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Answer BookDrill exercises in

MAtheMAtics

clAss Vi

ByPrernA GuPtA

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PrefAce

Drill Exercises in Mathematics, Class VI provides a plethora of questions to students to help them sharpen their mathematical skills and enhance understanding of the concepts. It was meant for students to help them excel in the subject.

The Answer book has been prepared to provide answers to every question. The book is meant for teachers to help them in their pedagogical endeavour. By using this book, the teachers can explain the concepts more clearly to students and make them interested in learning Mathematics.

Any suggestions for improvement will be highly appreciated.

— Publisher

contents

Chp. Drill Exercise Topic Page no. no. no.

1. 1 - 8 Knowing Our Numbers 1-3

2. 9 - 17 Whole Numbers 3-5

3. 18 - 28 Playing with Numbers 6-8

4. 29 - 37 Basic Geometrical Ideas 9-11

5. 38 - 43 Understanding Elementary Shapes 12-13

6. 44 - 47 Integers 13-14

7. 48 - 55 Fractions 14-17

8. 56 - 62 Decimals 18-20

9. 63 - 65 Data Handling 20-21

10. 66 - 73 Mensuration 21-23

11. 74 - 80 Algebra 23-25

12. 81 - 91 Ratio and Proportion 25-28

13. 92 - 101 Symmetry 28-30

Miscellaneous Drill Exercises 30-32

1

Drill Exercise – 1 1. (i) 94, 59120 (ii) 200, 50000 (iii) 3, 28475 (iv) 415, 20120 2. (i) 99 (ii) 1000 (iii) 10000 (iv) 99999 3. (i) 74320 (ii) 20374 4. (i) 10000 (ii) 9999 5. (i) double (ii) 2 (iii) 4 (iv) 4 6. (i) 1158, 8851 (ii) 3009, 9930 (iii) 1006, 6610 (iv) 3345, 5543 7. (i) 1050, 9959 (ii) 1009, 9999 (iii) 7000, 7999

Drill Exercise – 2 1. (i) 1033569 (ii) 9653310 2. (i) 9000 (ii) 0 (iii) 0 (iv) 100000 3. (i) 70070 (ii) 69930 (iii) 99900 (iv) 199998 4. (i) zero (ii) digit 5. (i) 100 (ii) 100000 (iii) 4 (iv) 0 6. (i) Three lakh one thousand two hundred fifty six (ii) Seventy one lakh twenty five thousand sixty four (iii) One crore twenty lakh one thousand two hundred

ninety nine (iv) Nine crore, ninety one lakh, nineteen thousand nine

hundred eleven. 7. (i) 421000 (ii) 600906 (iii) 5555055 (iv) 810315811

Drill Exercise – 3 1. (i) 6000132 (ii) 404010019 (iii) 333017903 (iv) 35423209 2. (i) Three hundred twelve, Five hundred seventy two, Nine

hundred eighty one (ii) Seven hundred eighty five, Three hundred twenty three,

One hundred twenty five (iii) Five hundred five, Nine, Eight (iv) Four hundred nineteen, Two hundred, One

2

3. (i) 9,75,85,762, 97,585,762 (ii) 5,80,01,234, 58,001,234 (iii) 9,99,00,909, 99,900,909 (iv) 1,29,83,467, 12,983,467 4. (i) thousand (ii) hundred (iii) thousand (iv) ten 5. (i) Ten (ii) Ten (iii) Ten (iv) Ten 6. (i) One (ii) Ten (iii) Hundred (iv) One 7. (i) 50 (ii) 10 (iii) 10000 (iv) 2 (v) 1000

Drill Exercise – 4 1. (i) > (ii) < (iii) > (iv) > (v) < (vi) > 2. (i) = (ii) < (iii) > (iv) < (v) = (vi) = (vii) = 3. (i) 3076897, 21345678, 61300012, 72899988, 129654503 (ii) 500005, 850040, 2880002, 7500075, 11223344 (iii) 56789123, 67898761, 76543219, 91234567, 789123456

(iv) 12034567, 12304567, 12340567, 12345067, 12345607

4. (i) 1097100, 1097010, 1091700, 1091070, 1091007 (ii) 1276534, 1267534, 1265734, 1257634, 1256734 (iii) 124003, 1234000, 1230400, 1230040, 1230004

Drill Exercise – 5 1. (i) 10 (ii) 100 (iii) 1000 (iv) 1000 (v) 1000000 2. (i) 1000 (ii) 1000 (iii) 10 (iv) 10 3. (i) 1000 (ii) 100 (iii) 10 (iv) 10 4. (i) 10 (ii) 100 (iii) 1000 (iv) 10 (v) 100 (vi) 1000 (vii) 10 (viii) 100 (ix) 1000 (x) 100 (xi) 1000 5. (i) 600000 (ii) 8000000 (iii) 95000 (iv) 9000000 (v) 54000 (vi) 18000

Drill Exercise – 6 1. 7590 2. 11104 3. 43965 4. 72958 5. 143760 6. 72380 7. 26708 8. 425

3

Drill Exercise – 7 1. 30, 30, 80, 320, 1550, 1820, 1600, 1500, 13900, 10000, 10000,

14000, 20000, 460000, 1470000, 600000, 1300000 2. 20000 3. 5000 4. 5000 5. 600000 6. (i) 945 (ii) 10302 (iii) 1526 (iv) 13230 (v) 10494 (vi) 5610

Drill Exercise – 8 1. (i) V, L, D (ii) V, L, D (iii) V, X (iv) L, C (v) D, M (vi) I, X, C, M 2. (i) its value is added that many times (ii) 3 (iii) right (iv) left (v) subtracted from 3. (i) XCV (ii) LXIX (iii) XLIV (iv) XCIX (v) CLIV (vi) CXL (vii) CDVIII (viii) CXXXIX 4. (i) 109 (ii) 172 (iii) 94 (iv) 68 (v) 49 (vi) 172 (vii) 569 5. (i) CLXXIV (ii) 198 (iii) 89 (iv) CCLXI

Drill Exercise – 9 1. (i) 1 (ii) 0 (iii) 0 (iv) 0 2. (i) 0 (ii) 0 (iii) 2 (iv) 1 3. (i) whole (ii) whole (iii) number itself (iv) number itself 4. (i) same (ii) 1 (iii) 0 (iv) zero 5. (i) same (ii) number itself (iii) 1 (iv) zero

Drill Exercise – 10

1. (i) algorithm (ii) 1 (iii) 1 (iv) 0 (v) even (vi) 9 (vii) 0 (viii) 1 (ix) 99 (x) 10 (xi) 100 2. (i) 1 (ii) whole number (iii) Multiplication (iv) 0

4

3. (i) 25 (ii) 202 (iii) 0 (iv) 315 4. (i) 1 (ii) 0 (iii) 912 (iv) 0 (v) 21815 (vi) 0

Drill Exercise – 11 1. (i) 5100, 5101, 5102 (ii) 11000, 10999, 10998 (iii) 10999, 11000, 11001 (iv) 99, 100 (v) 6 2. (i) 3440710 (ii) 500300 (iii) 3100000 (iv) 5672341 3. (i) 98 (ii) 29999 (iii) 308089 (iv) 7654300 4. (i) 1 (ii) 2 (iii) 99 (iv) 998 (v) 1000 5. (i) 0 (ii) 99 (iii) 98 (iv) 99 (v) 99 (vi) 97

Drill Exercise – 12 1. (i) 1 + 8 + 6 = 15 (ii) 4 + 6 = 10 (iii) 3 + 5 + 2 = 10 (iv) 5 + 2 + 2 = 9 (v) 3 + 4 + 4 + 4 = 15 2. (i) 9 – 6 = 3 (ii) 8 – 5 = 3 (iii) 3 × 3 = 9 (iv) 2 + 2 + 2 + 2 = 8 (v) 4 × 2 = 8

Drill Exercise – 13 1. (i) 736 (ii) 921 (iii) 1015 (iv) 2934 (v) 4500 (vi) 4000 2. (i) 628500 (ii) 1017000 (iii) 186700 (iv) 1218000 (v) 578000 (vi) 1000000

Drill Exercise – 14

1. (i) 7700 (ii) 556600 (iii) 19175000 (iv) 7126800 (v) 5312600 (vi) 3343700 2. (i) 95268 (ii) 64785 (iii) 320544 (iv) 159390 (v) 63063 (vi) 95888

5

Drill Exercise – 15 1. (i) 100 (ii) 1000 (iii) 459 (iv) 67800000 2. (i) 103 (ii) 22 (iii) 54 (iv) Read it as 36 × (312 – 55) = …… × 312 – 55 × 36 Ans. 36 3. (i) 1 (ii) 100 (iii) 100 (iv) 318 4. (i) 136800 (ii) 15730 (iii) 26350 (iv) 234000 (v) 94500 (vi) 392400 (vii) 1300000 (viii) 1458000 (ix) 1207000 (x) 1008000

Drill Exercise – 16 1. (i) 1 (ii) 0 (iii) 7112 (iv) 0 (v) 2142 (vi) 1 (vii) 1 2. (i) 100 (ii) 1344 (iii) 394 (iv) 100 (v) 1212 (vi) 100 (vii) 10 3. (i) 10 (ii) 90454 (iii) 15160 (iv) 212200 4. (i) 23, 68 (ii) 67, 24 (iii) 88, 45 (iv) 69, 19 (v) 79, 81 (vi) 18, 97 (vii) 105, 21 (viii) 501, 12

Drill Exercise – 17 1. (i) 1000, 10000 (ii) 630 × 4, 630 × 5 (iii) Read it as 63 × 5 = 63 × 10

2 = 630 × 1

2

63 × 15 = 63 × 302

= 630 × 32

63 × 25 = 63 × 502

= 630 × 52

63 × 35 = 63 × 702

= 630 × …………

63 × 45 = 63 × 902

= 630 × …………

Ans.: 72

, 92

(iv) 729999, 7299999 (v) 60000

2. (i) 1234, 12345 (ii) 7777, 77777 (iii) 55 + 555 + 5555, 55 + 555 + 5555 + 55555 (iv) 5 × 100 + (5 × 1) (v) 5 × 100 + (5 × 5)

6

Drill Exercise – 18 1. (i) factor (ii) number (iii) One (iv) divisor (v) factor (vi) factors (vii) factor (viii) every (ix) 1 and 5 (x) 1 (xi) 1 2. (i) divisible (ii) itself/one (iii) number (iv) greater (v) factors (vi) number itself (vii) 5, 10, 15 (viii) 1, 2, 3 (ix) 2, 4, 6, 8, 10 (x) 9, 18, 27, 36, 45

Drill Exercise – 19 1. (i) prime (ii) composite (iii) one (iv) 2 (v) 2 (vi) 3 (vii) 2 (viii) 2 (ix) 7 (x) 97 (xi) 11 (xii) twin 2. (i) 2, 3 (ii) 2, 3, 5, 7 (iii) 23, 29 (iv) 97 (v) 71, 73 (vi) 17, 71 (vii) 7 (viii) 4 (ix) 9 (x) 25 (xi) 10

Drill Exercise – 20 1. (i) 2 (ii) odd (iii) 2 (iv) 1 (v) 8 (vi) 9 (vii) 11 (viii) 10 (ix) 98 (x) 100 (xi) odd (xii) even (xiii) even (xiv) odd 2. (i) composite (ii) even (iii) perfect (iv) 6 3. (i) 1, 2, 3, 4 and 5 (ii) 0, 1, 2, 3 and 4 (iii) 2, 4, 6, 8 and 10 (iv) 1, 3, 5, 7 and 9 (v) 2, 3, 5, 7 and 11 (vi) 4, 6, 8, 9 and 10 (vii) 3 and 5, 5 and 7, 11 and 13, 17 and 19, 29 and 31.

Drill Exercise – 21

1. (i) 2 + 3 (ii) 3 + 7 (iii) 2 + 13 (iv) 7 + 13 (v) 2 + 23 (vi) 7 +23 (vii) ignore this question (viii) 11 + 29 (ix) 2 + 43 (x) 19 + 31 2. (i) ignore this question (ii) 3 + 3 (iii) 3 + 5 (iv) 7 + 11 (v) 5 + 7 (vi) 5 + 11 (vii) 5 + 17 (viii) 3 + 11 (ix) 3 + 23 (x) 5 + 23 (xi) 5 + 31 (xii) 3 + 41

7

3. (i) 2 + 3 +5 (ii) 2 + 5 + 7 (iii) 2 + 3 + 7 (iv) 2 + 5 + 11 (v) 3 + 5 + 7 (vi) 2 + 5 + 17 (vii) 3 + 7 + 11 (viii) 3 + 5 + 17 (ix) 2 + 7 + 17 (x) 5 + 11 + 17 4. (i) 3 + 7 + 13 (ii) 3 + 5 + 23 (iii) 13 + 17 + 23 (iv) 7 + 13 + 41 (v) 5 + 7 + 17 (vi) 3 + 5 + 29 (vii) 5 + 7 + 29 (viii) 3 + 7 + 37 5. (i) 5 + 7 (ii) 29 + 31 (iii) 11 + 13 (iv) 41 + 43

Drill Exercise – 22 1. (i) 2 (ii) 3 (iii) 5 (iv) 7 (v) 11 (vi) 13 (vii) 17 (viii) 19 (ix) 23 (x) 29 (xi) 31 (xii) 37 (xiii) 41 (xiv) 43 (xv) 47 2. (i) 53 (ii) 59 (iii) 61 (iv) 67 (v) 71 (vi) 73 (vii) 79 (viii) 83 (ix) 89 (x) 97 3. (i) 3 and 5 (ii) 5 and 7 (iii) 11 and 13 (iv) 17 and 19 (v) 29 and 31 (vi) 41 and 43 (vii) 59 and 61 (viii) 71 and 73 4. (i) 2 (ii) 5 (iii) 3 (iv) 9 (v) 10 (vi) 4 (vii) 6 (viii) 12 (ix) 11 (x) 8

Drill Exercise – 23 1. (i) 2 × 2 × 3 (ii) 2 × 3 × 3 (iii) 2 × 2 × 2 × 2 × 3 (iv) 2 × 2 × 2 × 7 2. (i) 2 × 2 × 3 × 5 (ii) 2 × 2 × 3 × 3 (iii) 2 × 2 × 2 × 2 × 3 × 3 (iv) 2 × 2 × 37

Drill Exercise – 24 1. (i) one (ii) co-prime (iii) 2 (iv) 9 (v) 5 (vi) 0 (vii) 2 (viii) 3 (ix) 5 (x) 3 (xi) 2 2. (i) even (ii) odd (iii) co-prime (iv) 3 (v) 90, 91, 92, 93, 94, 95, 96.

8

3. (i) 2, 3, 5, 7, 11, 13, 17, 19 (ii) 3 and 5, 5 and 7, 11 and 13 (iii) 3, 5, 7

Drill Exercise – 25 1. (i) Yes (ii) No (iii) No (iv) Yes (v) No (vi) Yes (vii) Yes (viii) Yes (ix) Yes (x) No (xi) Yes (xii) No (xiii) No (xiv) Yes (xv) Yes (xvi) No (xvii) No (xviii) Yes (xix) No (xx) No (xxi) Yes (xxii) Yes (xxiii) Yes 2. (i) 2 (ii) 0/1 (iii) 5 (iv) 3 (v) 9 (vi) 0 (vii) 6 (viii) 2 (ix) 8 (x) 6 (xi) 1 (xii) 0 (xiii) 4 (xiv) 1 (xv) 1 (xvi) 9 (xvii) 3

Drill Exercise – 26 1. (i) 4 (ii) 1 and 5 (iii) 1 and 5 (iv) 1, 2, 4 and 8 2. (i) 1 and 2 (ii) 1 and 5 (iii) 1, 3, 5 and 15 (iv) 36, 72 and 108 (v) 24, 48 and 72 3. (i) 1, 2 and 4 (ii) 1, 2 and 4 (iii) 1 and 3 (iv) 12, 24 and 36 (v) 20, 40, 60 and 80 (vi) 24, 48 and 72 (vii) 12, 24, 36 and 48 (viii) 18 and 36 (ix) 36 and 72

Drill Exercise – 27 1. (i) 4 (ii) 4 (iii) 12 (iv) 6 (v) 5 (vi) 4 2. (i) 360 (ii) 36 (iii) 48 (iv) 120 (v) 48 (vi) 300

Drill Exercise – 28 1. (i) 1 (ii) 1 (iii) 2 (iv) 2 (v) 1 (vi) 1 2. (i) 2 (ii) 4 (iii) 10 (iv) 4 (v) 9 (vi) 20 3. (i) 288 (ii) 1152 (iii) 120 (iv) 960 (v) 149

9

Drill Exercise – 29 1. (i) end (ii) indefinitely (iii) point (iv) plane (v) no (vi) 2 (vii) 1 (viii) intersecting (ix) point (x) two (xi) colinear (xii) intersect (xiii) A 2. (i) concurrent (ii) Infinite (iii) 3 (iv) 1 (v) concurrent (vi) line (vii) ray (viii) line segment (ix) A and B (x) parallel (xi) B (xii) concurrence

Drill Exercise – 30 1. (i) C (ii) B (iii) B (iv) XY and RS (v) PQ and RS 2. (i) LM, PQ and XY (ii) LM, PQ and XY (iii) B 3. (i) A, P, T, R and B (ii) G, Q, T, S and H (iii) J, R, S and K (iv) C, P, S and D 4. (i) non-collinear (ii) non-collinear (iii) collinear (iv) non-collinear (v) non-collinear

Drill Exercise – 31 1. (i) ray (ii) line segment (iii) (a) PS (b) PQ (c) QR (d) RS (e) PR (f) QS (iv) AB, BC and CD (v) AC, BC and AD (vi) OA, OB, OE, CE and CF 2. (i) OA, OC, OB and OD (ii) DE, EB, OB and EO 3. AF, AG, AB and AE 4. (i) Infinite (ii) 1 5. (i) FD, FA, FB, FC and FE (ii) AF, AD, AB, AC and AE (iii) BC, BE, BA, BF and BD

10

Drill Exercise – 32 1. (i) same as (ii) different from (iii) same as (iv) different from 2. (i) one (ii) three (iii) six (iv) one (v) three 3. (i) intersection (ii) always (iii) one (iv) more than one 4. (i) concurrent (ii) intersecting (iii) parallel

Drill Exercise – 33 1. (i) curve (ii) ends (iii) an open (iv) boundary (v) simple 2. (i) closed (ii) not simple (iii) open (iv) Option is [closed/simple/open] Ans. closed (v) closed 3. (i) polygon (ii) sides (iii) vertex (iv) adjacent (v) adjacent (vi) diagonal 4. (i) A, B, C, D and E (ii) AB, BC, CD, DE and EA (iii) AB and BC; BC and CD; CD and DE; DE and EA;

EA and AB. (iv) diagonal (v) adjacent (vi) diagonal

Drill Exercise – 34 1. (i) the same (ii) arms (iii) vertex (iv) interior 2. (i) angle (ii) O (iii) arms (iv) O, C, A and B (v) P and R (vi) Q and S (vii) O 3. (i) DOC (ii) exterior (iii) exterior (iv) interior (v) exterior (vi) EOD (vii) DOE, DOC, COB, BOA, AOC, AOD, EOC, EOB, AOE

and DOB.

11

4. (i) G and A (ii) B, E, O and P (iii) G, C, A and D

Drill Exercise – 35 1. (i) 3 (ii) triangle (iii) 3 (iv) 4 2. (i) A, B and C (ii) AC, CD and DA (iii) ∠ABD, ∠BDA and ∠DAB (iv) ADC and ABC (v) P, R and C (vi) ABD, ABC and ADC (vii) ABD and ABC 3. (i) A, B, C and D (ii) AB, BC, CD and DA (iii) adjacent (iv) opposite (v) opposite (vi) adjacent (vii) DC (viii) ∠B (ix) AB (x) diagonal (xi) diagonals

Drill Exercise – 36 1. (i) circle, centre (ii) circumference (iii) chord (iv) radius (v) diameter (vi) diameter 2. (i) a chord (ii) diameter (iii) radius (iv) centre (v) the radii 3. (i) AB (ii) AD (iii) OC, OB and OA (iv) O (v) A and B (vi) A and D 4. (i) circumference (ii) diameter (iii) sector (iv) segment

Drill Exercise – 37 1. (i) in (ii) equal (iii) equal (iv) double (v) half (vi) true (vii) semicircle (viii) An arc (ix) is not (x) many (xi) in 2. (i) circumference (ii) circumference (iii) circumference (iv) interior 3. (i) PQ (ii) AB (iii) O (iv) OA, OB and OC (v) O, R, S (vi) M, L (vii) PQ, AB, T, C

12

Drill Exercise – 38 1. (i) line (ii) angle (iii) triangle (iv) 4 (v) polygons (vi) prisms (vii) right (viii) triangular (ix) length (x) protractor 2. (i) 90° (ii) complete (iii) straight (iv) 0°, 90° (v) 0° (vi) obtuse (vii) reflex (viii) 2 (ix) 4 (x) 4 (xi) A straight angle

Drill Exercise – 39 1. (i) 2 right angles (ii) 1 right angle (iii) 3 right angles (iv) 2 right angles 2. (i) obtuse (ii) acute (iii) reflex (iv) straight (v) obtuse 3. (i) 2 right angles (ii) 1 right angle (iii) 2 right angles (iv) 1 right angle (v) 3 right angles (vi) 2 right angles 4. (i) 180°, 0°, 90° (ii) 540° (iii) 45° (iv) 135° (v) 30° (vi) 22.5°

Drill Exercise – 40 1. (i) an isosceles (ii) scalene (iii) equilateral (iv) an acute angled (v) an obtuse angled (vi) right angled 2. (i) equilateral (ii) isosceles (iii) scalene 3. (i) an isoscles right angled (ii) 60° (iii) 2 (iv) equal (v) 2 (vi) unequal (vii) 90°, 45° and 45° (viii) equilateral (ix) right angled

Drill Exercise – 41 1. (i) scalene triangle (ii) equilateral triangle (iii) right triangle (iv) isosceles triangle

13

(v) Isoscles (vi) Isoscles right triangle (vii) Isoscles triangle 2. (i) equal (ii) equal (iii) trapezium (iv) square (v) rectangle (vi) equal (vii) 90° (viii) equal (ix) non-parallel (x) perpendicular (xi) unequal

Drill Exercise – 42 1. (i) parallelogram (ii) rhombus (iii) square (iv) square (v) rectangle (vi) trapezium (vii) square 2. (i) Triangle (ii) 8 (iii) quadrilateral (iv) decagon (v) 9 (vi) 5 (vii) hexagon 3. (i) regular (ii) equilateral (iii) square

Drill Exercise – 43 1. (i) equilateral (ii) a square (iii) 108° (iv) 90° (v) 60° (vi) hexagon (vii) 120° 2. (i) polyhedron (ii) triangular (iii) triangles (iv) hexagonal (v) triangular (vi) rectangular (vii) polyhedron

Drill Exercise – 44 1. (i) integers (ii) –1, –2, –3 (iii) 1, 2, 3… (iv) 0 (v) 0 (vi) positive (vii) integer (viii) integer (ix) 0 (x) positive (xi) negative (xii) zero 2. (i) smaller (ii) greater (iii) the integer itself (iv) smaller (v) –1 (vi) 1 (vii) right (viii) left (ix) successor (x) predecessor

14

Drill Exercise – 45 1. (i) 0 (ii) 0 (iii) –1 (iv) 1 (v) 0 (vi) 1 2. (i) 0 (ii) –104 (iii) –20 (iv) 0 3. (i) greater (ii) smaller (iii) greater (iv) smaller 4. (i) –8, 0, 1, 2, 5 (ii) –4, –3, –1, 0, 2 5. (i) 6, 2, 0, –2, –5 (ii) 6, 1, 0, –1, –6 6. (i) > (ii) < (iii) < (iv) > (v) > (vi) > (vii) < (viii) < (ix) > (x) <

Drill Exercise – 46 1. (i) 0 (ii) –9 (iii) –8 (iv) –4 (v) 1 (vi) –46 (vii) 1 2. (i) –18 (ii) –4 (iii) 35 (iv) –37 (v) –35 3. (i) –3 (ii) –1 (iii) –4 (iv) –4 (v) 0 (vi) –12 4. (i) –5 (ii) 2 (iii) –2 (iv) 0 (v) –14 (vi) 0 (vii) 14 5. (i) –27 (ii) 24 (iii) 12 (iv) 1 (v) –7 6. (i) –3 (ii) 3 (iii) –3 (iv) 2 (v) 4

Drill Exercise – 47 1. (i) < (ii) < (iii) < (iv) < (v) < (vi) < (vii) = 2. (i) 55 (ii) (+18) (iii) (–7) (iv) (–33) (v) (+3) (vi) (–11) 3. (i) (+9) (ii) (–13) (iii) (0) (iv) (–5) (v) (+5) 4. (i) (+8) (ii) (–6) (iii) Option is [(–18)/(–2)] Ans. –18 (iv) (–8) 5. (i) 1 (ii) –3 (iii) 12 (iv) 5 (v) –12

Drill Exercise – 48

1. (i) fraction (ii) 1 (iii) 1 (iv) like 2. (i) 0 and 1 (ii) 0 and 1 (iii) 2 and 3 (iv) a proper (v) an improper (vi) denominator 3. (i) > (ii) < (iii) = (iv) > (v) = (vi) <

15

4. (i) unit (ii) numerator

(iii) 174

(iv) 56

(v) 2 35

(vi) 69

Drill Exercise – 49

1. (i) 25

(ii) 87

(iii) 79

(iv) 512

(v) 58

(vi) 56

2. (i) 8, 3, 16 (ii) 5, 10, 20 (iii) 16, 5, 12 (iv) 40, 15, 18 (v) 2, 15, 14

3. (i) 110

, 12

(ii) 12

, 54

(iii) 23

, 33

4. (i) 521

, 23

, 127

(ii) 12

, 35

, 54

(iii) 12

, 23

, 55

(iv) 13

, 25

, 34

(v) 12

, 23

, 22

(vi) 45

, 67

, 55

(vii) 221

, 310

, 103

5. (i) 35

, 815

, 13

(ii) 23

, 512

, 14

(iii) 77

, 57

, 314

(iv) 52

, 38

, 14

(v) 45

, 34

, 120

(vi) 33

, 512

, 16

(vii) 83

, 56

, 49

(viii) 76

, 38

, 14

Drill Exercise – 50

1. (i) 2 17

(ii) 2 25

(iii) 2 58

(iv) 3 13

(v) 2 316

(vi) 3 15

(vii) 8 17

(viii) 1 15

(ix) 2 14

(x) 2 47

2. (i) 32

(ii) 447

(iii) 125

(iv) 438

(v) 114

(vi) 133

(vii) 116

(viii) 218

(ix) 234

(x) 233

3. (i) 34

(ii) 35

(iii) 32

(iv) 47

16

(v) 15

(vi) 47

(vii) 23

(viii) 1128

(ix) 15

(x) 79

4. (i) 1881

(ii) 924

(iii) 2456

(iv) 1015

(v) 45

(vi) 37

(vii) 57

(viii) 7590

(ix) 3648

(x) 2665

(xi) Read it as Equivalent fraction of 7085

with numerator 14

is ………… Ans. 1417

(xii) 3663

Drill Exercise – 51 1. (i) like (ii) unlike (iii) unlike (iv) unlike

(v) proper (vi) improper (vii) 66242

(viii) 98126

(ix) 144216

2. (i) 18

(ii) 2 12

(iii) 149

(iv) smaller

(v) greater (vi) smaller (vii) greater (viii) smaller

(ix) 1 16

(x) 3 14

Drill Exercise – 52

1. (i) 23

(ii) 12

(iii) 12

(iv) 23

(v) 18

(vi) 13

(vii) 1 (viii) 1

2. (i) 13

(ii) 12

(iii) 111

(iv) 12

(v) 13

(vi) 718

3. (i) Option is [ 615

/ 25

] Ans. 25

(ii) 14

(iii) 56

(iv) 12

(v) 12

(vi) 12

(vii) 14

(viii) 34

(ix) 16

(x) 13

17

Drill Exercise – 53

1. (i) 35

(ii) 1 (iii) 12

(iv) 1 18

(v) 12

(vi) 118

(vii) 13

(viii) 12

2. (i) 1 (ii) 28

(iii) 0 (iv) 65

(v) 212

(vi) 321

(vii) 515

(viii) 95

3. (i) 23

(ii) 6 (iii) 5 15

(iv) 4 13

(v) 2 15

(vi) 3 15

(vii) 2 17

(viii) 5 25

Drill Exercise – 54

1. (i) 56

(ii) 1415

(iii) 1 49

(iv) 23

(v) 1 212

(vi) 1727

2. (i) 1 16

(ii) 1 320

(iii) 3136

(iv) 1 726

(v) 1 635

3. (i) 1 112

(ii) 1920

(iii) 2 1360

(iv) 1 25

4. (i) 23

(ii) 215

(iii) 19

(iv) 16

(v) 13

(vi) 727

5. (i) 16

(ii) 720

(iii) 1136

(iv) 726

(v) 135

6. (i) 712

(ii) 120

(iii) 1 14

(iv) 110

Drill Exercise – 55

1. (i) 23

(ii) 715

(iii) 49

(iv) 57

(v) 25

(vi) 23

2. (i) 34

(ii) 16

(iii) 14

(iv) 34

3. (i) 1 13

(ii) 4 23

(iii) 2 14

(iv) 3 56

4. (i) 710

(ii) 12

(iii) 12

(iv) 34

(v) 56

(vi) 34

5. (i) 13

(ii) 16

(iii) 45

(iv) 1112

(v) 120

6. (i) 3 16

(ii) 1 23

(iii) 1 23

(iv) 45

(v) 2 15

(vi) 2

(vii) 1 710

18

Drill Exercise – 56 1. (i) example (ii) Two-tenths

(iii) 3-parts (iv) 410

(v) Five-tenth (vi) 610

(vii) 7-parts (viii) Eight-tenths (ix) 9 parts 2. (i) 10 (ii) 0.2 (iii) 3

10 (iv) 0.4

(v) 5 (vi) ……… (vii) 8100

(viii) 6

(ix) 0.7 3. (i) one-hundredth (ii) three-hundredths

(iii) 4100

(iv) 6100

(v) nine (vi) hundredths 4. (i) example (ii) Five-tenths

(iii) 710

(iv) 310

(v) Eight-tenths 5. (i) example (ii) 0.02

(iii) Five-hundredths (iv) 7100

(v) 17100

(vi) Twenty four-hundredths

Drill Exercise – 57 1. (i) example (ii) 48.1 (iii) 66 (iv) 4 (v) 2 (vi) 100 (vii) 700 (viii) 50 (ix) 786.24 (x) 438.33 2. (i) example (ii) 232.03 (iii) 0 (iv) 5

(v) 510

(vi) 6100

(vii) 700 (viii) 436.32

3. (i) 1.35 (ii) 200.56 (iii) 40.12 (iv) 3

(v) 810

(vi) 200 (vii) 7 (viii) 2100

(ix) 405.03 (x) 987.02

19

Drill Exercise – 58

1. (i) 22

(ii) 0.25 (iii) 510

(iv) 125100

(v) 45

(vi) 0.15 (vii) 44

2. (i) 125100

(ii) 1.2 (iii) 55

(iv) 1.4

(v) 2525

3. (i) 502.3 (ii) 28.07 (iii) 15.06 (iv) 302.6 (v) 5.025 (vi) 11.032 4. (i) 15.235 (ii) 32.156 (iii) 81.81 (iv) 402.19 (v) 175.7 (vi) 92.305 (vii) 69.069

Drill Exercise – 59 1. (i) Seven and eighteen hundredths (ii) Eighteen and seven hundredths (iii) Three hundred sixty two thousandths (iv) Ninety one and five thousandths (v) Fourteen and fifty seven hundredths (vi) Three hundred ten and five hundredths (vii) Six and four thousandths 2. (i) 39.31 (ii) 40.23 (iii) 730.45 (iv) 70.02 (v) 405.09 (vi) 0.231 (vii) 111.001 (viii) 99.909 3. (i) example (ii) 0.3 and 0.4 (iii) 0.6 and 0.7 (iv) 0.9 and 1 (v) 0.0 and 0.1 (vi) 0.7 and 0.8 (vii) 0.1 and 0.3 (viii) 0.1 and 0.2 (ix) 0.5 and 0.6 (x) 0.2 and 0.3 4. (i) < (ii) > (iii) < (iv) > (v) = (vi) < (vii) > (viii) = (ix) < (x) <

Drill Exercise – 60

1. (i) 0.03 (ii) 9 (iii) 15 (iv) 0.35 (v) 0.01 (vi) 0.75 (vii) 0.20 (viii) 0.38 (ix) 0.10 2. (i) 5.20 (ii) 840 (iii) 3.05 (iv) 9.19 (v) 102 (vi) 18.81 (vii) 42, 2 (viii) 36.10

20

(ix) 105.02 (x) 105, 20 (xi) 108, 8 (xii) 55.05 (xiii) 7 3. (i) 0.5 (ii) 2 (iii) 1 (iv) 15 (v) 2.3 (vi) 3.5 4. (i) 0.08 (ii) 0.18 (iii) 72 (iv) 2, 36 (v) 38.12 (vi) 20 (vii) 2 5. (i) 10.8 (ii) 321.5 (iii) 1.36 (iv) 258 (v) 2580 (vi) 17.90 (vii) 7.8 (viii) 74.2 (ix) 18.18

Drill Exercise – 61 1. (i) 0.009 (ii) 0.019 (iii) 0.822 (iv) 12 (v) 2180 (vi) 2.018 (vii) 2, 108 (viii) 55.010 (ix) 5, 510 2. (i) 0.005 (ii) 0.055 (iii) 505 (iv) 5.005 (v) 5, 500 (vi) 5, 1 (vii) 3005 (viii) 14.007 (ix) 1.407 (x) 14070 3. (i) 4.05 (ii) 1010 (iii) 12.5 (iv) 13.2 (v) 1320 (vi) 5038 (vii) 0.1 (viii) 20 (ix) 15001 (x) 0.002 (xi) 0.005

Drill Exercise – 62 1. (i) equivalent (ii) different (iii) different (iv) different (v) unlike (vi) like (vii) unlike (viii) unlike 2. (i) greater (ii) smaller (iii) greater (iv) greater (v) smaller (vi) greater (vii) smaller (viii) greater (ix) greater (x) greater (xi) greater

Drill Exercise – 63

1. (i) data (ii) pictograph (iii) pictograph (iv) uniform width (v) length 2. (i) 8 (ii) (iii) 12 (iv) (v) 3. (i) 13 (ii) 7 (iii) 16 (iv) 10

21

(v) 17 (vi) 14 4. (i) (ii) (iii) (iv) (v) (vi) (vii) 5. Read it as, If represents 1 student and represent

2 students, then (i) represent …………… students. Ans. 3

(ii) represent …………… students. Ans. 4

(iii) …… represent 5 students. Ans.

(iv) …… will represent 6 students. Ans.

Drill Exercise – 64 1. (i) 24 (ii) 32

(iii) 20 (iv)

(v) (vi) (vii)

(viii)

2. (i) 40 (ii) 35

(iii) 25 (iv)

(v) (vi)

(vii)

Drill Exercise – 65 1. (i) 16, 6, 10, 8 (ii) 24, 9, 15, 12 (iii) 40, 15, 25, 20 2. (i) 1200 (ii) 1600 (iii) 2000 (iv) 2400 (v) 400 (vi) 1 : 2

Drill Exercise – 66 1. (i) Read it as The perimeter of simple closed figure is the

……………… around the boundary. Ans. distance

22

(ii) rectangle (iii) 4 × [length of a side) (iv) regular (v) regular (vi) length of a side (vii) surface 2. (i) 10 (ii) 10000 (iii) 1000 (iv) 10000 (v) 10 (vi) 1000000 3. (i) 110 (ii) 1.08 (iii) 128 (iv) 1000 (v) 9 (vi) 2500 4. (i) 3, 350 (ii) 11, 903 (iii) 2615 (iv) 25085 (v) 38036 (vi) 543.692 5. (i) Length × Breadth (ii) Length × Length (iii) 3.2 (iv) 12 (v) 50000 (vi) 15 (vii) 105000000 (viii) 200

Drill Exercise – 67 1. (i) 3 (ii) 5 (iii) 6 (iv) Length × Breadth (v) Length × Length 2. (i) 12 (ii) 66 (iii) 15 (iv) 6 (v) 60 (i) 48 (ii) 13 (iii) 76 3. (i) 100 cm (ii) 64 cm2 (iii) 302 (iv) 10 cm (v) 10 cm (vi) 25 cm (vii) 48

Drill Exercise – 68 1. (i) 21.28 (ii) 33.8, 67.2 (iii) 9.2 (iv) 15 2. (i) 10.24 (ii) 144 (iii) 7.6 (iv) 121 (v) 32 (vi) 16 (vii) 6

Drill Exercise – 69 1. (i) 8000 (ii) 600 (iii) 27 (iv) 75 (v) 24 (vi) 6 (vii) 8 (viii) 8 2. (i) 5 (ii) 14 (iii) 10 (iv) 5 (v) 9 (vi) 5 (vii) 10 (viii) 7

Drill Exercise – 70 1. For a rectangle: (i) 45 m2 (ii) 20 m (iii) 2500 m (iv) 2

(v) 25

m2 (vi) 20 m (vii) 5

23

For a square: (i) 81 cm2 (ii) 12 m (iii) 6.25 cm2 (iv) 6.5 cm

(v) 10.24 m2 (vi) 4.2 m (vii) 3.24 cm2 (viii) 2.8 m

2. (i) 54 (ii) 93.5 (iii) 20.25 3. (i) 2.1 cm (ii) 20.3 m (iii) 24.3 cm2 (iv) 10.201 (v) 36.1201 (vi) 11 cm (vii) 1.21

Drill Exercise – 71 1. (i) 16 cm, 15 cm2 (ii) 30 cm, 47.25 cm2

(iii) 25.6 cm, 36.55 cm2 (iv) 16.8 cm, 17.64 cm2

(v) 9.6 cm, 5.76 cm (vi) 16 cm, 16 cm2

2. (i) 16 cm2 (ii) 13.2 cm (iii) 20 (iv) 36.75 (v) 28 (vi) 104 (vii) 29 (viii) 39.69

Drill Exercise – 72

1. (i) 10.1 (ii) 56 (iii) 23 (iv) 32 (v) 75 (vi) 10, 5, 50 2. (i) 5.52 (ii) 2.5 (iii) 3 (iv) 1, 75 3. (i) 64 (ii) 144 (iii) 160

Drill Exercise – 73 1. (i) 26, 26 (ii) 75, 103.5 (iii) 98.5, 171 2. (i) 36, 45 (ii) 56, 96 (iii) 63, 90

Drill Exercise – 74 1. (i) variable (ii) letters (iii) constants, variables (iv) term (v) equation (vi) solution (vii) solving (viii) L.H.S., R.H.S. (ix) does not change 2. (i) x + 5 (ii) x – 3 (iii) 4x (iv) x + 8 (v) x – 9 (vi) 12 – x

(vii) x ÷ 8 or x8

(viii) 10 ÷ x or 10x

(ix) –3x (x) x ÷ –5 or – x5

(xi) x – 7

24

Drill Exercise – 75

1. (i) x + 21 (ii) 2x (iii) –10y (iv) z6 (v) –10 – m (vi) 15 – t

2. (i) 3x – y (ii) 9p + 7 (iii) z5

+ 13 (iv) –5 m + 16

(v) 5x + 15 (vi) – 3n8

3. (i) 18 – x (ii) –10 – z (iii) 2t – p (iv) 15 – q3

(v) –15 – x4

(vi) 20 – 3x (vii) 6x – 2

Drill Exercise – 76 1. (i) 2x (ii) z + 10 (iii) x – 4 (iv) x + 15 (v) 4p (vi) x – 10 (vii) x – 4 (viii) x + 5

2. (i) 5x (ii) y+3 (iii) x7

(iv) x+2 (v) x3

(vi) 3x+2

Drill Exercise – 77 1. (i) x = 10 (ii) x = 40 (iii) p = 10 (iv) p = 4 (v) x = 7 (vi) x = 63 (vii) x = 5 (viii) x = 3 (ix) x = – 6 (x) x = 30 2. (i) Option [x = 4, x = 5] Ans. x = 5 (ii) x = 25

(iii) x = 83

(iv) x = –20 (v) x = 263

(vi) x = 45

(vii) x = 5 (viii) x = 32

(ix) – 32

(x) x = 283

Drill Exercise – 78 1. (i) x + 9 = 16 (ii) 3x + 12 = 42 (iii) 3x + 9 = 27 (iv) 5x – 5 = 35 (v) 24 – 4x = 8 (vi) x

9 = 12

(vii) x12

+ 10 = 22 (viii) 11 + 2x5

= 21

(ix) 34

x – 9 = 9 (x) 9 + x4

= 15

(xi) x – x6

= 6

2. (i) x – 9 = 16 (ii) 3x – 9 = 27

(iii) 34 – 5x = 9 (iv) 34

x = 12

(v) 4 + 35

x = 13 (vi) 10 + x7

= 20

(vii) 7 + x5

= 12 (viii) 23 x – 11 = 17

25

Drill Exercise – 79

1. (i) 9 (ii) 12 (iii) 16 (iv) 23 (v) 10 (vi) –24

(vii) 92

2. (i) 6 (ii) 263

(iii) –1 (iv) 20

(v) –11 (vi) 11 (vii) –2

Drill Exercise – 80 1. (i) 15 (ii) 19 (iii) 63 and 65 (iv) 120 and 122 (v) 11 (vi) 20 (vii) 12 (viii) 2 (ix) 8 (x) 64

Drill Exercise – 81 1. (i) Ratio (ii) multiplying, dividing (iii) no (iv) proportion (v) simplest (vi) extremes (vii) means (viii) product (ix) number of quantities (x) number of quantities 2. (i) : (ii) proportion (iii) two (iv) four (v) extremes (vi) means (vii) More (viii) Less

Drill Exercise – 82 1. (i) 2 : 3 (ii) 2 : 3 (iii) 3 : 1 (iv) 3 : 8 (v) 5 : 6 (vi) 7 : 12 (vii) 3 : 2 (viii) 3 : 10 (ix) 3 : 2 (x) 8 : 3 2. (i) 24 : 15 (ii) 3 : 5 (iii) 1 : 4 (iv) 3 : 2 (v) 1 : 1 (vi) 2 : 3 (vii) 3 : 13 (viii) 7 : 8 (ix) 2 : 9 (x) 1 : 6 3. (i) 121, 121, 3 : 11 (ii) 40, 40, 15 : 4 (iii) 200, 200, 3 : 20 (iv) Read it as 15 km to 900 m = 15000 m to …… m or 15000 : …… , Lowest form ……

Ans. 900, 900, 50 : 3

26

(v) 2000, 2000, 9 : 40 (vi) 90, 90, 1 : 3 (vii) 50, 12 : 5

Drill Exercise – 83 1. (I) (a) 48 (b) 5 : 3 (c) 3 : 5 (d) 3 : 8 (e) 5 : 8 (f) 8 : 5 (g) 8 : 3 (II) (a) 3400 (b) 3 : 2 (c) 5 : 3 (d) 9 : 10 (e) 3 : 5 (f) 9 : 34 (g) 15 : 34 (h) 34 : 9 (i) 34 : 15 (j) 10 : 34 2. (I) (a) 50 m (b) 3 : 2 (c) 6 : 25 (d) 25 : 9 (e) 2 : 3 (f) 25 : 6 (g) 9 : 25 (II) (a) 6000 (b) 5 : 2 (c) 3 : 5 (d) 2 : 5 (e) 5 : 3 (f) 3 : 2 (g) 2 : 3 (III) (a) 5 : 3 (b) 3 : 5

Drill Exercise – 84 1. (i) 1 : 10 (ii) 15 : 1 (iii) 1 : 5 (iv) 3 : 2 (v) 1 : 15 (vi) 1 : 3 (vii) Option [3 : 1/1 : 6] Ans. 3 : 1 (viii) 10 : 1 (ix) 3 : 10 (x) 3 : 1 2. (i) 3 : 2 (ii) 3 : 5 (iii) 5 : 2 (iv) 2 : 3 (v) 2 : 5 3. (i) 2 : 5 (ii) 1 : 5 (iii) 5 : 1

Drill Exercise – 85 1. (i) 14, 3, 12 (ii) 4, 12, 2 (iii) 5, 4, 1 (iv) 35, 27, 21 (v) 88, 49, 121 (vi) 75, 16, 45 2. (i) 5 : 6 (ii) 13 (iii) 16 (iv) 10 3. (i) 6 : 8, 9 : 12, 12 : 16 (ii) 10 : 18, 15 : 27, 20 : 36 (iii) 32 : 14, 48 : 21, 64 : 28 (iv) 4 : 18, 6 : 27, 8 : 36 (v) 22 : 20, 33 : 30, 44 : 40 (vi) 4 : 3, 16 : 12, 12 : 9 (vii) 30 : 32, 45 : 48, 60 : 64 (viii) 18 : 2, 27 : 3, 36 : 4 (ix) 6 : 22, 9 : 33, 12 : 44 (x) 26 : 4, 39 : 6, 52 : 8 4. (i) 2 : 1 (ii) 2 : 1 (iii) 1 : 5 (iv) 6 : 1 (v) 1 : 1

Drill Exercise – 86 1. (i) 45 (ii) 45 (iii) 16 (iv) 24

27

(v) 72 (vi) 221 (vii) 45 (viii) 945 (ix) 45 2. (i) 45 (ii) 252 (iii) 4 (iv) 6 (v) 2 (vi) 85.33 (vii) 35 : (viii) 45 : (ix) 60 (x) 48 3. (i) Read it as $ 15 : $ 75 = …… : 200 Ans. 40 (ii) 9 hours (iii) 64 m (iv) 99 (v) 15 litres (vi) 9.24 kg (vii) 945 (viii) 16 hours (ix) 220 kg (x) 150

Drill Exercise – 87 1. (i) 10.5 (ii) 45 (iii) 40.5 (iv) x = 21 (v) x = 24 (vi) x = 18 (vii) x = 42 2. (i) x = 45 (ii) x = 4 (iii) x = 35 (iv) x = 6 (v) x = 88 (vi) x = 2 (vii) 12 (viii) 22 (ix) 8

Drill Exercise – 88 1. (i) 45 (ii) 7 (iii) Read it as If 5, 15, 10 are the first, second and third

terms of a proportion respectively, then fourth term is …………

Ans. 30 (iv) 96 (v) 35 (vi) 8 (vii) 14 2. (i) 4.5 (ii) 0.126 (iii) 27 (iv) 4 (v) 44 (vi) 8 (vii) 12 (viii) 18 (ix) 9 (x) 22

Drill Exercise – 89

1. (i) 2.5 (ii) 12.5 2. (i) 12 (ii) 2.5 (iii) 6 (iv) 10 (v) 36 3. (i) 2.1 (ii) 300 (iii) 350 (iv) 1.2 4. (i) 32.26 (ii) 100 (iii) 155 (iv) 232.5 5. (i) 15 (ii) 144 (iii) 192 (iv) 3.75

28

Drill Exercise – 90Column 1 1. (i) 30 (ii) 270 (iii) 12 (iv) 9 2. (i) 120 (ii) 2160 (iii) 3840 (iv) 80 3. (i) 546 (ii) 780 (iii) 26Column 2 1. (i) 4.44 (ii) 11.11 (iii) 7.99 (iv) 1.99 2. (i) 8000 (ii) 96000 (iii) 56,000 (iv) 5 (v) 11 3. (i) 100 (ii) 360 (iii) 6 (iv) 18

Drill Exercise – 91Column 1 1. (i) 150 (ii) 300 (iii) 594 (iv) 891 2. (i) 136.4 (ii) 306.9 (iii) 6 (iv) 25Column 2 1. (i) 14 (ii) 20.5 (iii) 10 (iv) 2.5 2. (i) 8 (ii) 5 (iii) 15180 (iv) 11385 (v) 5060

Drill Exercise – 92 1. (i) symmetry (ii) axis (iii) scalene (iv) one (v) circle (vi) two (vii) equilateral (viii) line (ix) Lateral difference (x) image 2. (i) no (ii) countless (iii) three (iv) isosceles (v) equilateral (vi) two (vii) four

Drill Exercise – 93

1. (i) Symmetrical (ii) Symmetrical (iii) Symmetrical (iv) Symmetrical (v) Non-symmetrical (vi) Symmetrical (vii) Symmetrical (viii) Non-symmetrical (ix) Symmetrical

29

2. (i) Symmetrical (ii) Symmetrical (iii) Non-symmetrical (iv) Symmetrical (v) Non-symmetrical (vi) Symmetrical (vii) Non-symmetrical

Drill Exercise – 94 1. (i) one (ii) one (iii) one (iv) two (v) Options [none/two] Ans. none (vi) four 2. (i) one (ii) two (iii) one (iv) one (v) non-symmetrical (vi) non-symmetrical

Drill Exercise – 95

1. (i) (a) AD (b) BE (c) CF (ii) (a) HF (b) EG (iii) (a) GH (b) BE 2. (i) (a) AC (b) FH (c) BD (d) EG (ii) (a) A (b) FC (c) EH (d) JB (e) DG

Drill Exercise – 96 1. (i) Symmetrical (ii) Non-symmetrical (iii) Non-symmetrical (iv) Symmetrical (v) Non-symmetrical (vi) Non-symmetrical (vii) Non-symmetrical (viii) Non-symmetrical (ix) Symmetrical 2. (i) Symmetrical (ii) Symmetrical (iii) Symmetrical (iv) Non-symmetrical (v) Symmetrical (vi) Symmetrical (vii) Symmetrical

Drill Exercise – 97 1. (i) Symmetrical (ii) Symmetrical (iii) Symmetrical (iv) Non-symmetrical (v) Symmetrical (vi) Non-symmetrical (vii) Non-symmetrical 2. (i) Non-symmetrical (ii) Non-symmetrical (iii) Symmetrical (iv) Symmetrical

30

(v) Non-symmetrical (vi) Symmetrical (vii) Non-symmetrical

Drill Exercise – 98 1. (i) 2 (ii) 4 (iii) 3 (iv) 1 (v) 2 (vi) 2 (vii) 1 (viii) 6 (ix) 5 (x) 1 (xi) 2

Drill Exercise – 99 1. (i) 1 (ii) 1 (iii) 2 (iv) 1 (v) 1 (vi) 1 (vii) 1 (viii) 1 (ix) 2

Drill Exercise – 100 1. (i) 6 (ii) 1 (iii) 1 (iv) 1 (v) 2 (vi) 4 (vii) 1 (viii) 1 (ix) 1 (x) 1

Drill Exercise – 101 1. (i) 2 (ii) 1 (iii) 1 (iv) 1 (v) 1 (vi) 1 (vii) nil (viii) 4 (ix) 2

Miscellaneous Drill Exercise 1. (i) 90090 (ii) 49950 (iii) one crore nineteen lakh ninety one thousand one

hundred ninety nine. (iv) ten-thousand (v) thousand (vi) 1000000 (vii) XLIX (viii) 49 2. (i) 1 (ii) 0 (iii) 1729000 (iv) 2100 (v) 155 (vi) Read it as If 197209 ÷ 991 = 199, then 199 × 991 = ………

Ans. 197209 3. (i) 1 (ii) 0 (iii) predecessor (iv) 2 (v) 0 (vi) 1 (vii) 0 (viii) 1

31

4. (i) perfect number (ii) number itself (iii) factors (iv) 9, 18, 27 5. (i) prime (ii) composite (iii) 1 6. (i) 2 (ii) 4 (iii) 10 (iv) odd (v) even (vi) 5 (vii) 3 (viii) prime-triplet 7. (i) indefinitely (ii) 1 (iii) 2 (iv) A (v) unlimited (vi) line (vii) always (viii) one 8. (i) polygon (ii) triangle (iii) diameter (iv) in (v) 2 (vi) two (vii) four (viii) equilateral (ix) right 9. (i) quadrilateral (ii) triangles (iii) 90° (iv) 2 (v) scalene (vi) parallel (vii) 90° (viii) equal (ix) square 10. (i) 120° (ii) 540° (iii) greater (iv) –1 (v) 1 (vi) 1 (vii) 1 (viii) 0 (ix) 0 (x) –8 (xi) 20 (xii) –4 (xiii) –144

11. (i) 1 and 6 (ii) 1220

(iii) 18148

(iv) an improper (v) 2 35

(vi) 23

(vii) 12

12. (i) 0 (ii) 0 (iii) 14

(iv) –4 110

(v) 2 12

13. (i) 210

(ii) 510

(iii) 5 (iv) 10 (v) 510

14. (i) 16.316 (ii) 113.286 (iii) 92.623 (iv) 18.18 (v) 1.001

32

15. (i) 0.35 (ii) 815 (iii) 3, 5 (iv) 0.8 (v) 2.8 (vi) 35.17 (vii) 17.35 (viii) 72.2 (ix) 10.06 (x) 0.932 (xi) 2002 (xii) 2.002 (xiii) 2, 2 (xiv) 3 (xv) 4023 (xvi) 18001 (xvii) 0.021 (xviii) 0.1 16. (i) 100000 (ii) 130000 (iii) 70000 17. (i) 10000 (ii) 100 (iii) 1000000 (iv) 1000000 (v) 100 (vi) 10000 18. (i) breadth (ii) 3 (iii) side × side (iv) 2 length + 2 breadth (v) side (vi) 8 cm (vii) 20 cm 19. (i) (a) 180 (b) 54 (ii) (a) 25 (b) 20 (iii) 256 (iv) 16 (v) 9 (vi) 8 (vii) 80 20. (i) 180, 72 (ii) 58.5, 45 (iii) 216, 84 21. (i) 64 (ii) 48 (iii) 104 (iv) 30.25,22 (v) 32.6, 60.9 (vi) 5.5 22. (i) root (ii) equation (iii) +, –

23. (i) x – 25 (ii) 8x – y (iii) 15 + x6

(iv) 6x + 18

24. (i) 2(x + 18) (ii) – 8 – x (iii) 3x – y (iv) 10 + 8x

(v) x + 5 (vi) x = 20 (vii) x = 2 25. (i) 3 (ii) 2 (iii) no (iv) infinite 26. (i) (a) RS (b) PQ (ii) (a) CD (b) EF (c) AB (d) GH 27. (i) one (ii) two (iii) symmetrical (iv) non-symmetrical (v) symmetrical (vi) one (vii) one 28. (i) equal (ii) second, third (iii) extremes (iv) 4 (v) anticedent, consequent (vi) 3 : 7 (vii) 5 : 18 29. (i) 15, 72, 30 (ii) 1 : 2 (iii) 45 30. (i) Read it as 15, 12, 20 and …… are in proportion. Ans. 16 (ii) 48 (iii) 8 (iv) 13.5 (v) 5.83