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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 . (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)

7. 


(vii) (AB) = AB

 

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) 51/2 (iv) 53/2

2. (i) 42 (ii) 43/2 (iii) 45/2

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

4. (i) 51/2 (ii) 71/2 (iii) 710/3 (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 > 23√5 > 34√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

2. 

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

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 24 pq + 12qr6pr (iii) 8 p 3 24 p2 14 p + 60  (iv) 27a 3 + 27a 218a8

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) (am)(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) am+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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