Chapter: 9th Maths

9th Maths Book Back Exercise Answers

Book Back, Exercise, Example Numerical Question with Answers, Solution: 9th Maths

ANSWERS

Chapter 1

Set Language

Exercise 1.1

1. (i) set (ii) not a set (iii) Set (iv) not a set

2. (i) {I, N, D, A} (ii) {P, A, R, L, E, O, G, M} (iii) {M, I, S, P}(iv) {C, Z, E, H, O, S, L, V, A, K, I}

3. (a) (i) True (ii) True (iii) False (iv) True (v) False (vi) False

(b) (i) A (ii) C (iii) ∉ (iv) ∈

4. (i) A = {2, 4, 6, 8, 10, 12, 14, 16, 18} (ii) B = { 1/2, 1/4, 1/6 , 1/8 , 1/10 } (iii) C = {64, 125} (iv) D = {- 4, − 3, − 2, − 1, 0,1, 2}

(i) B = {x : x is an Indian player who scored double centuries in One Day International} (ii) C = { x : x = n / [n + 1], n ∈ ℕ. (iii) D = {x : x is a tamil month in a year} (iv) E = {x : x is an odd whole number less than 9}

6. (i) P = The set of English months starting with letter ‘J’

(ii) Q = The set of Prime numbers between 5 and 31

(iii) R = The set of natural numbers less than 5

(iv) S = The set of English consonants

Exercise 1.2

1. (i) n(M) = 6 (ii) n(P) =5 (iii) n(Q) = 3 (iv) n(R) = 10 (v) n(S) =5

2. (i) finite (ii) infinite (iii) infinite (iv) finite

3. (i) Equivalent sets (ii) Unequal sets (iii) Equal sets (iv) Equivalent sets

4. (i) null set (ii) null set (iii) singleton set (iv) null set

5. (i) overlapping (ii) disjoint (iii) overlapping

6. (i) {square, rhombus} (ii) {circle} (iii) {triangle} (iv) { }

7. { }, {a}, {a, b}, {a, {a, b}}

8. (i) {{ }, {a}, {b}, {a, b}}

(ii) {{ }, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3 }, {1, 2, 3}}

(iii) {{ }, {p}, {q} {r}, {s}, {p, q}, {p, r}, {p, s}, {q, r}, {q, s}, {r, s}, {p, q, r}, {p, q, s}, {p, r, s}, {q, r, s}, {p, q, r, s}} (iv) P(E)= {{ }}

9 (i) 8, 7 (ii) 1024, 1023

10. (i) 16 (ii) 1 (iii) 8

Exercise 1.3

1. (i) {2, 4, 7, 8, 10} (ii) {3, 4, 6, 7, 9, 11} (iii) {2, 3, 4, 6, 7, 8, 9, 10, 11} (iv) {4, 7} (v) {2, 8, 10} (vi) {3, 6, 9, 11} (vii) {1, 3, 6, 9, 11, 12} (viii) {1, 2, 8, 10, 12} (ix) {1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12}

2 (i) {2, 5, 6, 10, 14, 16}, {2, 14}, {6, 10}, {5, 16} (ii) {a, b, c, e, i, o, u}, {a, e, u}, {b, c}, {i, o} (iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, {1, 2, 3, 4, 5}, {6, 7, 8, 9, 10,}, {0} (iv) {m, a, t, h, e, i, c, s, g, o, r, y}, {e, m, t,}, {a, h, i, c, s}, {g, o, r, y}

3. (i) {a, c, e, g} (ii) {b, c, f, g} (iii) {a, b, c, e, f, g} (iv) {c, g} (v) {c, g} (vi) {a, b, c, e, f, g} (vii) {b, d, f, h} (viii) {a, d, e, h}

4. (i) {0, 2, 4, 6} (ii) {1, 4, 6} (iii) {0, 1, 2, 4, 6} (iv) {4, 6} (v) {4, 6} (vi) {0, 1, 2, 4, 6} (vii) {1, 3, 5, 7} (viii) {0, 2, 3, 5, 7}

5. (i) {1, 2, 7} (ii) {m, o, p, q, j} (iii) {6, 9, 10}

6. (i) Y–X (ii) ( X ∪ Y)′ (iii) ( X – Y) ∪ (Y – X)

(vii) (A∩B)′ = A′∪B′

Exercise 1.4

(i) {1,2,3,4,5,7,9,11} (ii) {2,5} (iii) {3,5 }

Exercise 1.5

1. (i) { 3,4,6 } (ii) { −1, 5, 7 } (iii) { −3, 0,1,2, 3, 4,5,6,7, 8} (iv) { −3, 0,1,2 } (v) { 1,2,4,6 } (vi) {4, 6} (vii) {−1, 3, 4,6}

2. (i) { a,b,c,d,e,f } (ii) {a,b,d } (iii) { a,b,c,d,e,f } (iv) {a, b, d }

Exercise 1.6

1. (i) 15, 65 (ii) 250, 600

4. (i) 17 (ii) 22 (iii) 47

5. (i) 10 (ii) 10 (iii) 25

6. 1000

7. 8

8. Not correct

9. (i) 185 (ii) 141 (iii) 326 10. 70

11. x = 20 , y = 40 , z = 30

12. (i) 5 (ii) 7 (iii)8

13. 5

Exercise 1.7

1. (2) 2. (1) 3. (3) 4. (2) 5. (4) 6. (1) 7. (2) 8. (4) 9. (3) 10. (4)

11.(2) 12.(1) 13.(1) 14.(3) 15.(4) 16.(1) 17.(4) 18.(3) 19.(3) 20.(1)

Chapter - 2 :

Real Numbers

Exercise 2.1

1. D

2. – 6/11, − 5/11, − 4/11,... 1/11

3. (i) 9/40 , 19/80 , 39/160 , 79/320 , 159/640 ;

The given answer is one of the answers. There can be many more answers

(ii) 0.101, 0.102, ... 0.109

The given answer is one of the answers. There can be many more answers

(iii) – 3/2,- 5/4,- 9/8,- 17/16,- 33/32

The given answer is one of the answers. There can be many more answers

Exercise 2.2

1. (i) 0.2857142..., Non terminating and recurring (ii) , Non terminating and recurring (iii) , Non terminating and recurring (iv) 1.635, Terminating

5. (i) Terminating (ii) Terminating (iii) Non terminating (iv) Non terminating

Exercise 2.3

2. (i) 0.301202200222..., 0.301303300333... (ii) 0.8616611666111 ..., 0.8717711777111 ... (iii) 1.515511555..., 1.616611666...

3. 2.2362, 2.2363

Exercise 2.5

1.(i) 5⁴ (ii) 5^-1 (iii) 5^1/2 (iv) 5^3/2

2. (i) 4² (ii) 4^3/2 (iii) 4^5/2

3.(i) 7 (ii) 9 (iii) 1/27 (iv) 25/16

4. (i) 5^1/2 (ii) 7^1/2 (iii) 7^10/3 (iv) 10^-14/3

5. (i) 2 (ii) 3 (iii) 10 (iv) 4/5

Exercise 2.6

1. (i) 21√3 (ii) 3³√5 (iii) 26√3 (iv) 8³√5

2. (i) √30 (ii) √5 (iii) 30 (iv) 49a − 25b (v) 5/16

3. (i) 1. 852 (ii) 23. 978

4. (i) ³√5 > ⁶√3 > ⁹√4 (ii) √√3 > ²√³√5 > ³√⁴√7

5. (i) yes (ii) yes (iii) yes (iv) yes

6. (i) yes (ii) yes (iii) yes (iv) yes

Exercise 2.7

1. (i) √2 / 10 (ii) √5 / 3 (iii) 5√6 / 6 (iv) √30 / 2

2. (i) 4/3 (5+2√6) (ii) 13 - 4√6 (iii) [9+4√30] / 21 (iv) -2√5

3. a = −4/3 ,b = 11/3

4. x² + 1/x² = 18

5. 5.414

Exercise 2.8

1. (i) 5. 6943 ×10¹¹ (ii) 2. 00057 ×10³ (iii) 6.0×10⁻⁷ (iv) 9. 000002 ×10⁻⁴

2. 3459000 (ii) 56780 (iii) 0.0000100005 (iv)0.0000002530009

3. (i) 1. 44 ×10²⁸ (ii) 8.0×10⁻⁶⁰ (iii) 2.5×10⁻³⁶

4.(i) 7. 0 ×10⁹ (ii) 9. 4605284 ×10¹⁵ km (iii) 9. 1093822 ×10⁻³¹ kg

5. (i) 1.505×10⁸ (ii) 1. 5522 ×10¹⁷ (iii) 1.224 ×10⁷ (iv) 1. 9558 ×10⁻¹

Exercise 2.9

1. (4) 2. (3) 3. (2) 4. (1) 5. (4) 6. (2) 7. (2) 8. (2) 9. (4) 10. (1)

11. (4) 12. (4) 13. (4) 14. (2) 15. (2) 16. (3) 17. (2) 18. (4) 19. (2) 20. (3)

Chapter 3

Algebra

Exercise 3.1

1. (i) not a polynomial (ii) polynomial (iii) not a polynomial (iv) polynomial (v) polynomial (vi) not a polynomial

3. (i) 7 (ii) 4 (iii) 5 (iv) 6 (v) 4

5. (i) 6x³+6x²–14x+17, 3 (ii) 7x³+7x²+11x–8, 3 (iii) 16x⁴–6x³–5x²+7x–6, 4

6 (i) 7x²+8, 2 (ii) –y³+6y²–14y+2, 3 (iii) z⁵–6z⁴–6z²–9z+7, 5

7. x³–8x²+11x+7

8. 2x⁴–3x³+5x²–5x+6

9 (i) 6x⁴+ 7x³–56x²–63x+18, 4 (ii) 105x²–33x–18, 2 (iii) 30x³–77x²+54x–7, 3

10. x²+y²+2xy, ₹ 225

11. 9x²–4, 3596 sq. units

12. cubic polynomial or polynomial of degree 3

Exercise 3.2

1. (i) 6 (ii) –6 (iii) 3

2. 1

3. (i) 3 (ii) −5/2 (iii) 3/2 (iv) 0 (v) 0 (vi) – b/a

4. (i) 6/5 (ii) –3 (iii) −9/10 (iv) 4/9

6. (i) 2 (ii) 3 (iii) 0 (iv) 1 (v) 1

Exercise 3.3

1. p(x) is not a multiple of g(x)

2. (i) Remainder : 0 (ii) Remainder : 3/2 (iii) Remainder : 62

3. Remainder : –143

4. Remainder : 2019

5.K=8

6. a = –3, Remainder : 27

7. (i) (x -1) is a factor (ii) (x -1) is not a factor

8. (x − 5) is a factor of p(x)

9. m = 10

11. k = 3

12. Yes

Exercise 3.4

1. (i) x ² + 4y ² + 9z ² + 4xy + 12yz + 6xz (ii) p ² + 4q ²+ 9r ² − 4 pq + 12qr − 6pr (iii) 8 p ³ − 24 p² −14 p + 60 (iv) 27a ³ + 27a ² −18a – 8

2. (i) 18,107,210 (ii) −32, −6, +90

3. (i) 14 (ii) 59/70 (iii) 78 (iv) 78/70

4. (i) 27a³ – 64b³ – 108a²b + 144ab²(ii) x³ + 1/y³ + 3x²/y + 3x/y²

5. (i) 941192 (ii) 1003003001

6. 29

7. 280

8. 335

9. 198

10. ±5, ±110

11. 36

12.(i) 8a ³ + 27b ³ + 64c ³ − 72abc

(ii) x ³ − 8y ³+ 27z ³ + 18xyz

13.(i) −630 (ii) -9/4

14. 72xyz

Exercise 3.5

1.(i) 2a ² (1 + 2b + 4c) (ii) (a − m)(b -c)

2. (i) (x+2)² (ii) 3(a − 4b)² (iii) x (x + 2) (x − 2)(x² + 4) (iv) (m + 1/m + 5) ( m + 1/m − 5) (v) 6(1 + 6x )(1 − 6x) (vi) (a – 1/a + 4)( a −1/a – 4)

3. (i) (2x + 3y + 5z)² (ii) (− 5x + 2y + 3z)² (or) (5x − 2y − 3z)²

4. (i) (2x + 5y)(4x ² −10xy + 25y² ) (ii) (3x − 2y)(9x ² + 6xy + 4y² ) (iii) (a + 2)(a − 2)(a ² + 4 − 2a)(a ² + 4 + 2a)

5. (i) (x + 2y −1)(x ² + 4y ² + 1 − 2xy + 2y + x) (ii) (l − 2m − 3n )(l ² + 4m ² + 9n² + 2lm − 6mn + 3ln)

Exercise 3.6

1. (i) (x + 6) (x + 4)

(ii) (z + 6) (z − 2)

(iii) ( p − 8) ( p + 2)

(iv) (t − 9)(t − 8)

(v) (y − 20)(y + 4)

(vi) (a + 30)(a − 20)

2. (i) (2a + 5)(a + 2)

(ii) (x − 7y)(5x + 6y)

(iii) (2x − 3)(4x − 3)

(iv) 2(3x + 2y )(x + 2y)

(v) 3x² (3y + 2)²

(vi) (a + b + 6) (a + b + 3)

3. (i) ( p − q − 8) ( p − q + 2)

(ii) (m + 6n)(m − 4n)

(iii) (a + √5 ) (√5a − 3)

(iv) (a + 1)(a −1)(a ² − 2)

(v) m (4m + 5n )(2m − 3n)

(vi) (1/x + 1/y)²

Exercise 3.7

1. (i) Quotient : 4x²–6x–5, Remainder : 33

(ii) Quotient : 4y²–6y+5, Remainder : –10

(iii) Quotient : 4x²+2x+1, Remainder : 0

(iv) Quotient : 8z²–6z+2, Remainder : 10

2. Length : x+4

3. Height : 5x–4

4. Mean : x²–5x+25

5. (i) x ² + 4x + 5, 12

(ii) (x ² − 1), − 2

(iii) 3x ² − 11x + 40, −125

(iv) 2x³ − x²/2 − 3x/8 + 51/32 , 109/32

6. 4x³ − 2x² + 3, p = −2, q = 0, remainder = −10

7. a = 20, b = 94 & remainder=388

Exercise 3.8

1. (i) (x − 2)(x + 3)(x − 4)

(ii) (x + 1)(x − 2)(2x −1)

(iii) (x − 1)(2x −1)(2x + 3)

(iv) (x + 2)(x + 3)(x − 4)

(v) (x − 1)(x − 2)(x + 3)

(vi) (x − 1)(x −10)(x + 1)

Exercise 3.9

1. (i) p⁵

(ii) 1

(iii) 3a ²b²c³

(iv) 16x ⁶

(v) abc

(vi) 7xyz ²

(vii) 25ab

(viii) 1

2. (i) 1

(ii) a^m+1

(iii) (2a + 1)

(iv) 1

(v) (x+1)(x−1)

(vi) (a − 3x)

Exercise 3.10

2. (i) (5,2) (ii) Infinite number of solutions (iii) no solution (iv) (−3, −3) (v) (1,3) (vi) (−3, 3)

3. 75 km/hr, 25 km/hr

Exercise 3.11

1. (i) (2, −1) (ii) (4,2) (iii) (40,100) (iv) ( √8, √3)

(2) 45

(3) 409

Exercise 3.12

1. (i) (2,1) (ii) (7,2) (iii) (80,30) (iv) (1, 3/2) (v) (1/3, −1) (vi) (2,4)

(2) ₹30000, ₹40000

(3) 75, 15

Exercise 3.13

1. (i) (3,4) (ii) (3, −1) (iii) (−1/2, 1/3)

(2) Number of 2 rupee coins 60; Number of 5 rupee coins 20

(3) Larger pipe 40 hours; Smaller pipe 60 hours

Exercise 3.14

1. 64

2. 5/7

3. ∠A =120º, ∠B = 70º, ∠C = 60º, ∠D =110º

4. Price of TV = ₹20000; Price of fridge = ₹10000

5. 40, 48

6. 1 Indian – 18 days; 1 Chinese – 36 days

Exercise 3.15

1. (4) 2. (3) 3. (4) 4. (4) 5. (2) 6. (1) 7. (4) 8. (4) 9. (4) 10. (3)

11. (2) 12. (3) 13. (3) 14. (2) 15. (3) 16. (3) 17. (4) 18. (2) 19. (3) 20. (2)

21. (4) 22. (3) 23. (2) 24. (1) 25. (2) 26. (3) 27. (1) 28. (3) 29. (2)

Chapter 4

Geometry

Exercise 4.1

1. (i) 70° (ii) 288° (iii) 89°

2. 30°, 60°, 90°

5. 80°, 85 °, 15 °

Exercise 4.2

1. (i) 40°, 80°, 100°, 140°

2. 62°, 114°, 66°

3. 44°

4. 10cm

7. (i) 30° (ii) 105° (iii) 75° (iv) 105°

8. 122°, 29°

9. Ratios are equal

10. d = 7.6

Exercise 4.3

1. 24cm

2. 17cm

3. 8cm, 45°, 45°

4. 18cm

5. 14 cm

6. 6 cm

7. (i) 45° (ii) 10° (iii) 55° (iv) 120° (v) 60°

8. ∠BDC = 25°, ∠DBA = 65°, ∠COB = 50°

Exercise 4.4

1. 30°

2. (i) ∠ACD = 55° (ii) ∠ACB = 50° (iii) ∠DAE = 25°

3. ∠A = 64°; ∠B = 80°; ∠C = 116°; ∠D = 100°

4. (i) ∠CAD = 40° (ii) ∠BCD = 80°

5. Radius=5cm

6. 3.25m

7. ∠OAC = 30°

8. 5.6m

9. ∠RPO = 60°

Exercise 4.7

1. (2) 2. (3) 3. (1) 4. (4) 5. (4) 6. (3) 7. (2) 8. (2) 9. (4) 10. (2)

11. (3) 12. (3) 13. (1) 14. (1) 15. (4) 16. (2) 17. (2) 18. (3) 19. (2) 20. (4)

Chapter 5

Coordinate Geometry

Exercise 5.1

1. P(–7,6) = II Quadrant; Q(7,–2) = IV Quadrant; R(–6, –7) = III Quadrant; S(3,5) = I Quadrant; and T (3,9) = I Quadrant

2. (i) P = (– 4,4) (ii) Q = (3,3) (iii) R=(4,–2) (iv) S = (–5,–3)

3. (i) Straight line parallel to x –axis (ii) Straight line which lie on y -axis.

4. (i) Square (ii) Trapezium

Exercise 5.2

1. (i) √10 units (ii) 2√26 units (iii) c–a (iv)13 units

2. (i) Collinear (ii) Collinear

7. 5 or 1

8. Coordinates of A (9, 9) or (–5,–5)

9. y = 4x+9

10. Coordinates of P(2,0)

12. 30√2

Exercise 5.3

1. (i) (−4, −1) (ii) (0, −1) (iii) (a + b, a) (iv) (1, −1)

2. (−5, −3)

3. P = −15

4. (9, 3)(−5, 5) and (1,1)

5. (9/2 , 3/2)

6. (1,8)

Exercise 5.4

1. (7,3)

2. 5:2

3. (3, 4)

4. (−2,3) ,(1,0)

5. (19/2 , 13/2) , ( −9/2, −15/2)

7. (3,2)

Exercise 5.5

1. (i) (2, −3) (ii) (−8/3, −11/3)

2. (4, −6)

3. 5 units

4. 20

5. 3√(5/2) units

6. (1,0)

7. (5, −2)

Exercise 5.6

1. (3) 2. (3) 3. (3) 4. (2) 5. (2) 6. (4) 7. (3) 8. (3) 9. (3) 10. (3)

11. (4) 12. (1) 13. (3) 14. (4) 15. (2) 16. (3) 17. (2) 18. (2) 19. (4) 20. (2)

Chapter 6

Trigonometry

Exercise 6.1

1. sin B = 9/41 ;cos B = 40/41 ; tan B = 9/40 ; cosecB = 41/9 ;sec B = 41/40 ;cot B = 40/9

2. (i) sin B = 12/13 (ii) sec B = 13/5 (iii) cot B = 5/12 (iv) cosC = 4/5 (v) tanC = 3/4 (vi) cosecC = 5/3

3. sin θ = 1/2 ;cos θ = √3/2 ; tan θ = 1/√3 ; cosec θ = 2/1 ;sec θ = 2/√3 ;cot θ = √3

4. 3/40

5. sin A = [1 − x²] / [1 + x²]; tan A = [1 − x² ] / 2x

7. 1/2

8. 1/2

9. sin α = 4/5 ;cos β = 4/5 ; tanφ = 4/3

10. 7m

Exercise 6.2

2.(i) 0 (ii) 7/4 (iii) 3

4. 2

Exercise 6.3

1.(i) 1 (ii) 1 (iii) 1 (iv) 2

Exercise 6.4

1. (i) 0.7547 (ii) 0.2648 (iii) 1.3985 (iv) 0.3641 (v) 0.8302 (vi) 2.7907

2.(i) 85°57′ (or) 85°58′ (or) 85°59′ (ii) 47°27′ (iii) 4°7′ (iv) 87°39′ (v) 82°30′

3.(i) 1.9970 (ii) 2.8659

4. 18.81 cm²

5. 36°52′

6. 54.02 m

Exercise 6.5

1. (1) 2. (2) 3. (2) 4. (3) 5. (2) 6. (3) 7. (3) 8. (1) 9. (2) 10. (2)

Chapter 7

Mensuration

Exercise 7.1

1. (i) 120 cm²(ii) 7.2 m²

2. 1320 m², ₹26400

3. 12000 m²

4. 1558.8 cm²

5. ₹ 1050

6. 240 cm²

7. 138 cm²

8. 354m²

9. 1536 m²

10. 672 m²

Exercise 7.2

1. 1160cm², 560cm²

2. ₹1716

3. ₹3349

4.(i) 384 m², 256 m²(ii) 2646 cm², 1764 cm²(iii) 337.5 cm², 225 cm²

5. 1600 cm²

6. 253.50m², ₹6084

7. 224cm², 128cm²

Exercise 7.3

1. (i) 576 cm³(ii) 2250 m³

2. 630 cm³

3. 25 cm, 20 cm, 15 cm

4. 2624000 litres

5. 25000

6. 12 m

7.(i) 125 cm³ (ii) 42.875 m³ (iii) 9261 cm³

8. 5 m

9. 15 cm

Exercise 7.4

1. (3) 2. (2) 3. (4) 4. (3) 5. (3) 6. (1) 7. (2) 8. (3) 9. (4) 10. (1)

Chapter 8

Statistics

Exercise 8.1

1. 27°C

2. 44kg

3. 56.96 (or) 57 (approximately)

4. 142.5 mm³

5. p = 20

6. 40.2

7. 29.29

8. 29.05

Exercise 8.2

1. 47

2. 44

3. 21

4. 32

5. 31

6. 38

Exercise 8.3

1. 6600, 7000, 7000

2. 3.1 and 3.3 (bimodal)

3. 15

4. 40

5. 24

6. 58.5

Exercise 8.4

1. (1) 2. (3) 3. (3) 4. (2) 5. (1) 6. (4) 7. (1) 8. (2) 9. (2) 10. (3)

Chapter 9

Probability

Exercise 9.1

1. 1/7

2. 3/13

3. 1/2

4.(i) 5/24 (ii) 1/8 (iii) 2/3

5. 1/4

6.(i) 0 (ii) 1/12 (iii) 1

7. 1/280

8. 1/5

9. 3/4

Exercise 9.2

1. 0.9975

2. 209/400

3. 15/8

4. 0.28

5.(i) 1/6 (ii) 43/75 (iii) 1/75

Exercise 9.3

1. (4) 2. (2) 3. (1) 4. (4) 5. (1) 6. (4) 7. (4) 8. (4) 9. (1) 10. (2)

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