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Answer BookDrill exercises in
MAtheMAtics
clAss Vi
ByPrernA GuPtA
AryA Publishing ComPAnyVillage Johron, Trilokpur Road, Kala Amb-173030, Distt. Sirmour (H.P.)
Delhi Office: 1002 Faiz road, Karol bagh, new Delhi 110 005
Web support available at
www.apcplus.in
All rights reserved.
No part of this book may be reproduced or transmitted in any form or by any means [graphic, electronic or mechanical, including photocopying, recording, taping or in-formation retrieval system] without the written permission of the publisher. Breach of this condition is liable for legal action.
Published by :AryA Publishing ComPAnyVillage Johron, Trilokpur RoadKala Amb 173 030, Distt. Sirmour (H.P.)
Delhi office :1002 Faiz Road (opp. Hanuman Murti)Karol Bagh, New Delhi-110 005 (India)Phone : 011-25862745, 25822604Fax : 011-25716921E-mail : [email protected] : www.apcbooks.co.in | www.apcplus.in
© Reserved
ISBN–978–81–8296–577–5
First Edition : 2016
Price : $ 36.00
Typeset & Designed at :Eltee Printmaster
Printed at :Capital offsetBawana Industrial Area, Delhi
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