3y = 5 a

17. P(3, 2) x- x-

18. (3, 5) (7, 1) (a, 0) a

19. (0, a), ,

2 2b a

(b, 0)

20. AB A

(3, –4) B

X – Maths 99

21. ABC A (3, 2) B(–2, 1) G

5 1,

3 3 C

22. p, (–3, 9), (2, p) (4, –5)

23. (x, y) (7, 1) (3, 5) x y

24. P Q A(1, –2) B (–3, 4)

P

25. (x, 2) (3, 4) 8 x

26. (1, –1), (–3, 5)

(2, –7)

27. Y- (–2, 5) (2, –3)

28. (5, 7) (3, 9) (8, 6)

(a, b) a b

29. (1, 3) (2, 7)

3 : 4

30. x P (2, 3) Q (x, 5)

10

31. K (1, 2) E (6, 8) F (2, 4)

K EF

32. ABC A (–1, 3), B (1, –1) C (5, 1) A

100 X – Maths

33. A (a, b) B (b, a) a – b = 4

34. (–3, 1), (1, 1)

(3, 3)

35. ABC AB = AC A, y-

B C (–5, –2) (3, 2) A

36. A (3, 0), C (–1, 4) D (–2, –1)

ABCD

37. (3, 1) (–2, 5) 34

38. (6, –3), (3, K) (–7, 7)

15 K

39. 4 (5, 0)

5

40. X- P, (4, 5) (1, –3)

P

41. ABC, B = 90° 34AB B C

(4, 2) (–1, y) (ABC) = 17 y

42. A (–3, 2) B (x, y) C (1, 4)

AB = BC (2x + y)

43. P (3, 4) A (a + b, b – a) B (a – b, a + b)

3b – 4a = 0.

X – Maths 101

44. ABCD A (–5, 7), B (–4, 5),

C (–1, –6) D (4, 5) ABCD

45. PQR (1, 2), (0, 1) (1, 0)

46. A (2, 1) B (5, –8) P Q

P,A P 2x – y + k = 0

K

47. (3, 4) (1, 2) P Q

P Q (p –2)

5,

3q

p q

48. A(–5, 7), B (–4, –5), C (–1, –6) D (4, 5) ABCD

49. ABC A (5, 2), B (–5, –1) C (3, –5)

AD ABC

50. A(a, 0) B (0, b) P(x,y)

1.x ya b

51. (x, y), (–5, –2) (3, –5)

3x + 8y + 31 = 0.

1. c 2. a

3. b 4. b

5. c 6. d

7. c 8. a

102 X – Maths

9. a 10. d

11. b 12. b

13. d 14. c

15. c 16. 13

a

17. 2 18. a = 2

20. (–3, 4) 21. (4, –4)

22. p = – 1 23. x – y = 2

24.

1, 0

3 25. x = 1, 5

26. 5 27. (0, 1)

28. a = 0, b = 10 29.

10 33,

7 7

30. 4, –8 31. 5

32. 5 33. 4 2

34. (–1, 3) 35. (0, –2)

37.

3, 4

4 38. 2113

K

39. 2, 8 40.

17, 0

8

41. –1 42. 1

44. 72 45. (2, 1), (0, 3), (0, –1)

46. K = – 8 47. 7

, 03

p q

48. 72

X – Maths 103

4

1. :

2. :

3. :

1.

(a) 90° (b) 60°

(c) 45° (d) 30°

2. 30 10 3

(a) 30° (b) 60°

(c) 45° (d) 90°

104 X – Maths

3. 25 25

(a) 45° (b) 60°

(c) 30° (d) 15°

4. 10 18

30°

(a) 10 (b) 18

(c) 12 (d) 16

5. 20

30°

(a) 20 3 (b)203

(c) 40 3 (d)403

6. 1

1 : .3

(a) 30° (b) 45°

(c) 60° (d) 90°

7. 50 3

60°

(a) 100 (b) 50

(c) 150 (d) 75

X – Maths 105

8. (2) ABCD

30°

D C

BA

10

(2)

(a) 40 (b) 20 3 1

(c) 60 (d) 10 3 1

9. 10

30°

(a) 30 (b) 20

(c) 10 (d) 15

10.13

(a) 30° (b) 45°

(c) 60° (d) 90°

11. (4) D, BC, CAB = 1 DAB = 2

tan 1 : tan 2

106 X – Maths

A

BC D

2

1

(4)

(a) 2 : 1 (b) 1 : 2

(c) 1 : 1 (d) 1 : 3

12. (5) 8

tan15

PQ = 16 PR P

QR

(5)

(a) 16 (b) 34

(c) 32 (d) 30

13. 50 45° 30°

x x

(a) 50 (b) 50 3 1

(c) 50 3 (d)50

3

X – Maths 107

14. 9 16

(a) 18 (b) 16

(c) 10 (d) 3012

15. 5

A 60° A

45° 3 1.732

16. 30

45° 60°

17. 60

30° 60°

18. h

2 sectan tan

h

19. 60° 50

30°

500 3

20. A 60° 15

30° 720

3 1.732 .

108 X – Maths

21. 20

60° 45°

22. 1800

60° 45°

23. A B

15 30° 60°

B

3 1.732 .

24. P 10

30° P

45°

P

25. 12

30° 60°

26. 45° 30°

10

3 1.73

27. A

30° 12

60°

28. 18

60°

30°

X – Maths 109

29.

60° 40

30°

30. 3000

60° 45°

31. 10

30° 45°

32. 100

30° 20

45°

33. 10

60°

30°

34. P Q

36° 54° P Q

10 20

2 1.414

1. c 2. b

3. a 4. d

110 X – Maths

5. b 6. c

7. a 8. b

9. a 10. c

11. b 12. b

13. b 14. d

15. 6.83 16. 30 3 1

17. 30 3 19. 20 m/sec.

20. 2598 21. 20 3 1

22. 600 3 3

23. = 12.97 , = 7.5

24. 10 2 1 10 3 .

25. 24 3 26. 13.6

27. 18 28. 18 3 , 72

29. = 34.64 , = 20

30. 1000 3 3

31. 5 3 3 , 5 3 3

32. 30

33. = 10 3 = 40

34. 14.14

X – Maths 111

5

1.

2.

3.

1. (1) PQ POQ + QOP

P

Q

O

(1)

112 X – Maths

(a) 120° (b) 90°

(c) 80° (d) 100°

2. PQ, 5 PQ = 12 , Q

OP

(a) 13 (b) 17

(c) 7 (d) 119

3. (2) PQ PR QOP = 70°, QPR

P

Q

O

70°

R

(2)

(a) 35° (b) 70°

(c) 40° (d) 50°

4. (3) PQ PQ = 8 OQ = 6 PS

P

Q

O S

(3)

(a) 10 (b) 2

(c) 3 (d) 4

X – Maths 113

5. (4) PQ PR PQ

= 4 OQ = 3 OR = 2 PR

PO

Q

R

(4)

(a) 5 (b) 21

(c) 4 (d) 3

6. (5) P, Q R AB = 4 BR = 2

ABC

O

RQ

B cP

A

(5)

(a) 12 (b) 8

(c) 10 (d) 9

114 X – Maths

7. (6) ABC

B PC

A

5

3

Q

R

2

(6)

(a) 10 (b) 15

(c) 20 (d) 25

8. 12

(a) 13 (b) 6

(c) 10 (d) 8

9. (7) ABCD, AB

= 6 BC = 5 AD = 8 CD

C

BA

D

(7)

X – Maths 115

(a) 6 (b) 8

(c) 5 (d) 7

10. 17

23 16

(a) 34 (b) 17

(c) 15 (d) 30

11. (8) P OPB

B

P

A

O

40°

(8)

(a) 50° (b) 40°

(c) 35° (d) 45°

12. (9) PQ PR O QPR =

45° QOR

P

Q

R

45°o

(9)

116 X – Maths

(a) 90° (b) 110°

(c) 135° (d) 145°

13. (10) O PA PB AQB

A

Q

B

Po 45°

(10)

(a) 70° (b) 80°

(c) 60° (d) 75°

14. (11) ABC P, Q R

AP = 4 BP = 6 AC = 12 BC

RP

Q

A

B C

(11)

(a) 6 (b) 14

(c) 10 (d) 18

X – Maths 117

15. (12) ABC P, Q R P,

BC AR = 4 , AC = 9 BC

QR

PB C

A

(12)

(a) 10 (b) 11

(c) 8 (d) 9

16.

17. E F

D

D

18. 2.5 P 6

P

19. ‘O’ T TP TQ

OPQ = 30° TQP

118 X – Maths

20. (13) AP = 4 BQ = 6 AC = 9 ABC

PR

Q

A

C

9

4

6 B

(13)

21. (14) OP O

ABP

A

B

o P

(14)

22. (15)

BE BF

43 A AC

X – Maths 119

C

D E FAB

(15)

23. ABC 8 10 12

AD, BE CF

C

DB A

F E

(16)

24. ABC AB

AC P PB = PC.

25. P PA PB, O

APB = 2 OAB

A

O

PB

(17)

120 X – Maths

26. 9 ABC, AB =

AC = 6

27. (18) AB = AC, ‘D’ AC BD 1

.4

AE AC

B D

A

C

E

(18)

28. (19) 5 8

P 15

Po

B

A

(19)

29.

6 2.5

30. (20) AB = 13 , BC = 7 AD = 15 PC

X – Maths 121

o

BR

A

Q

DPC

S 4

(20)

31. (21)

o

BR

A

Q

DPC

S r

23

5

29

(21)

122 X – Maths

32. (22) 3 ABC

3 5

35

A

B

Co

(22)

33. ABC BC P AB

AC Q R AQ,

ABC

34. (23) XP XQ X ‘O’

R XA + AR = XB + BR.

X

A

B

P

Q

R

(23)

X – Maths 123

35.

1.

2. PT ‘O’ T

OT = 6 , OP = 10 PT

3. (24) PQ PB x y

P

A

B

Qo y

y

35°

x

(24)

4. (25) AC ‘O’ A

x

o

C

A

B

40°

x

P Q (25)

36.

124 X – Maths

1. (26) PA PB KN = AK + BN.

P

K

N

A

B

o

(26)

2. 5 3

3. (27) PA PB ‘O’

OP, AB

P

A

B

o

(27)

4. (28) PQ 6 6

TP TQ PTQ

T

P

Q

o

(28)

8

X – Maths 125

1. b 2. a

3. c 4. d

5. b 6. a

7. c 8. b

9. d 10. a

11. a 12. c

13. a 14. b

15. a 16. 30°

18. 14 19. 60°

20. 15 22. 12

23. 4

24. AD = 7 BE = 5 CF = 3

25. = 4 26. 8

28. 266 29. 1

30. 5 31. 11

32. 32 35.(2) 8

35.(3) x = 35°, y = 55° 35.(4) 40°

36.(2) 8 36.(4) 120°

126 X – Maths

6

1.

2.

1. AB = 7 AB P

AP : PB = 3 : 4

2. PQ = 10 PQ A 25

PAPQ

PA AQ

3. ABC BC = 6.5 , AB = 4.5

ACB = 60°. ABC

ABC 45

4. XYZ XY = 5 , YZ = 7 XYZ = 75°.

XYZ ~ XYZ32

5. 8 5

34

X – Maths 127

6. ABC AB = AC BC = 7

120° A´B´C´ ~ ABC

ABC 1

13

7. PQR Q = 90°, PQ = 6 QR = 8 PQR

~ PQR PQR23

8.

1.5

9. PQR 5 P´Q´R´

1

.´ ´ 2

PQ

P Q P´Q´

10. 4 O P

OP = 6 P PA PB

PA PB

11. AB = 8 AB

O OPAB P

12. OP = 3 PQR =45°

OQ = 5 Q

13. 3.5 O P

PA PB APB = 45°, AOB +

APB

14. 4 P

128 X – Maths

15. AB = 9 A B

5 3

16. 3.5 O P

OP = 6 . OP T PQ PR

Q R T AB || QR

A B PQ PR

17. 7

60°

18. O 3.5

P Q OP = OQ = 7 PA

QB

PQ || AB ?

X – Maths 129

7

1. C = 2r C_____

r_____

227 3.14

2. = r2 ‘r’

3. 212

r

4. = (R2 – r2) = (R + r) (R – r); R > r

‘R ’ ‘r’ = (R + r) (R – r); R > r

5.

=360

180°

× 2 rl

180r

l

6.

2

360r

130 X – Maths

7. 60 =

1 360 6 .60

8. ‘a’ = 6a2

9. ‘a’ = a3

10. l, b h = 2 (l × b + b × h + h × l)

11. l, b h = l × b × h

12. r h = 2rh

13. r h = 2r + h)

14. r h = r2h

15. r h = rl, l

2 2 l r h

16. = r (l + r)

17. 213

r h

18. r = 4r2

19. r = 2r2

20. r = 3r2

21. r 343

r

22. r 323

r

X – Maths 131

23. = l (r + R) ‘l’

r R

24. = l (r + R) + (r2 + R2)

25. = h (r2 + R2 + rR)

1. ‘d’

(a) 2d (b)2

4d

(c) d (d) d2

2.

(a) r = 1 (b) r = 7

(c) r = 2 (d) r = c

3. 7

(a) 36 (b) 14

(c) 7 (d) 14

4. 13 6

(a) 19 (b) 19

(c) 25 (d) 32

132 X – Maths

5. 4 : 5

(a) 4 : 4 (b) 16 : 25

(c) 64 : 125 (d) 8 : 10

6.

(a) 4 (b) 33

(c)3 3

4(d) 8 : 10

7. 440 3 66 2

(a)403 (b)

203

(c) 440 (d) 66

8. 8 : 125

(a) 8 : 125 (b) 2 : 5

(c) 4 : 25 (d) 16 : 25

9. ‘l’ ‘r’

(a) l . r (b) l . r 2

(c)2

2lr

(d) l 2. r

X – Maths 133

10. 5 10 2

(a) 2 (b) 4

(c) 22 (d) 8

11. ‘a’

(a) a2 (b) 3a3

(c) a3 (d) 6a3

12. 7

(a) 11 2 (b) 121 2

(c) 154 2 (d) 44 2

13.

14. BC

CB

A

12 5

134 X – Maths

15.

14

9 9

16. 30

17. 7

45°

18. 7

19.

120° 90°

20. 16 × 12 × 8 4

21.

22.

23. 10 500

X – Maths 135

24. 15

660 2

25. 729 3

26.

27. 30

28. 12 10

29. 10

440

30. 14 (D)

31. 15 5

32. 3 4

33. ‘l’

o

A B‘l’

14 90°

14

34. ABC 30

10 A

136 X – Maths

35. 20

45°

45°

36.

4

6

37. 7 14

AOC = 120°

o

120° D

CB

A

X – Maths 137

38.

14 1414

39.

24

P

QR

o

7

40. 3 : 4

6

41. ‘r’

42. 20

60°

43. 12 8.00 a.m

8.05 a.m.

44. 3.14

138 X – Maths

20

20

20 20

45.

2

5

5

2

46.

60°

3

3

47. ABCD

X – Maths 139

4

4

4

C

DA

B

48. 8a3

49. 17.32 (3 = 1.732).

50. 6 , 8 10

51. 4 3

6

52. 448 3 7

53. 64 2

54. 24 2 8

55. 30 × 24 × 18

56. 16 2 4

140 X – Maths

57. 50 12 7

58. 2 14

59. 7

60. 60° 3

61. (8 × 4 × 2) 3

62. ‘2h’

‘r’

63.

64. 5 2

(1 = 10000 2)

65. ‘R’

66. ABC 4

o

4

4

4

A

CB

X – Maths 141

67.

12

60°

6

12

12

68. 7

69.

‘h’

70.

36 18

27

71. 5.5 15.5 24

72. 2 6

60

30

142 X – Maths

73.

5

12

74.

28

28

75.

14

14

X – Maths 143

76. AB CD CD = 8

A

B

C Do

77. ABC (A = 90) AB.BC AC

A

CB

4 3

78.

14 7

5.5 10.5

144 X – Maths

14

7

5.5

10.5

79. AB = 6 BC = 10

‘O’

( = 3.14)

A

B

C

o

6

10

1. b 2. c

3. a 4. b

5. b 6. d

7. b 8. c

X – Maths 145

9. c 10. b

11. b 12. b

13. 3 14.3

377

15. 49 3 16. 14

17. 19.5 18. 154 2

19. 4 : 3 20. 24

21. 3 : 1 22. 3 : 1 : 2

23. 20 24. 7

25. 9 26. : 3

27. 14 28. 150°

29. 7 30. 36

31. 550 2 32. 5

33. 22 34. 250m

3

35. 200 36. (16 + )

37. 154 2 38. 42

39. 25 40. 10

41. r2 42.60

43. 2 44. 86 2

45. (25 – 4) 2 46. 3 2

47. (16 – 4) 2 48. 24 a2

49. 1000 3 50. 123

51. 5 52. 8

53. 4 54. 6

146 X – Maths

55. 302 2 56. 2

57. 25 ; 3850 3 58. 44 3

59. 3.5 60. 27

61. 4 62. 22. r . h

3

63. r = h 64. 1000 3

65. 3R2 66. 29.46 3

67. 266036 3 cm

7

68. 154 2

69.2

h.3 70. 36

71. 1716 2 72. 3

73.1019

14 2 74. 154 2

75. 77 2 76.108

7

77. 6 2 78. 2926 3

79. 11.44 2.

[ A, B C O

(ABC) = (OAB) + (OBC) + (OAC)

1 1 1 1

AB r BC r AC r r AB BC AC2 2 2 2

(r = 2 cm)]

X – Maths 147

8

1. E

E

P E

2. 1

3.

4. E P(E) + P(E ) = 1.

5.

O P(E) 1.

1. E P(E) + P E = ........

(a) 0 (b) 1

(c) 2 (d) –1

148 X – Maths

2.

(a) 0 (b) 2

(c) 1 (d) –1

3.

(a)23 (b)

–32

(c) 15% (d) 0.7

4. P(E) = .65 P (E )

(a) .35 (b) .25

(c) 1 (d) 0

5. 38%

(a) 12% (b) 62%

(c) 1 (d) 0

6. 9 6

(a)7

16 (b)9

16

(c)1816 (d)

1416

7.

(a)15 (b)

45

(c)35 (d) 1

X – Maths 149

8. 11

(a)1

12 (b)17

(c)1

365 (d)1

366

9. 52

(a) 12 (b) 16

(c) 4 (d) 52

10.

(a)34 (b)

16

(c)12 (d)

13

11.

(a) 0 (b) 1

(c) –1 (d)

12. "MOBILE"

(a)13 (b)

37

(c)16 (d)

12

150 X – Maths

13. 1 12

(a) 10 (b)

(c) 3 (d)

14.

15.

16. 100, 500 1000

17. 6

18. 50

35 15

19. 5 25

10 15

20. 1000 5

21. 600 42

22.

X – Maths 151

23. 10 10

24. 52

25. 53

26. 2 101

27. 1 20

3 7

28. 52

P 13

P 23

29. 5 ‘n’ P( ) = 3 × P ( )

‘n’

30.

31. 12

32. (1, 4, 9, 16, 25, 29) 29

33.

152 X – Maths

34.

(i) 2 (ii) 2

(iii) 3

35. 52

(i) (ii)

(iii)

36. 5 8 4

(i) (ii) (iii)

37. 120 12

38. 1, 2 3 x

1, 4 9 y

xy 9

39. 1 90 90

(i)

(ii) (iii) 5

40.

41. (i) 7 (ii)

10 (iii) 5

X – Maths 153

42.

(a) (b)

(c) (d)

43. 24

23

1. b 2. c

3. b 4. a

5. b 6. b

7. b 8. c

9. a 10. b

11. a 12. d

13. (i) 1

12 (ii) 12 (iii)

13 (iv)

13 14.

16

15.12 16.

13

17. 0 18.3

10

19.27 20.

1200

21.93

100 22. S = [HH, TT, HT, TH]

154 X – Maths

23.16 24.

524

25.27 26.

9100

27.25 28. , 13

29. 15 30.12

31.3536 32.

33.9

13 34. (i) 38 ; (ii)

38 ; (iii)

18

35. (i) 1349 ; (ii)

349 ; (iii)

1049 36. (i)

517 ; (ii)

817 ; (iii)

1317

37.9

10 38.59

39. (i) 9

10 ; (ii) 1

10 ; (iii) 15 40.

34

41. (i) 16 ; (ii)

112 ; (iii)

2536

42. (i) 4

13 ; (ii) 1

26 ; (iii) 1113 ; (iv)

213

43. 8.

X – Maths 155

BLUE PRINT

SA-2

I II

1 2 3 4

3 (3) 2 (4) 3 (9) 1 (4) 9 (20)

1 (1) 2 (4) 2 (6) 1 (4) 7 (16)

1 (1) 1 (2) 2 (6) 3 (12) 6 (20)

2 (2) 1 (2) — 1 (4) 4 (8)

2 (2) 1 (2) 2 (6) — 5 (12)

1 (1) 1 (2) 1 (3) — 3 (6)

10 (10) 8 (16) 10 (30) 6 (24) 34 (80)

156 X – Maths

X (SA - 2)

: 3 3½ : 80

1.

2. 34 A, B, C, D

A 10 1 B 8

2 C 10 3 D 6

4

3. 1 10

4. 1 2

3 3 2 4

5.

SECTION A

1 10 1

1. 2x2 + 13x + 11 + 0

(a) –13 (b)132

(c)112 (d) –11

X – Maths 157

2. –5, –3, –1..... n

(a) 2n – 7 (b) 7 – 2n

(c) 2n + 7 (d) 2n + 1

3. P, Q R AB = 6 ,

BP = 3 , ABC

A

CB

Q R

P

o

(a) 12 (b) 18

(c) 9 (d) 15

4. 8 12

30° –

(a) 10 (b) 12

(c) 8 (d) 4

5. y + 3 = 0 2y – 5 = 0 –

(a) 8 (b)112

(c) 6 (d) 5

158 X – Maths

6. .12x

23 x = ........

(a) 2 (b) 3

(c) 4 (d) 6

7. –9, –14, –19, ............ a30 – a20

(a) –50 (b) 50

(c) 10 (d)

8. 6 45

4

(a) 3 (b) 4

(c) 5 (d) 6

9.

(a) 30° (b) 45°

(c) 60° (d) 90°

10. (0, 0), (3, 0) (0, 3)

(a) 6 (b) 9

(c) 2 32 (d) 2 22

SECTION B

11 18 2

11. 3 6 11 15

X – Maths 159

12. 4x2 + mx + 1 = 0 ‘m’

13. 5 3

o

B

R

A

Q

DPC

Sr

29

23

5

14. P PA PB, O

APB = 2 OAB.

A

O

PB

15. 3 3

1.5 2

160 X – Maths

16. 4 9

17. Y- (–2, 5)

(2, –3)

18.

(a) (b)

SECTION C

19 28 3

19. 8

5 34

20.

1 32 7 5, 3, 1

3 1x x

x xx x

21. ABC 4

D, E F AB AC A

BC D

EF

o

8 6

X – Maths 161

22. 2.2 0.50

14

(Sweep)

23. –4 29

150

24. 10 300 4 3

25. 10 8

26. ABC B = 90° 34AB B C

(4, 2) (–1, y) ABC 17

y

27. 1, 2, 3 ‘x’ 1,4,9

‘y’

9

12 x 6

x

28. (x, y), (–5, –2) (3, –5)

3x + 8y + 31 = 0.

162 X – Maths

SECTION D

29 34 4

29. 6

5

90

15 ½

30.

31. 12 28 16

12

(a) (b)

32. 12 15

12

6

33. 20

45° 60°

34. 36

3 6

X – Maths 163

440 14

20

2

1. b 2. a

3. b 4. c

5. b 6. c

7. a 8. c

9. b 10. d

11. 67 12. m 4 or m – 4

13. 8 or 112 15. 5

16. 6 17. (0, 1)

18. (a) 0, (b) 12 20.

23, – 1

5

21. AB = 15 , AC = 13 22. 112 10.26 2

23. d = 3 24. 73

25. 8 : 7 26. y = – 1, 5

27.5

3.9 29. 10 15

45

31.3 22 6

10258 , 33187 7 32. 10

33. 33 20 3 1 34. 72 1355.20,

1056