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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
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