Under the guidance of · 1. Mr. Pradeep Kumar Jain RPVV Rajniwas Marg, Delhi Lecturer (Maths) 2....
Transcript of Under the guidance of · 1. Mr. Pradeep Kumar Jain RPVV Rajniwas Marg, Delhi Lecturer (Maths) 2....
Under the guidance of :
Co-ordinators :
[Class-X – Maths] 2
Group Leader :
MR. S.B. TRIPATHI (V.P.) CRG SKV No. 2, Ghonda, Delhi
1. Mr. Pradeep Kumar Jain RPVV Rajniwas Marg, DelhiLecturer (Maths)
2. Ms. Ritu Tiwari RPVV Surajmal Vihar, DelhiTGT (Maths)
3. Mr. Syed Athar Hasan RPVV Gandhi Nagar, DelhiTGT (Maths)
4. Mr. Neeraj Gupta GBSSS, GT Road, Shahdra, DelhiTGT (Maths)
3 [Class-X – Maths]
Mat
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ode
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041
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[Class-X – Maths] 4
S.A. - I
1. 5
2. 12
3. 19
4. 30
5. 43
6. 53
65
5 [Class-X – Maths]
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) = b
3 r 0 b r
(a, b)
3.
4. x , 0px qq
q
2m5n m n x
[Class-X – Maths] 6
5.
pxq q
2m5n m, n x
6. p p
, 0p q
q
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)
7 [Class-X – Maths]
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.
3 421
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...
[Class-X – Maths] 8
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.
3 3– 5 54 4
(a) (b)
(c) (d)
15. (x, y) = 150 xy = 1800 (x, y) =
(a) 120 (b) 90
(c) 12 (d) 0
16.
(a)91
2100 (b)64
455
(c) 2 3 3
3435 2 7 (d) 3
297
17. 18 50.
9 [Class-X – Maths]
18.
19. a = 4q + r a q r
20. 5 3
21. 96
22. 3 5
23. 16 28
24. 120
25.
12 5
26. 25 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
[Class-X – Maths] 10
33. 56, 96 324
34. m 3m
3m + 1
35. q 6q + 1,
6q + 5
36. 398 436 7
11
37. 7
38. 420 130
(Tray)
(i)
(ii)
39. 616 32
40.
18
11 [Class-X – Maths]
12
(i)
(ii)
1. b 2. c3. a 4. c5. c 6. b7. a 8. b9. b 10. a
11. b 12. b
13. d 14. d
15. c 16. c
17. 30, 18. 2
19. 0 r < 4 20. 5 3 , 2
21. 1 23. 4
24. 2 × 2 × 2 × 3 × 5 28. = 112, = 56
30. 31.
32. HCF (210, 55) = 55 = 210 × 5 + 55 y y = –19
33. 4 34. a = 3q + r
35. a = 6q + r 36. 17
38. 10,
39. 8,
40. 36
[Class-X – Maths] 12
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)
13 [Class-X – Maths]
1. f(x)
(a) f() > 0 (b) f() = 0
(c) f() < 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(y) (y – a) f(y)
(a) y (b) a
(c) 2a (d) 2y
5. x2 – x + k k
(a) 0 (b) –2
(c) 1 (d) 3
6. x = f(y), y-
(a) (b)
(c) (d)
7. x2 + 1
(a) (b)
[Class-X – Maths] 14
(c)
(d)
8. ax2 – bx + 1 1
(a) a – b = 0 (b) a – b – 1 = 0
(c) a + 1 = b (d) a + b + 1 = 0
9. f(x) ‘n’
(a) n (b) 2n
(c) n + 1 (d) n – 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
13. x2 + x + 1
1 1 .........
(a) –1 (b) 0
(c) 1 (d) 2
15 [Class-X – Maths]
14. 2x2 – 7x + 3
15. p(x) = x2 – a (x + 1) – b ( + 1) ( + 1) = 0
b
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. g(x) = (k2 + 4) x2 + 13x + 4k
k
21. , 2 – 3x – x2 + (1 + )
22. 2 54
23. kx2 + 3k + 2x k
24. 4x2 – 9 – 8kx k
[Class-X – Maths] 16
25. 2 –3
26. (a2 + a) x2 + 13x + 6a
a
27. 2x2 + px – 15 (–5) p(x2 + x) + k
k
28. 2x3 + 5x2 – 14x + 10
(2x – 3)
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. –1 2 2x4 – 2x3 – px2 + qx – 6 p q
35. 2+3 2–3 x4 – 4x3 – 8x2 + 36x – 9
36. 8x4 + 14x3 – 2x2 + 7x – 8 4x2 + 3x – 2
17 [Class-X – Maths]
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. ax2 + bx + c, a 0
(i) a c
(ii)
41. NGO K
K x2–100x–20000
(i) NGO
(ii)
42. x3 – 12x2 + 47x – 60 3
(i)
(ii)
1. b 2. a
[Class-X – Maths] 18
3. a 4. b
5. a 6. c
7. b 8. c
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 12
5x x 20. 2
21. k = – 5 22. x2 – 4x – 1
23.3
2
24. 0
25. x2 + x – 6 26. 5
27.77,4
p k 28. 7
29. g(x) = x2 – 1 30. –2, 3
31. k = 6 32. k = 2
33. –2, –1 34. 1, –3
35. ± 3 36. 14x – 10
37. 61x – 65
38. 0 1 7 0 1 and 7r x a x b a b
39. r (x) = x + 2 = ax + b a = 1 and b = 2
40. a = c,
41. (i) 200, (ii)
42. (i) 9 (ii)
19 [Class-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
[Class-X – Maths] 20
1 1
2 2
a ba b
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)
21 [Class-X – Maths]
5.
(a) (b)
(c) (d)
6. 6x – 2y = 3 Kx – y = 2
K =
(a) K = 3 (b) K = 4
(c) K 3 (d) K 4
7. ax + by = c y–
(a)
0, cb (b)
0, bc
(c)
, 0cb
(d)
0, c
b
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)
[Class-X – Maths] 22
11. x – y = 2
x + y = 2
(a) (b)
(c) (d)
12. 2x + 3y = 4 x y
(a)
4 2
3xy (b)
4 32
xy
(c)
4 32
yx (d)
4 2
3xy
13. p 2x + py = 8, x + y = 6
x = 10 y = –4
(a) –3 (b) 3
(c) 2 (d) 6
14. x – 2y = 6 y–
(a) (–3, 0) (b) (0, 6)
(c) (6, 0) (d) (0, –3)
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
23 [Class-X – Maths]
17.
70
95
18. 9000
20 160
19. x = –1
y = 4
20. a (3, a) 2x – 3y = 5
21.
x + 2y – 8 = 0
2x + 4y = 16
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
[Class-X – Maths] 24
26. k
(3 K + 1) x + 3y – 2 = 0
(K2 + 1) x + (k–2)y – 5 = 0
27. x + 3y = 4,
(i)
(ii)
(iii)
28. x – y = 4 x + y = 10 p y = 3 x –p.
29. a b
2x + 3y = 7
a(x + y) – b(x – y) = 3a + b – 2
30. 5 1
10
31. x y
1 11 18; 92 3 3 2
y yx x
32. x y
x + y = a + b
ax – by = a2 – b2
25 [Class-X – Maths]
33. x y
139x + 56y = 641
56x + 139y = 724
34. x y
5 1 2x y x y
15 5 2, 0, 0.x y x yx y x y
35.
x + 2y = 5, 2x – 3y = –4
x–
1– ,12
36.
x + 3y = 0, 2x – 3y = 12
x–
y– x– y–
37. x y
1 12 122 2 3 7 3 2x y x y
7 4 22 3 3 2x y x y
2x + 3y 0 and 3x – 2y 0
[Class-X – Maths] 26
38. p q
2, 6, 0, 0.p q p q p q
pq pq
39. 5% 10%
2000 10% 5%
1500
40. x y
2 3 4 92, 1, 0, 0x yx y x y
41. 20
5
42.
39 132
43. 8 1
13 2
44. 1
1/4 120 90
45. 32 36
7 9 40 48
27 [Class-X – Maths]
46. 10 A B
20 B A
A B
47. 21
20
1
48. 100
370 433 300 398
400
49. 2 1
35 3
4 65
(i)
(ii)
50.3 2
4 1
600 550
(i)
(ii)
[Class-X – Maths] 28
1. d 2. c
3. c 4. b
5. a 6. c
7. a 8. a
9. b 10. c
11. c 12. d
13. b 14. d
15. b 16. a
17. = x = y
2 702 95x y
x y
18. = x,
201 1 4
225
y xy
x y
19. 20.13
21. 22. (2, 2)
23. (2, 0) p = 7 24.
25. p 4 26. 191,2
k k
28. (7, 3), 18 29. 5, 1
30. –5, 10 10, 5
31. (7, 13) 32. x = a, y = b
33. (2, –1) 34. (3, 2)
29 [Class-X – Maths]
35. (1, 2), (1, 0) 36. (6, 0), 1 : 2
37. (2, 1) 38.
1 1,2 4
39. 20000, 10000 40. (4, 9)
41. 15, 10 42. 27, 12
43. 41 14 (2) 44. 96
45. 2 / , 10 / 46. 100, 80
47. 101, 5 48. 448 298, 12
49. (i) 15, 5 (ii)
50. (i) 100, 150. (ii)
[Class-X – Maths] 30
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.
31 [Class-X – Maths]
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
[Class-X – Maths] 32
4. 5 : 7
(a) 25 : 49 (b) 7 : 5
(c) 1 : 1 (d) 5 : 7
5. AD, A BD = 4 DC = 3 AB = 6
AC
(a) 4.2 (b) 4.5
(c) 4.8 (d) 5
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
33 [Class-X – Maths]
8. ABC ~ QRP
ABC 9 ,4PQR
AB = 18 , BC = 15
PR = ...........
(a) 10 (b) 9
(c) 4 (d) 18
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
ABC 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
(a) 1 (b) –1
(c) 3 (d) –3
12. ABC ~ PQR 13
BCQR
ar PRQar BCA
[Class-X – Maths] 34
(a) 9 (b) 3
(c)13 (d)
19
13. 12
(a) 12 (b) 6 2
(c) 6 (d) 6 3
14.
10
(a) 26 (b) 24
(c) 30 (d) 16
15. ABC PQR 36 24
PQ = 10 AB = ..........
(a) 10 (b) 20
(c) 25 (d) 15
16. ABC ~ APQ, BC = 8 PQ = 4 AC = 6.5
AP = 2.8 AB AQ
B
P
Q
C
A
35 [Class-X – Maths]
17. ABC AD BC, BD 1 .3
CD CA2 = AB2 × 212
BC
18. ABC AD BC
AD2 = 3 DC2
19. ABC, PQR AC = AB = 4
RQ = 10 BC = 6 PR PQR
20. AE
E
DCB
A
8
6 3
4
21. PQR DE || QR 1 .4
DE QR
ar PQRar PDE
P
ED
RQ
[Class-X – Maths] 36
22. ABC PQR B = Q 12
AB BCPQ QR
PRAC
23. ABC B A C AD CE
AC = 5 3 5
2AD CE
24. DE || BC, DE 10
2
A
ED
CB3
25. 16
8
26. DE||AC ,BE BCEC CP DC||AP
BE C P
A
D
37 [Class-X – Maths]
27. ABC PBC BC
AB = BP.
28. ABCD B = 90°, AD2 = AB2 + BC2 + CD2. ACD =
90°.
BA
C
D
29. DE || BC, DE = 3 BC = 9 (ADE) = 30 2
BCED) A
ED
CB9
3
30. 8
17 10
31. PRQ PR 6
8 Q P R PQ = 24
RQ = 26 QPR
[Class-X – Maths] 38
32. SQ PQRS PQ RS E F EF, SQ G
SG × QE = QG × SF.
33. a b
aba b
D
O
C A
B
L
a b
34. PQRS O PQ||RS PQ =3RS, POQ ROS
35.
36.
37.
38. BL CM ABC A = 90°. 4(BL2 + CM2) = 5 BC2.
39. ABCD
39 [Class-X – Maths]
40. DE || BC AD : DB = 5 : 4
ar DEFar CFB
A
B C
D
F
E
41.
D, E, F
ABC
(i)( )
( )
DEF 14ABC
(ii)
42.
ABC PQR
(i) x y
(ii) ABC PQR
(iii)
[Class-X – Maths] 40
(iv)
A
C
B12
15
9
Q
8
P
R
43. A B C
CB,AC AC = 2x CB = 2(x+7)
26 B
A A B
44.
(i)( )
( )
ABC AODODBC
(ii)
A C
DB
O
41 [Class-X – Maths]
45.
ML NR 40°
K ML a MN=b
NK=c
(i) NR
(ii)
40° 40°
M b N C K
xa
L
R
1. c 2. b
3. a 4. d
5. b 6. d
7. a 8. a
9. b 10. c
11. c 12. a
13. d 14. b
15. d 16. AB = 5.6 AQ = 3.25
[Class-X – Maths] 42
18. APQ ~ ABC
19.203 20. 55
21. 16 : 1 22.12
23. 1 25 – 6 54 24. 2.5
25. 163 29. 240 2
30. 9 , 6
31. 90° 34. 9 : 1
39. 4 : 1 40.2581
41. (ii)
42. (i) x = 10, y = 6, ( )
( )
ABC 94PQR
(ii)
(iii)
43. (i) 8
(ii)
44. (ii)
45. (i) acx
b + c
(ii)
43 [Class-X – Maths]
5
1. ABC B = 90° ‘A’
sin A
cos A
tan A
cot A
sec A
cosec A
2
1 1sin , coseccosec sin
1 1cos , secsec cos
[Class-X – Maths] 44
1 1tan , cotcot tan
3.
sin costan , cotcos 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 1 32
12
12 0
tan A 013 1 3
cosec A 2 223 1
sec A 123 2 2
cot A 3 113 0
45 [Class-X – Maths]
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
[Class-X – Maths] 46
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) 112
8. sec + tan = x, sec =
(a) 2 1xx
(b) 2 12
xx
(c) 2 12
xx
(d) 2 1xx
9. cot sin cos2 2
(a) cot cos2 (b) cot2
(c) cos2 (d) tan2
10. sin – cos = 0, 0 90°
(a) cos (b) 45°
(c) 90° (d) sin
47 [Class-X – Maths]
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 2sin 20 sin 70 sec 60
2 cos 69 cos 21 K k
(a) 1 (b) 2
(c) 3 (d) 4
15. 1tan7
2 2
2 2cosec sec ................cosec sec
(a)34 (b)
57
(c)37 (d)
112
[Class-X – Maths] 48
16. PQR Q = 90° 3sin5
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 21 tan
3
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 3sin 32 tan 15 tan 60 tan 75
29. sin + sin2 = 1 cos2 + cos4
30. sin 2 = cos ( – 36°), 2 – 36°
49 [Class-X – Maths]
31.
cosec4 – cosec2 = cot2 + cot4 .
32. sin (3x + 2y) = 1 3cos 3 2 ,
2x 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 cos cos 45 .1 tan 1 cot
A A A AA A
35.
sec 1 sec 1 2cosecsec 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°
40. p = tan + sec 1pp
[Class-X – Maths] 50
41.
2 2– tan 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
46.
1 : 1 ACB
51 [Class-X – Maths]
47. x = sin2, y = cos2 x y
(a)
(b)
(c)
48. A B
1sin (A – B) =21cos (A +B) =2 0° < A +B 90°
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. 3cos5
P
17. 90° 18.2512
[Class-X – Maths] 52
19. 5 20. 7
21.54 22. 30°
23. 30° 24. 1
25. x = 20. 26. 10°
27. 9 28. 1
29. 1 30. 42°
32. x = 20, y = 15
33. 3 1 3 1,
2 2 2 2 takee A = 45°, B = 30°
36.172 38.
1312
40. 2 sec 41. 2 3
46. 45°,
47. (a) 1 (b) (c)
48. A = 45°, B = 15°
53 [Class-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
l =
f1 =
f0 =
f2 =
h =
[Class-X – Maths] 54
3.
2n Cfl hf
l =
n =
Cf =
f =
h =
4. = 3 – 2
5.
x-
x-
x-
x-
55 [Class-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) 2
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
[Class-X – Maths] 56
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)
57 [Class-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
19. 11 50 49
52
[Class-X – Maths] 58
(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 p 8 4
59 [Class-X – Maths]
25. 20-30
10 1
20 14
30 36
40 59
50 60
26. 40
27. 40
[Class-X – Maths] 60
28. 62.8 x y
0–20 20–40 40–60 60–80 80–100 100–120
5 x 10 y 7 8
29.
300 0
250 12
200 21
150 44
100 53
50 59
0 60
30. 46 x y
10–20 20–30 30–40 40–50 50–60 60–70 70–80
12 20 x 65 y 25 18 230
31.
0–10 10–20 20–30 30–40 40–50 50–60 60–70
6 8 10 15 5 4 2
61 [Class-X – Maths]
32. 100
10 10
20 15
30 30
40 50
50 72
60 85
70 90
80 95
90 100
33.
20–30 30–40 40–50 50–60 60–70 70–80 80–90
8 12 24 6 10 15 25
34. 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
35.
18-20 20-22 22-24 24-26 26-28 28-30
63 50 35 27 16 9
[Class-X – Maths] 62
36.
18-28 28-38 38-48 48-58 58-68 68
6 11 21 23 14 5 8 0
37. 50
0-20 20-40 40-60 60-80 80-100
6 11 17 12 4
38.
50-55 55-60 60-65 65-70 70-75 75-80
10 12 17 13 16 22
63 [Class-X – Maths]
39. 35 IGL LPG
38-40 40-42 42-44 44-46 46-48 48-50 50-52
3 2 4 5 14 4 3
40. 35
HB 8 10 12 14 16
3 7 13 23 35
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
[Class-X – Maths] 64
21. 161 22. x = 25
23. 14 24. p = 3
25. 22 26. 40
27. 147.5 28. x = 8, y = 12
29. 182.50 30. x = 34, y = 46
31. (Mean) = 30, (Median) = 30.67, (Mode) = 33.33
32. 41.81 33. 60
34. x = 10, y = 5.
35. (a) 22.1 year (b) for safety (c) (discipline) (Knowledge & obeying traffic rules)
36. (mode) - 49.81 (Social responsibilities)
37. (median) = 49.41m (Awarenessfor physical fitness) (Importance of sports) (Healthy competition)
38. (a) (mean) = 66.88, (median) = 67.3, (b) (generationgap), (developing moral & social value),
(motivation), (c) (moral values)
39. 45.8, 46.5, 47.9
40. (Awareness for Fitness), (moralvalues).
65 [Class-X – Maths]
– I
X (SA - 1)
Time Allowed : 3 hours Maximum Marks : 90
1.
2. 31 A, B, C D
A 4 1 B 6
2 C 10 3 D 11
4
3. 1 4
4.
1 10
1. XY QR PX 1XQ 2
P
YX
Q R
[Class-X – Maths] 66
(a) XY=QR (b) 1
XY QR3
(c) (XY)2 (d) 1
XY QR2
2. sin(60° + A) = 1 cosecA
(a) 1 (b) 0
(c) 12 (d) 2
3. .( ).( ) 2sec 1+ sin 1– sin k k
(a) 0 (b) 1
(c) –1 (d) 2
4. 2, 3, 5, 4, 2, 6, 3, 5, 5, 2 x 2 x
(a) 2 (b) 3
(c) 4 (d) 5
5. 6n n
6. ax2 – 6x – 6 4 a
7. ABC ~ QRP,
9 ,4
ar ABCar PQR
AB = 18 , BC = 15 PR
8. 16 cot A = 12sin cossin – cos
A AA A
9. 56, 96 324
67 [Class-X – Maths]
10. 24, 25, 26, x + 2, 30, 31, 34 27.5
x
11.
12. x4 – 20x3 + 23x2 + 5x – 6 2 3
13.
3m 3m + 1
14. sin (3x + 2y) = 1 3cos 3 2
2x y 0 3x + 2y 90°
x y
15. 5x3 – 13x2 + 21x – 14 3 – 2x + x2
16. x y
30 4 10x y x y
40 55 13x y x y
x ± y
17. 62.8 50 x
y
0–20 20–40 40–60 60–80 80–100 100–120
5 x 10 y 7 8
[Class-X – Maths] 68
18. PQRS O PQ||RS
PQ = 3RS, POQ ROS
19. A, B C ABC
sin cos2 2
B C A
20.
38–40 40–42 42–44 44–46 46–48 48–50 50–52
3 2 4 5 14 4 3
21. 5 2 – 5
22.
x + 3y = 6, 2x – 3y = 12
23.
tan cot1– cot 1– tan = 1+ sec . cosec
24. K
2
3 1 3 2 0
1 2 5 0
K x y
K x K y
25.
50-55 55-60 60-65 65-70 70-75 75-80
2 8 12 24 38 16
69 [Class-X – Maths]
26. 4x3 – 8x2 + 8x – 1 d(x)
(2x2 – 3x + 2) (x + 3) d(x)
27.
28.
cos 1 sin 2 sec .1 sin cos
A A AA A
29. ABC, AB=AC B AC
BD
BD2–CD2 = 2CD . AD.
30.
2 2sec . cosec (90° – ) – tan . cot (90° – ) + sin 55° + sin 35°tan10° . tan20° . tan60° . tan70° . tan80°
31.
50-55 55-60 60-65 65-70 70-75 75-80
10 12 17 13 16 22
(a)
(b)
(c)
1. b 2. d
3. c 4. a
6. a = –3/2 7. 10 cm
[Class-X – Maths] 70
8. 7 9. 4
10. x = 25 12. ±12
13. x = 20, y = 15 14. A = 60°, B = 30°
15. Q = 5x – 3, R = –5 16. x = 5, y = 3
17. x = 8, y = 12 18. 9 : 1
20. 46. 5 Kg. 22. 1 : 2
24. K = –1, 192
K 26. d (x) = 2x – 1
30.23
31. (a) 66.8.
(b) Generation gap, lack of social and moral values.
(c) Impart social and moral values in the society.
71 [Class-X – Maths]
– 2
- 1
- X
3 90
(i)
(ii) 311-1 4 6
2 10 311 4
(iii)
(iv)
1 8 1
1. ACB APQ BA = 6 cm, BC = 8 cm PQ = 4 cm
AQ
(a) 2 cm (b) 2.5 cm
(c) 3 cm (d) 3.5 cm
[Class-X – Maths] 72
P
QA?
C
B 6
8
4
2. 1sin2
1cos2 , +
(a) 0° (b) 30°
(c) 75° (d) 90°
3. sin – cos = 0 ) 4 4(sin + cos
(a) 1 (b)34
(c)12 (d)
14
4.
10 20 30 40 50
2 13 33 48 54
(a) 40 - 50 (b) 30 - 40
(c) 20 - 30 (d) 10 - 20
73 [Class-X – Maths]
9 14 2
5. 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5
6. 2 3 2
(a) 0 (b) 1
(c) 2 (d) 3
7. 135 225
8.AO OB 1OC OD 2
= = AB = 5 cm DC
D C
O
A B5
9. tanA = cotB A + B = 90°
10. 15 'p'
x
5 6
10 p
15 6
20 10
25 5
[Class-X – Maths] 74
15 24 3
11. 3 + 2 5
12. 3x4 + 6x3 – 2x2 – 10x – 5
53
5–3
13. 'k'
x + 2y = 3y
(k – 1)x + (k + 1)y = k + 3
14. A B 200 km
A B
10
2
15.
CD
F
A B
E
75 [Class-X – Maths]
16. ADC = BAC BC × CD = ACC2
A
CB D
17. 2 2 2cos 30°cos 45° + 4sec 60° 2 21 cos 90° – 2tan 60°2
18.
(secA + tanA)(1–sinA) = cosA
19.
0-10 10-20 20-30 30-40 40-50 50-60
8 10 16 24 15 7
20. 62.8 x
0-20 20-40 40-60 60-80 80-100 100-120
5 8 x 12 7 8
25 34 4
21. 867 255 HCF
[Class-X – Maths] 76
22. x3 + 2x2 + kx + 7 x – 3 25
'k'
23. x + 2y = 4 7x + 4y=18
(2, 1)
24.
25.
26.
2 2
2 2cosec 65° – tan 25° 1 tan10 tan30 tan80
3sin 17° + sin 73°
27.–
–
secA 1 secA 1+secA 1 secA 1
28. sin (A+B) = sinAcosB + cosAsinB sin75°
29. [ ]
0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40
10 16 30 42 50 30 16 1
30.
77 [Class-X – Maths]
5-15 15-25 25-35 35-45 45-55 55-65
6 11 21 23 14 5
v k¡d M +ksa d k 35.5
31. x y
99x + 101y = 1499
101x + 99y = 1501
79 [Class-X – Maths]
S.A. - 2
1. 81
2. 90
3. 99
4. 108
5. 117
6. 134
7. 139
8. 153
163
[Class-X – Maths] 80
81 [Class-X – Maths]
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 ,2
b b acxa
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
[Class-X – Maths] 82
7. ax2 + bx + c = 0, a 0, D = b2 – 4ac
1. ax2 + bx + c = 0, a 0 b2 – 4ac
(a) 0 (b) 0
(c) 0 (d)
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. x2 – ax – 4 = 0 a
(a) 0 (b) 1
(c) 2 (d) 4
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
83 [Class-X – Maths]
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
[Class-X – Maths] 84
13. x2 + px + 12 = 0 1 : 3 p
(a) ± 2 (b) 8
(c) 4 (d) 8
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 0, 0ax bx c a c
(a) b (b) a
(c) c (d) 0
16. x2 + 7x + k = 0 –2 k
17. 4x2 + 3px + 9 = 0 ‘p’
18. m mx2 + 6x + 4m = 0
19. 63
20. 1 14 , 0.
4x x
x
85 [Class-X – Maths]
21. C 4x2 – 2x + (c – 4) = 0
22. 51 378
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. k x2 – 5x + 3(k – 1) 11
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 2
x x x xx x
31. 1 1 1 1 , , , 0 & –a b x x a ba b x a b x
[Class-X – Maths] 86
32. 24 3 5 2 3 0.x x
33. abx2 + (b2 – ac)x – bc = 0
34.
1 3 10 , 2, 4.2 4 3
x x x xx x
35.
1 1 11 , 4, 7.4 7 30
x xx x
36. 100
30
37. 80 4
1
38. 35 18
39.
46
40. 9 12
3
41. 360
5
42. 6
2
43. 2 224 2
87 [Class-X – Maths]
44.
5 2 50
45.
160
46.
47.
15
48.8211
1
49. 6500 15
30
50. A B 10 A B
12 B
[Class-X – Maths] 88
1. b 2. c
3. c 4. a
5. a 6. d
7. d 8. b
9. a 10. a
11. b 12. c
13. b 14. a
15. b 16. k = 10, = – 5
17. p < – 4 or p > 4 18.32
19. x2 + 2x – 63 = 0 20. 14,4
21. c = 8 22. 9, 42
23. k = 14 24.77,4
25. K = –7 26. 10, 5
27. D = 0.
28. (a) (b) 33, .2
29. 5, 10 30. 6, 1
31. –a, –b 32. 3 2,4 3
33. ,c bb a
34.55,2
35. 1, 2 36. 5 × 20, 10 × 10
37. 16 38. 57
39. 4, 5, 6 40. 3
89 [Class-X – Maths]
41. 40 42. 26 24 10,
43. 16 44. 20
45. 6 , 12 46. 29 , 5
47. 5 , 3
48. 5, 6
49. 50
50. 30
[Class-X – Maths] 90
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 12nnS a n d
‘l’
.2nnS a l
91 [Class-X – Maths]
6. (i) an d = an – an–1.
(ii) sn n an = sn – sn–1
(iii) a, b, c 2b = a + c.
(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 ca (b)
2
a cb
(c)
2a bc (d) b = a + c
[Class-X – Maths] 92
6. x – 7, x – 2, x + 3 12 .............
(a) x + 62 (b) x – 48
(c) x + 48 (d) x – 62
7. 1 2 38 , 8 , 8 ,8 8 8
.............
(a) 18
(b) 118
(c) 188
(d) 1
8. –5, –2, 1, ............. n
(a) 3n + 5 (b) 8 – 3n
(c) 8n – 5 (d) 3n – 8
9. n 5 – 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
93 [Class-X – Maths]
13. n n2, n
(a) 2n – 1 (b) 2n + 1
(c) n2 – 1 (d) 2n – 3
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. 4 81
7
20. –
3 23 406
21. 6 102 6
22. n sn = 3n2 – 4n, n
[Class-X – Maths] 94
23. 24
44
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
1 76
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
95 [Class-X – Maths]
35. 2 29
155
36. 8 15
28
37. 5
3
38. 6 42 10 30
1 : 3 11
39. 200
40 30
40.a15
41. 8 140 24 996
42. 15 594
43.
3 12
375
44. 20 20
1 30
45. 16 528 16
1552
[Class-X – Maths] 96
46. 2 4 6
2011
47. 120000 8%
300
48. 10
150 50
550
600
49. 200
20 19, 18
200
50. 165
15 14 13
10 12
14
97 [Class-X – Maths]
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. 12 20. 14
21. 15 22. 6n – 7, = 6
23. –13, –8, –3, 2 24. 9800
25. 23 26. 0, 2
27. 0
28.1 5 7 9 11 13 15 17, , , , , , ,2 6 6 6 6 6 6 6
29. = 3, = 2 30. –76, –80
31. 59 32. 19 or 20, {20 }
33. 5, 8, 11 34. –1520
35. 3 36. 1217, 72
d
37. 99090 38. = 2, 11 = 22
39. 1360 40. 3
[Class-X – Maths] 98
41. 7, 10, 13, 16, ........ 42. 852
43. 25 44. 900
45. = 3, = 4
46. 812,
47. 2520, 2220, 1620, 1320
48. 600,
49. 16,
50. 6
99 [Class-X – Maths]
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 y
m 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
[Class-X – Maths] 100
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, 7b) (d) (2a, 0)
101 [Class-X – Maths]
6. A (4, 0), B (0, –7) 0 OAB
(a) 11 (b) 18
(c) 28 (d) 14
7.
11 2, 5 , 53 3
P 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. P (3, 2) x- x-
(a) 2 (b) 3
(c) 13 (d)
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
[Class-X – Maths] 102
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, 3)
(a, b)
(a) (4, 5) (b) (5, 4)
(c) (5, 2) (d) (3, 2)
16. (3, a) 2x – 3y = 5 a
17. PQR P (–4, 2) QR S (2, 5)
18. (3, 5) (7, 1) (a, 0) a
19. (0, a), ,
2 2b a
(b, 0)
20. AB A
(3, –4) B
103 [Class-X – Maths]
21. C, A (1,1 ) B(2, –3)
3AC=BC, C
22. p, (–3, 9), (2, p) (4, –5)
23. A (6, 7 ), B (4, –5 ), C (x, 2x )
3 x
24. P Q, A(1, –2) B (–3, 4)
P
25. (2 –1, 7) (–3, –1)
20
26. 4 (5,
0) 5
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, 4), (–5, –2) (3, –5)
3x + 8y + 31 = 0
31. K (1, 2) E (6, 8) F (2, 4)
K EF
32. ABC 5 A(2, 1) B(3, –2)
C, x – y – 3 = 0 C
[Class-X – Maths] 104
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), B (4, 5), C (–1, 4) D (–2, –1)
ABCD
37. (3, 1) (–2, 5) 34
38. (6, –3), (3, K) (–7, 7)
15 K
39. A(1, 3) B(2, 7) 3x+y=9
40. X- P, (4, 5) (1, –3)
P
41. ABC, B = 90° 34AB B C
(4, 2) (–1, y) (ABC) = 17 y
42. P (3, 4) A (a + b, b – a) B (a – b, a + b)
3b – 4a = 0.
43. ABCD A (–5, 7), B (–4, –5),
C (–1, –6) D (4, 5) ABCD
105 [Class-X – Maths]
44. A (2, 1) B (5, –8) P Q
P,A P 2x – y + k = 0
K
45. (3, –4) (1, 2) P Q
P Q (p –2)
5 ,3
q
p q
46.
P(–1, 3), Q(1, –1) R(5, 1)
Q R
S P
47. A(7, 5), B(2, 3)
C(6, –7)
48. (7, 3) (4, –3)
(2, 2)
49. A(a, o), B(o, b) C(1,1) 1 1+ = 1a b
50.
100
(5, 6), (1,
5), (2, 1) 1 cm2 2
[Class-X – Maths] 106
1. c 2. a
3. b 4. b
5. c 6. d
7. c 8. a
9. a 10. d
11. b 12. b
13. d 14. c
15. c 16. 13
a
17. (0, 4) 18. a=2
19. – 20. (–3, 4)
21.
05 ,3 22. p=–1
23. x = 8 24. –
01,3
25. = 2, –4 26. 2, 8
27. (0, 1) 28. a=0, b=10
29.
10 33,7 7 30. —
31. 5, 32. (5, 2)
33. 4 2 34. (–1, 3)
35. (0, –2) 36. —
37. –
3 , 44 38.
21k13
107 [Class-X – Maths]
39. 3 : 4 40.
17 , 08
41. y = –1, 5 42. —
43. 72 (72 square units) 44. k = –8
45.7 , 03
p q
46. 5 (units)
(interest in mathematics),
(friendship)
(cooperation)
47. (a) (Right Angled Triangle),
(b) (sports), (activeness), (Critical thinking)
48. (a) (Mona)
(b) (Time bound), (Reality)
49. –
50. 11500
[Class-X – Maths] 108
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°
109 [Class-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. 11 : .3
(a) 30° (b) 45°
(c) 60° (d) 90°
7. 50 3
60°
(a) 100 (b) 50
(c) 150 (d) 75
[Class-X – Maths] 110
8. (1) ABCD
30°
D C
BA
10
(1)
(a) 40 (b) 20 3 1
(c) 60 (d) 10 3 1
9. 10
30°
(a) 30 (b) 20
(c) 10 (d) 15
10. 15 15
(a) 30° (b) 45°
(c) 60° (d) 75°
11. (2) D, BC, CAB = 1 DAB = 2
tan 1 : tan 2
(a) 2 : 1 (b) 1 : 2
(c) 1 : 1 (d) 1 : 3
111 [Class-X – Maths]
A
BC D
2
1
(2)
12. (3) 8tan
15 PQ = 16 PR
P
QR
(3)
(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
[Class-X – Maths] 112
14. 9 16
(a) 18 (b) 16
(c) 10 (d) 3012
15. (4) ABCD AL + AM =
A B
CD
60°
60°M45
60
L
(4)
(a) 70 3 (b)70
3
(c) 210 3 (d) 70
16. 30
45° 60°
17. 60
30° 60°
18. h
2 sectan tan
h
113 [Class-X – Maths]
19. 60° 50
30°
500 3
20. A 60° 15
30° 720
3 1.732 .
21. 20
60° 45°
22. 180060° 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
[Class-X – Maths] 114
27. A
30° 12
60°
28. 18
60°
30°
29.
60° 40
30°
30. 3000
60° 45°
31. 10
30° 45°
32. 100
30° 20
45°
33. 100
30° 60°
3 1.732
34. P Q
115 [Class-X – Maths]
54° 36° P Q
10 20
2 1.414
35. 5
A 60° A
45° 3 1.732
36. 20
30°
37. P Q 20
B
B P 60° Q 45°
38. 1.2 88.2
60°
30°
[Class-X – Maths] 116
1. c 2. b
3. a 4. d
5. b 6. c
7. a 8. b
9. a 10. b
11. b 12. b
13. b 14. d
15. a 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. 115.47
34. 14.14 35. 6.83
36. 10
37. P, 14.64
38. 58 3
117 [Class-X – Maths]
5
1.
2.
1. (1) PQ POQ + QPO
P
Q
O
(1)
(a) 120° (b) 90°
(c) 80° (d) 100°
2. PQ, 5 PQ = 12 , Q
OP
[Class-X – Maths] 118
(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
5. (4) PQ PR
PQ = 4 OQ = 3 OR = 2 PR
119 [Class-X – Maths]
PO
Q
R
(4)
(a) 5 (b) 21
(c) 4 (d) 3
6. (5) P, Q R AB = 4 BP = 2
ABC
O
RQB cP
A
(5)
(a) 12 (b) 8
(c) 10 (d) 9
[Class-X – Maths] 120
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)
121 [Class-X – Maths]
(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)
[Class-X – Maths] 122
(a) 90° (b) 110°
(c) 135° (d) 145°
13. (10) O PA PB AQB
A
Q
B
Po 40°
(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
123 [Class-X – Maths]
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. d1 d2 (d2 > d1) C
d12 = c2 + d1
2
17. 2.5 P 6
P
18. ‘O’ T TP TQ
OPQ = 30° TQP
19. (13) AP = 4 BQ = 6 AC = 9 ABC
[Class-X – Maths] 124
PR
Q
A
C
9
4
6 B
(13)
20. a, b c c
r
+
2a b – cr
21.
22.
23. (14) AC ‘O’ A x
o
C
A
B
40°
x
P Q (14)
125 [Class-X – Maths]
24. (15) PA PB KN = AK + BN.
P
K
N
A
B
o
(15)
25. (16) PQ 6 6 TP
TQ PTQ
T
P
Q
o
(16)
6
26. ABC AB = 12 BC = 8
AC = 10 AD, BE CF C
DB A
F E
(17)
[Class-X – Maths] 126
27. ABC AB
AC P PB = PC.
28. P PA PB, O
APB = 2 OAB
A
O
P B
(18)
29. 9 ABC,
AB = AC = 6
30. (19) AB = AC, ‘D’ AC BD 1 .4
AE AC
B D
A
C
E
(19)
31. (20) OP O
ABP
127 [Class-X – Maths]
A
B
o P
(20)
32. (21) AB = 13 , BC = 7 AD = 15 PC
o
BR
A
Q
DPC
S 4
(21)
33. 22 P O PT
PAB ON AB
(i) PA . PB = PN2–AN2
(ii) PN2–AN2 = OP2–PT2
(iii) PA . PB = PT2
[Class-X – Maths] 128
O
ANB
A
T
22
34. O AB AC BAC = 30° C
AB D BC=BD
35. (23) PA PB ‘O’
OP, AB
P
A
B
o
(23)
36. (24)
o
BR
A
Q
DPC
S r
23
5
29
(24)
129 [Class-X – Maths]
37. (25) 3 ABC
3 5
35
A
B
Co
(25)
38. ABC BC P AB
AC Q R AQ,
ABC
39. (26) XP XQ X ‘O’
R XA + AR = XB + BR.
X
A
B
P
Q
RO
(26)
40. (27) PQ PB x y
[Class-X – Maths] 130
P
A
B
Qo y
y
35°
x
(27)
41. A B 7 B C 5
C A 8 A, B, C
(iii)
(ii)
42.
(i)
(ii)
43. 1700
AB CD
AD BC
(i) AB + CD = AD + AC
(ii)
131 [Class-X – Maths]
A B
CD28
44. P A B
P A 10
P B
(i)
(ii)
A
P
B
10
29
45.
(i)
(ii)
(iii)
[Class-X – Maths] 132
A B
D C
6 ft
3 ft
5 ft
4 ft
30
1. b 2. a
3. c 4. d
5. b 6. a
7. c 8. b
9. d 10. d
11. a 12. c
13. a 14. b
15. a
17. 4 18. 60°
19. 15 23. 40°
25. 120°
26. AD = 7 BE = 5 CF = 3
29. 8
32. 5 36. 11
37. 32 40. x = 35°, y = 55°
133 [Class-X – Maths]
41. (i) A, B, C
(ii)
42. (i) (ii)
43. (i)
44. (i) 10 (ii)
45. (i) 36 (ii)
(iii)
[Class-X – Maths] 134
6
1.
2.
1.
(a) 185° (b) 90°
(c) 120° (d) 60°
2. AB 2:3 AX
BAX AX
(a) 3 (b) 6
(c) 5 (d) 2
3. AB 3:8 AX
BAX AX
A1, A2, A3, . . . . . . B
135 [Class-X – Maths]
(a) A12 (b) A11
(c) A3 (d) A8
4.
(a) 6 : 2 (b) :122
(c) )(2 + 3 ): (2 – 3 (d) ) : )( 3 + 2 ( 3 – 2
5.
m : n
(a) m > n (b) m = n
(c) m < n (d)
1. a 2. c
3. b 4. b
5. a
1. AB = 7 AB P AP : PB = 3 : 4
2. PQ = 10 PQ A 25
PAPQ
PAA AQ
3. ABC BC = 6.5 , AB = 4.5
ACB = 60°. ABC
[Class-X – Maths] 136
ABC 45
4. XYZ XY = 5 , YZ = 7 XYZ = 75°.
ABC ~ XYZ XYZ 32
5. 8 5
34
6. ABC AB = AC BC = 7
120° A´B´C´ ~ ABC
ABC 113
7. PQR Q = 90°, PQ = 6 QR = 8
P´QR´ ~ PQR PQR23
8.
1.5
9. PQR 5 PQ´R´
1 .
´ 2PQPQ
10. 4 O P
OP = 6 P PA PB
PA PB
11. AB = 8 AB
O OPAB P
137 [Class-X – Maths]
12. OP = 3 PQR =45°
OQ = 5 Q
13. 3.5 O P
PA PB APB = 45°, AOB +
APB
14. 4 P
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
19. 7
7
[Class-X – Maths] 138
(i)
(ii)
20.
ABCBC = 7 B = 45° A = 105°
(i)3/4
(ii)
19. (i) 3.5 (ii)
20. (ii)
139 [Class-X – Maths]
7
1. = r2 ‘r’
2. 212
r
3.
= (R2 – r2) = (R + r) (R – r); R > r
‘R ’ ‘r’
4.
=3 60
180°
× 2 rl
180r
l
5.
2360
r
6. 60 = 360°,
1 360 6 .60
7. r h = 2rh
r
R
r
r
l
r
[Class-X – Maths] 140
8. r h = 2rr + h)
9. r h = r2h
10. r h = rl, l
2 2 l r h
11. = r (l + r)
12. 213
r h
13. r = 4r2
14. r = 2r2
15. r = 3r2
16. r 343
r
17. r 323
r
18. = l (r + R) ‘l’
r R
19. = l (r + R) + (r2 + R2)
20. = h (r2 + R2 + rR)
2 2l h R r
1.
(a) r = 1 (b) r = 7
(c) r = 2 (d) r = 0
141 [Class-X – Maths]
2. 7
(a) 36 (b) 14
(c) 7 (d) 14
3. 13 6
(a) 19 (b) 19
(c) 25 (d) 32
4. 4 : 5
(a) 4 : 5 (b) 16 : 25
(c) 64 : 125 (d) 8 : 10
5. 3
40°
(a) 2 cm2 (b) cm2
(c) 3 cm2 (d) 4 cm2
6. 5 10 2
(a) 2 (b) 4
(c) 22 (d) 8
7. 23m
(a) 4 (b) 33
(c)3 3
4(d) 2
[Class-X – Maths] 142
8. ‘r ’ ‘C’ ‘A’
(a)12
C Ar (b)12
A Cr
(c) C = 2 Ar (d) A = 2 Cr
9. 440 3 66 2
(a)403 (b)
203
(c) 440 (d) 66
10. ‘a’
(a) a2 (b) 3a3
(c) a3 (d) 6a3
11.
(a) 1 : 1 (b) 1 : 2
(c) 3 : 1 (d) 1 : 3
12. 16 8
20
(a) 28 (b) 10
(c) 44 (d) 20
13. r h
143 [Class-X – Maths]
(a) 2 rh (b) 2 ( + )r r h
(c) 2 (2 + )r r h (d) 2 (3 + )r r h
14. 8:27 r R
r : (R–r) is
(a) 9 : 4 (b) 3 : 2
(c) 3 : 1 (d) 2 : 1
15.
(a) (b)
(c) (d)
16. 7 45°
17. 108
18. 10 5000
19.
20. 7
21. 10 440
22.
[Class-X – Maths] 144
4
6
23.
24
P
QR
o
7
24. ‘r’
25. 20
60°
26. 12 8.00 a.m
8.05 a.m.
27. 3.14
145 [Class-X – Maths]
20
20
20 20
28.
14 1414
29. ABCD
4
4
4
C
DA
B
30. 16 × 12 × 8 4
[Class-X – Maths] 146
31.
32. 15
660 2
33. 729 3
34. 6 , 8 10
35. 448 3 7
36. 64 2
37. 24 2 8
38. 30 × 24 × 18
39. 16 2 4
40. 7
41. 60° 3
42. (8 × 4 × 2) 3
43. ‘2h’
‘r’
147 [Class-X – Maths]
44. 6
45. ABC (A = 90) AB AC
A
CB
4 3
46. ABC 4
o
4 4
4
A
CB
47. 7
[Class-X – Maths] 148
48.
5
12
49.
2 8
2 8
50.
14
14
149 [Class-X – Maths]
51. 7
14
52. 80 66
10
53. BC
5
A
B C
12
54.
1 4
9 9
55.
56. 150 100 2
× 1.5 15
3
57.
36 18
[Class-X – Maths] 150
27
58. 5.5 15.5 24
59. 2 6
60 30
60.
14 7
5.5 10.5
14
7
5.5 10
.5
61.‘h’
62. 12 10
151 [Class-X – Maths]
63.
8 6
64.
1.45 30
( =3.14)
65. 10
3
10
3.14 10 cm
( =3.14)
1. c 2. c
3. b 4. b
5. b 6. b
7. d 8. b
9. b 10. b
11. c 12. d
13. c 14. d
15. d 16. 19.5 cm
17. 42 cm 18. 2m
[Class-X – Maths] 152
19. : 3 20. 81 cm2
21. 14m 22. (16 + ) cm
23. 25 cm 24. r2
25. 60 / cm 26. cm2
27. 86 cm2 28. 462 cm2
29. (16–4) cm2 30. 24
31. 3: 1: 2 32. 7 cm
33. 9 cm 34. 12 335. 8 cm 36. 4 cm
37. 6 cm 38. 30 2cm
39. 2 cm 40. 3.5 cm
41. 27 cm3 42. 4 cm
43. 223
r h unit3 44. 113.14 cm3
45. 6 cm2 46. (16 – 12 3 ) cm2
47. 154 cm2 48. 2101914
cm
49. 154 cm2 50. 21 cm2
51. 154 m2 52. 4375
53.337 cm7 54. 49 cm2
55. 3 units 56. 100 hour
57. 36 cm 58. 1811.07 cm2
59. 3 m 60. 2926 cm3
61.23
h 62. 660 cm2
63. (a) 2m (b)
64. (a) 56. 52 L, (b)
65. (a) 9 , (b)
153 [Class-X – Maths]
8
1. E
E
P E
2. 1
3.
4. E P(E) + P(E ) = 1.
5.
0 P(E) 1.
1. E P(E) + P E = ........
(a) 0 (b) 1
(c) 2 (d) –1
[Class-X – Maths] 154
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 7
(a)7
16 (b)9
16
(c)1816 (d)
1416
7.
(a)15 (b)
45
(c)35 (d) 1
155 [Class-X – Maths]
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
[Class-X – Maths] 156
13. 52
(a)3
26 (b)3
13
(c)4
13 (d)8
13
14. 7
(a)16 (b)
13
(c) 1 (d) 0
15. 'E' P(E) 1x x
(a) 0 (b) 1
(c) 0.5 (d) 2
16. 100, 500 1000
17. 6
18. 50 35 15
19. 5 2510 15
20. 1000 5
157 [Class-X – Maths]
21. 600 42
22.
23. 10 10
24. 52
25. 53
26. 2 101
27. 1 20 3 7
28. 5 ‘n’ P( ) = 3 × P ( ) ‘n’
29. (1, 4, 9, 16, 25, 29) 29
30.
31. 1 12
[Class-X – Maths] 158
(a) 10 (b)
(c) 3 (d)
32.
(a) (b) 2
33.
(i) 2 (ii) 2
(iii) 3
34. 52
(i) (ii)
(iii)
35. 5 8 4
(i) (ii) (iii)
36. 120 12
37. 1, 2 3 x
1, 4 9 y
9
38. 1 90 90
(i)
(ii) (iii) 5
39.
159 [Class-X – Maths]
40. (i) 7 (ii)
10 (iii) 5
41.
(i) (ii)
(iii)
(iv)
42. 24
23
43. 10 25
P(E) + P(E) = 1
44. 400 0.035
45. 12 x
(i)
(ii) 4 2
46. 1.3
[Class-X – Maths] 160
(a) (b)
(c) (d)
47. P(E) + (E) 1
48. E 0 P(E) x x
49. 24000 5000
12000 2000
(i)
(ii)
(iii)
(iv)
50. 240 50%
25% 15%
1. b 2. c
3. b 4. a
5. b 6. b
7. b 8. c
9. a 10. b
11. a 12. d
161 [Class-X – Maths]
13. b 14. c
15. a 16.13
17. 0 18.3
10
19.27 20.
1200
21.93
100 22.16
23.16 24.
524
25.27 26.
9100
27.25 28. 15
29. 0 30.9
13
31. (i) 1
12 (ii) 12 (iii)
13 (iv)
12 32. (a)
14 (b)
12
33. (i) 38 ; (ii)
38 ; (iii)
18
34. (i) 1349 ; (ii)
349 ; (iii)
1049 35. (i)
517 ; (ii)
817 ; (iii)
1317
36.1011 37.
59
38. (i) 9
10 ; (ii) 1
10 ; (iii) 15 39.
34
[Class-X – Maths] 162
40. (i) 16 ; (ii)
112 ; (iii)
2536
41. (i) 4
13 ; (ii) 1
26 ; (iii) 2
13 ; (iv) 1113 42. 8.
43.27 44. 14, 0.965
45. (i) 12 –
12x
(ii) + 4
18x
46. (a)
47. 48. x = 1,
49. (i) 12 (ii)
112 (iii)
524
50.1 ,
10
163 [Class-X – Maths]
- I
X (SA - 2)
: 3 : 90
1.
2. 31 A, B, C, D A 4 1 B 6
2 C 10 3 D 11 4
3. 4 8
4.
1. 2x2 + kx + 1=0 –½ k
(a) 3 (b) –3
(c) 5 (d) –5
2. 0 PQ PR PQR = 50°
OQR
(a) 25° (b) 30°
(c) 40° (d) 50°
[Class-X – Maths] 164
P
Q
O
R
3. "EDUCATION"
(a)79 (b)
29
(c)49 (d)
59
4. AB (0, 4) B (–2, 3) A
(a) (2, 5) (b) (–2, –5)
(c) (2, 9) (d) (–2, 11)
5. x2–2x(1+3m)+7(3+2m)=0 m
6. 6 102 6
7. PQR PQ=10 cm, QR=8 cm, PR=12 cm
PS QT
165 [Class-X – Maths]
R
QP S
TU
8.
7cm
7cm 7cm
7cm
A
C B
9.
66
10. 72 227
11. 2x2 – 5x + 3 = 0
12. 15 n
9–5n
13. ABC BC=6.5 cm, AB=4.5 cm ABC = 60°
ABC
¾
[Class-X – Maths] 166
14. y- A(6, 5) B(–4, 3)
15. (3, 5) (–7, 9) (½, 6)
16. PQ=24 cm,
PR=7 cm O
O
Q
PR
17. 6 m 1.5 m 10 km/h
8 cm 30
1 =10000m2)
18. 231 cm2 23
19. 5
(i)
(ii)
(iii)
209. 3 5
167 [Class-X – Maths]
21.
400
22. 51
273
23. 120000 8%
300
24.
25.
O
26. 100 m
P Q P, Q
P Q
30° 45°
27. 31 96
[Class-X – Maths] 168
(i) 3
(ii)
(iii) 40
28. 4 cm 18
cm 6 cm
29. A(2, 3), B(4, k) C(6, –3) k
30. 10 cm
31. 75 m
30° 45°
1. a 2. a
3. d 4. a
5.–10 , 29 6. 15
7. PS = 4cm, QT = cm 8. 24.5 cm2
9. 500 10. 308 cm2
11.3 ,12 12. –465
169 [Class-X – Maths]
14.270,2
15. 1 : 3
16. 161.53 cm2 17. 56.25 hectare
18. 3.5 cm, 7 cm 19. 1 1 38 8 4
i ii iii
20. 4 cm 21. 12, 16
22. 21
23. (i) 2520, 2220, 1920, 1620, 1320
(ii)
30. 36.6 m 27. (i) 5
12 , (ii) 1
16 , (iii) 9
64 , (iv) 12
28. 48 cm2 29. K = 0
30. 1 : 7 31. 75 3 1 m
[Class-X – Maths] 170
- II
X (SA - 2)
: 3 : 90
1.
2. 31 A, B, C, D A 4 1 B 6
2 C 10 3 D 11 4
3. 1 4
4.
1. 10 3 30m
(a) 25° (b) 60°
(c) 30° (d) 90°
2. 53
(a)17 (b)
27
(c)47 (d)
57
171 [Class-X – Maths]
3.
(a) 2 (b) 4
(c) 8 (d) 16
4. 4:5
(a) 16:25 (b) 25:16
(c) 4:5 (d) 5:4
9 14 2
5. k+1, 3k 4k+2 A.P. k
6.
7. 72m
227
8. A AB
(2, –3) B (1, 4)
9. (5, –2), (6, 4), (7, –2)
10. 72
227
11.
(i) (ii) 3
[Class-X – Maths] 172
12. 13m.
7
13. A.P. 12½
2:3
14. CA=6 cm, AB=5 cm BAC = 45°
ABC
ABC 35
15. P 10m.
30° P
45°
16. A(3, 2) B(5, 1) P 1:2
P 3x–18y+k=0 k
17.
D14cm
7cm
18. 3m
105m 53m
19. x 2 2 212 9 8 6 0abx a b x ab
20. 4 –8
173 [Class-X – Maths]
21.
90
22. 15 km/h 30 km
4 30
23. x
1 1 4 ; 1, 2, 4.+1 + 2 + 4
xx x x
24.
25. O T TP
TQ PTQ = 2 OPQ
26. 60
30° 60°
27. 52
(i) (ii)
(iii) (iv)
28. A(0, –1), B(2, 1) C(0, 3) ABC
[Class-X – Maths] 174
29.
7
4.9
30.
10 4 15
31.437
3m
227