ANSWERS EXERCISE 1.1 EXERCISE EXERCISE 1.3 EXERCISE 2.1

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1 ANSWERS EXERCISE.. (a) Ten 2. (a) 7,7,07 Ten 9,0,00,0 Ten 7,2, 2,02 (d) Ten (d) 8,2,202 (e) Ten (e) 2,0,00. (a) 8,7,9,762 Eight crore seventy-five lakh ninety-five thousand seven hundred sixty two. 8,6,28 Eighty-five lakh forty-six thousand two hundred eighty-three. 9,99,00,06 Nine crore ninety-nine lakh forty six. (d) 9,8,2,70 Nine crore eighty-four lakh, thirty-two thousand seven hundred one.. (a) 78,92,092 Seventy-eight million, nine hundred twenty-one thousand, ninety-two. 7,2,28 Seven million four hundred fifty-two thousand two hundred eighty-three. 99,98,02 Ninety-nine million nine hundred eighty-five thousand, one hundred two. (d) 8,09,8 Forty-eight million forty-nine thousand eight hundred thirty one. EXERCISE.2. 7,707 tickets 2.,020 runs. 2,28,800 votes. Rs. 6,86,69; second week, Rs.,,877. 2, ,7 screws 7. Rs. 0, , shirts, m 0 cm boxes. 22 km 00 m glasses. EXERCISE.. (a), (a),000 ;,090 6,00 ; 6,0 6,000 7,800 ; 7,80 (d) 7,000 (d),0,900 ;,0,980. (a),20,000,7,00,000 7,80,000 (d),00,000 EXERCISE 2..,000 ;,00 ;, ,000 ; 9,999 ; 9, (a) 2,0,702,00,200,000,00 (d) 2,,67 6. (a) 9 9,999 2,08,089 (e) 76,,20

2 MATHEMATICS 7. (a) 0 is on the left of 0 ; 0 > 0 07 is on the left of 70 ; 70 > 07 6,789 is on the left of 98,76 ; 98,76 > 6,789 (d) 98,0, is on the left of,00,2,00 ; 98,0, <,00,2,00 8. (a) F F T (d) T (e) T (f) F (g) F (h) F (i) T (j) F (k) F (l) T (m) F EXERCISE 2.2. (a),08, (a),76,800 6,600 2,9,000 (d) 27,90,000 (e) 8,00 (f) 0,00,000. (a),90,27,900 8,26,00 (d),92,2,000. (a) 76,0 87,08 2,60,06 (d),68,80. Rs, Rs,00 7. (i) (ii) (a) (iii) EXERCISE 2.. (a) 2. Yes. Both of them will be l. (a) 7,28,2,7 20,600 (d),,7 (e) 7, = = 9876 EXERCISE.. (a), 2,,, 6, 8, 2, 2,,,,, 7, 2 (d),, 9, 27 (e), 2,,, 6, 2 (f), 2,,, 0, 20 (g), 2,, 6, 9, 8 (h), 2 (i), 2,,, 6, 9, 2, 8, 6 2. (a), 0,, 20, 2 8, 6, 2, 2, 0 9, 8, 27, 6,. (i) (ii) (d) (iii) (a) (iv) (f) (v) (e). 9, 8, 27, 6,,, 6, 72, 8, 90, EXERCISE.2. (a) even number even number 2. (a) F T T (d) F (e) F (f) F (g) F (h) T (i) F (j) T. 7 and 7, 7 and 7, 79 and 97. Prime numbers : 2,,, 7,,, 7, 9 Composite numbers :, 6, 8, 9, 0, 2,,, 6, (a) (d) + (This could be one of the ways. There can be other ways also.)

3 ANSWERS 7., ;, 7 ;, 8. (a) and 9. 90, 9, 92, 9, 9, 9, (a) (d) (This could be one of the ways. There can be other ways also.). 2, ; 2, ;, 7; 7, ;, 9 2. (a) prime number composite number prime number, composite number (d) 2 (e) (f) 2 EXERCISE.. Number Divisible by Yes Yes No Yes Yes No Yes Yes Yes 86 Yes No No No No No No No No 27 No No No Yes No No No No Yes 6686 Yes No No No No No No No No 6920 Yes Yes No Yes Yes No No Yes Yes 297 Yes Yes No No Yes No Yes No No 286 Yes Yes Yes No Yes Yes No No No 060 Yes Yes Yes Yes Yes No Yes Yes No 0689 No Yes No No No No No No No 2. Divisible by : (a),,, (d), (f), (g), (h), (i) Divisible by 8 :, (d), (f), (h). (a), (f), (g), (i). (a),, (d), (e), (f). (a) 2 and 8 0 and 9 6. (a) 8 6 EXERCISE.. (a), 2,,, (d), 2,, 8 2. (a), 2,,. (a) 2, 8, 72 6, 72, 08. 2, 2, 6, 8, 60, 72, 8, 96. (a),, (e), (f ) , 2,,, 6 EXERCISE.. (a) F T F (d) T (e) F (f) F (g) T (h) T (i) F 2. (a) 29

4 MATHEMATICS. and the number itself. 9999, 9999 = , 0000 = = 7 9 The difference of two consecutive prime factors is 6 7. (i) 2 = 2 is divisible by 6. (ii) 6 7 = 20 is divisible by 6. 9., 0. Yes. No. Number 2 is divisible by both and 6; but 2 is not divisible by = 20 EXERCISE.6. (a) (d) 9 (e) 2 (f) (g) (h) 7 (i) 9 (j) 2. (a) 2. No ; EXERCISE.7. kg cm. 7 cm minutes 2 seconds past 7 a.m. 7. litres (a) (d) 60 Here, in each case LCM is a multiple of Yes, in each case LCM = the product of two numbers. (a) (d) The LCM of the given numbers in each case is the larger of the two numbers. EXERCISE.. (a) O, B, C, D, E. Many answers are possible. Some are: DE, DO, DB, EO etc. Many answers are possible. Some are: DB, DE, OB, OE, EB (d) Many answers are possible. Some are: DE, DO, EO, OB, EB etc. 2. AB, AC, AD, BA, BC, BD, CA, CB,CD, DA, DB, DC.. (a) Many answers. One answer is AE. Many answers. One answer is AE. CO or OC etc. 296 (d) Many answers are possible. Some are, CO, AE and AE, EF.

5 ANSWERS. (a) Countless Only one. 6. (a) T T T (d) F (e) F (f) F (g) T (h) F (i) F (j) F (k) T EXERCISE.2. Open : (a), ; Closed :, (d), (e).. (a) Yes Yes. (a) Not possible. EXERCISE.. A or DAB; B or ABC; C or BCD; D or CDA 2. (a) A A, C, D. E, B, O, F. EXERCISE. 2. (a) Δ ABC, ΔABD, Δ ADC. Angles: B, C, BAC, BAD, CAD, ADB, ADC (d) Line segments: AB, AC, BC, AD, BD, DC Δ ABC, Δ ABD EXERCISE.. The diagonals will meet in the interior of the quadrilateral. 2. (a) KL, NM and KN, ML K, M and N, L (d) KL, KN and NM, ML or KL, LM and NM, NK K, L and M, N or K, L and L, M etc. EXERCISE.6. (a) O OA, OB, OC AC (d) ED (e) O, P (f) Q (g) OAB (Shaded portion) (h) Segment ED (Shaded portion) 2. (a) Yes No. (a) True True EXERCISE.. Chances of errors due to improper viewing are more. 2. Accurate measurement will be possible.. Yes. (because C is between A and B).. B lies between A and C.. D is the mid point of AG (because, AD = DG = units). 6. AB = BC and BC = CD, therefore, AB = CD 7. The sum of the lengths of any two sides of a triangle can never be less than the length of the third side. 297

6 MATHEMATICS EXERCISE.2. (a) (d) (e) (f) 2 2. (a) (d) 2. (a) West West North (d) South (To answer (d), it is immaterial whether we turn clockwise or anticlockwise, because one full revolution will bring us back to the original position).. (a) 2. (a) 2 2 (d) (e) (f) 2 6. (a) (d) 2 ( clockwise or anticlockwise). 7. (a) (d) 7 (We should consider only clockwise direction here). EXERCISE.. (i) ; (ii) (d); (iii) (a); (iv) (e); (v). 2. Acute : (a) and(f); Obtuse : ; Right: ; Straight: (e); Reflex : (d). EXERCISE.. (i) 90 ; (ii) (a) T F T (d) T (e) T. (a) Acute: 2, 89 ; Obtuse: 9, (a) acute obtuse (if the angle is less than 80 ) straight (d) acute (e) an obtuse angle , 0, The view through a magnifying glass will not change the angle measure. EXERCISE.. (a) and One is a set square; the other is a 90 set square. The angle of measure 90 (i.e. a right angle) is common between them.. (a) Yes Yes BH, DF (d) All are true. 298 EXERCISE.6. (a) Scalene triangle Scalene triangle Equilateral triangle (d) Right triangle (e) Isosceles right triangle (f) Acute-angled triangle 2. (i) (e); (ii) (g); (iii) (a); (iv) (f); (v) (d); (vi) ; (vii).. (a) Acute-angled and isosceles. Right-angled and scalene. Obtuse-angled and isosceles. (d) Right-angled and isosceles. (e) Equilateral and acute angled. (f) Obtuse-angled and scalene.. is not possible. (Remember : The sum of the lengths of any two sides of a triangle has to be greater than the third side.)

7 ANSWERS EXERCISE.7. (a) T T T (d) T (e) F (f) F 2. (a) A rectangle with all sides equal becomes a square. A parallelogram with each angle a right angle becomes a rectangle. A rhombus with each angle a right angle becomes a square. (d) All these are four-sided polygons made of line segments. (e) The opposite sides of a square are parallel, so it is a parallelogram.. A square is a 'regular' quadrilateral EXERCISE.8. (a) is not a closed figure and hence is not a polygon. is a polygon of six sides. and (d) are not polygons since they are not made of line segments. 2. (a) A Quadrilateral A Triangle A Pentagon (-sided) (d) An Octagon EXERCISE.9. (a) (ii); (iv); (v); (d) (iii); (e) (i). 2. (a), and are cuboids; (d) is a cylinder; (e) is a sphere. EXERCISE 6.. (a) Decrease in weight 0 km south 26 A.D. (d) Gain of Rs 700 (e) 00 m below sea level 2. (a) (d) 700. (a) (d) (e) 6 299

8 MATHEMATICS. (a) F negative integer B +, E 0 (d) E (e) D, C, B, A, O, H, G, F, E. (a) 0 C, 2 C, + 0 C, + 20 C, C Siachin (d) Ahmedabad and Delhi 6. (a) 9 0 (d) 0 (e) 6 (f) 7. (a) 6,,,, 2,, 2,, 0,, 2,,, 2,, 0, 9 (d) 29, 28, 27, 26, 2, 2 8. (a) 9, 8, 7, 6, 2,, 9. (a) T F; 00 is to the left of 0 on number line F; greatest negative integer is (d) F; 26 is smaller than 2 0. (a) 2 to the left (d) to the right EXERCISE 6.2. (a) 8 0 (d) 2. (a) (d) 0 (e)

9 ANSWERS (f) 2. (a) 9 (d) 00 (e) 60 (f ) 7. (a) (d) 0. (a) 8 EXERCISE 6.. (a) 8 (d) (e) (f) 8 2. (a) < > > (d) >. (a) 8 0 (d) 8 (e). (a) (d) 92 EXERCISE (i) (ii) (iii) (iv) (v) (vi) (vii) 0 (viii) (ix) (x) Shaded portions do not represent the given fractions (a) Arya will divide each sandwich into three equal parts, and give one part of each sandwich to each one of them ,,,, 6, 7, 8, 9, 0,, 2; 9. 02, 0, 0, 0, 06, 07, 08, 09, 0,, 2, ; , 8 EXERCISE 7.2. (a) 0

10 MATHEMATICS 2. (a) (d) (e) 6 (f) 8 9. (a). (a) 2. (a) (ii) (d) EXERCISE 7. 2,,, ; Yes 2 6,,,, ; No 2 8 (iii) (iv) (d) (v) (a), (ii);, (iv);, (i); (d), (v); (e), (iii). (a) (d) 20 (e). (a). (a) (d) (a) equivalent not equivalent not equivalent 7. (a) 2 8. Ramesh 0 =, Sheelu 2 =, Jamaal 0 =. Yes (i) (d) (ii) (e) (iii) (a) (iv) (v) EXERCISE 7.. (a) < < < 6 < < 6 < (d) (e) (e) (e) 66 7 (f) (i) >, > 0, < 6, 8 >

11 ANSWERS 2. (a). (a) (e). (a) (e) (i) 6. (a) (g) < 6 6 < 6 < 6 > 2 6 < (f) 7 < (j) 8 6 (h) < 7 2 > 6 2 = 6 7 > (g) < (k) 0 6 (i) > (d) 2 2 > (d) 2 < (d) 2 = (h) 8 = (d) (j) < 6 = 6 2 > < 0 2 (a), (e), (h), (j), (k) ;, (f), (g) ;, (d), (i), (l) 7. (a) No ; =, = and No ; =, = and Yes ; = (d) No ; = 2 and Ila has read less 9. Rohit 0. Same fraction ( ) of students got first class in both the classes. 6 (e) (k) 6 6 (f) (l) 2 EXERCISE 7.. (a) (a) 9 (f) (g). The complete wall. (h) 2 7 (d) (e) (i) 0

12 MATHEMATICS. (a) 2 ( = ) ( ) 6 = (d) EXERCISE 7.6. (a) (f) (l) (g) (m) (h) (n) 6 6 ( = ) (i) (d) (e) (j) ( ) 6 = (k) 2. 2 metre (a) Length of the other piece = 8 metre 7. 2 The distance walked by Nandini = ( = ) km 0 8. Asha s bookshelf is more full; by 0 9. Rahul takes less time; by 9 20 minutes EXERCISE Hundreds Tens Ones Tenths (00) (0) () ( 0 ) (a) 0 2 0

13 ANSWERS 2. Hundreds Tens Ones Tenths (00) (0) () ( 0 ) (a) (d) (a) (d) 02.0 (e) (a) (d) 70.8 (e) 8.8 (f).2 (g). (h) 0. (i) 2. (j).6 (k).. (a) 6, ,, (d), (e), (f) , (g), (a) 0.2cm.0 cm.6 cm (d).2 cm (e) 6.2 cm (f) 8. cm 7. (a) 0 and ; and 6; 2 and ; (d) 6 and 7; 6 (e) 9 and 0; 9 (f) and ; A, 0.8 cm; B,. cm; C, 2.2 cm; D, 2.9 cm 0. (a) 9. cm 6. cm EXERCISE 8.2. Ones Tenths Hundredths Number (a) (a) (d) (e) 2.2. Hundreds Tens Ones Tenths Hundredths Thousandths (a) (d) (e)

14 MATHEMATICS. (a) (d) (e) (a) Zero point zero three One point two zero One hundred eight point five six (d) Ten point zero seven (e) Zero point zero three two (f) Five point zero zero eight 6. (a) 0 and and and 0.2 (d) 0.6 and 0.7 (e) 0.9 and.0 (f) 0. and (a) (f) 8 (g) EXERCISE 8.. (a) (d) 0. (e).2 (f) 0.9 (g) both are same (h).90 (i) both are same (j).6 EXERCISE 8.. (a) Re 0.0 Re 0.7 Re 0.20 (d) Rs 0.90 (e) Rs (a) 0. m 0.06 m 2. m (d) 9.07 m (e).9 m. (a) 0. cm 6.0 cm 6. cm (d) 9.8 cm (e) 9. cm. (a) km km km (d) km. (a) kg 0. kg.70 kg (d).008 kg (e) 26.0 kg EXERCISE 8.. (a) (d) 8. (e).7 (f) Rs 68.. Rs m..02 km km kg EXERCISE 8.6. (a) Rs m Rs.0 (d). km (e).79 kg 2. (a) (d).7. Rs.. Rs m km 7..2 kg EXERCISE 9. (d) 9 0 (e) 06. Marks Tally marks Number of students

15 ANSWERS (a) Sweets Tally marks Number of students Ladoo Barfi Jalebi 7 Rasgulla 9 Ladoo. Numbers Tally marks How many times? (a) and 6. (i) Village D (ii) Village C (iii) (iv) 28. (a) VIII No 2 6. (a) Number of bulbs sold on Monday are 2. Similarly, number of bulbs sold on other days can be found. Maximum number of bulbs were sold on Sunday. Same number of bulbs were sold. On Wednesday and Saturday. (d) Then minimum number of bulbs were sold on Wednesday and Saturday. (e) The total number of bulbs sold in the given week were (a) Martin 700 Anwar, Martin, Ranjit Singh 0. EXERCISE 9.2 (a) 6 Village B Village C 07

16 MATHEMATICS 2. A (a) 6 complete and incomplete B Second EXERCISE 9.. (a) (a) This bar graph shows the number of shirts sold from Monday to Saturday unit = shirts Saturday, 60 (d) Tuesday (e). (a) This bar graph shows the marks obtained by Aziz in different subjects. Hindi Social Studies (d) Hindi 80, English 60, Mathematics 70, Science 0 and Social Studies 0. EXERCISE 9.. Unit length = students 08 Reading story books.

17 ANSWERS 2. Unit length = books Days. Unit length = 00 bicycles 09

18 MATHEMATICS. (a) Number of thousands Unit length = 20 thousand Age group 0 (a) 0, 9 lakh 20 thousand EXERCISE 0.. (a) 2 cm cm 60 cm (d) cm (e) cm (f) 2 cm cm or m. 7. m. 06 cm. 9.6 km 6. (a) 2 cm 27 cm 22 cm 7. 9 cm 8. 8 m 9. m cm. (a) 7. cm 0 cm cm 2. 0 cm. Rs 20,000. Rs Bulbul 6. (a) 00 cm 00 cm 00 cm (d) 00 cm All the figures have same perimeter. 7. (a) 6 m 0 m Cross has greater perimeter EXERCISE 0.2. (a) 9 sq units sq units sq units (d) 8 sq units (e) 0 sq units (f) sq units (g) 6 sq units (h) sq units (i) 9 sq units (j) sq units (k) sq units (l) 8 sq units (m) sq units (n) 8 sq units EXERCISE 0.. (a) 2 sq cm 22 sq cm 6 sq km (d).0 sq m 2. (a) 00 sq cm 96 sq cm 2 sq m

19 ANSWERS. largest area smallest area. 6 m. Rs sq m 7. sq m 8. sq m 9. sq m 0. (a) 28 sq cm 9 sq cm. (a) 0 sq cm 2 sq cm 9 sq cm 2. (a) 20 tiles 2 tiles EXERCISE.. (a) 2n n n (d) 2n (e) n (f) n (g) 6n 2. (a) and (d); The number of matchsticks required in each of them is 2. n. 0b. s 6. t km 7. 8r, 6, (x ) years 9. l x + 0. (a) x +, x = number of squares 2x +, x = number of triangles EXERCISE.2. l 2. 6l. 2l. d = 2r. (a + b) + c = a + (b + c) EXERCISE. 2., (d). (a) Addition, subtraction, addition, subtraction Multiplication, division, multiplication Multiplication and addition, multiplication and subtraction (d) Multiplication, multiplication and addition, multiplication and subtraction. (a) p + 7 p 7 7 p (d) (e) m 7 (f) p (g) p (h) p. (a) 2m + 2m y + (d) y (e) 8y (f) 8 y + (g) 6 y (h) y (a) t t +, t, t,,, t, + t t 2y + 7, 2y 7, 7y + 2,...,..., EXERCISE.. (a) (i) y + (ii) y (iii) 6y (iv) 6y 2 (v) y + (b ) metres length = h cm, breadth = h 0 cm (d) s + 8, s 7, s 0 (e) (v + 20) km 2. (a) A book costs three times the cost of a notebook. Tony s box contains 8 times the marbles on the table. p 7

20 MATHEMATICS (d) (e) Total number of students in the school is 20 times that of our class. Jaggu s uncle is times older than Jaggu and Jaggu s aunt is years younger than his uncle. The total number of dots is times the number of rows. EXERCISE.. (a) an equation with variable x (e) an equation with variable x (f) an equation with variable x (h) an equation with variable n (j) an equation with variable p (k) an equation with variable y (o) an equation with variable x 2. (a) No Yes No (d) No (e) No (f) Yes (g) No (h) No (i) Yes (j) Yes (k) No (l) No (m) No (n) No (o) No (p) No (q) Yes. (a) (d) (e) (f) 2. (a) (d) 0. (i) 22 (ii) 6 (iii) 7 (iv) EXERCISE 2.. (a) : : 7 2. (a) : 2 2 :. (a) : 2 2 : 7 2 : 7. :., 2, 2, Yes 6. (a) : : 9 : (d) 2 : 7. (a) : : : 20 (d) : 8. (a) : : : 0 0. (a) : 26 0 : 0 : 26. (a) : 6 : : 2 2. : ; and and 6 6. (a) : 0 : : 6 (d) : EXERCISE 2.2. (a) Yes No No (d) No (e) Yes (f) Yes 2. (a) T T F (d) T (e) F (f) T. (a) T T T (d) T (e) F. (a) Yes, Middle Terms m, Rs 0; Extreme Terms 2 cm, Rs 60 Yes, Middle Terms 6 litres, 6 bottles; Extreme Terms 9 litres, 2

21 ANSWERS 0 bottles No. (d) Yes, Middle Terms 2. litres, Rs ; Extreme Terms 200 ml, Rs 0 EXERCISE 2.. Rs Rs mm. (a) Rs kg. degrees 6. Rs 0, bananas 8. kg litres 0. Manish. Anup EXERCISE.. Four examples are the blackboard, the table top, a pair of scissors, the computer disc etc. 2. The line l 2. Except all others are symmetric. EXERCISE.2. (a) (d) (e) 6 (f) (g) 0 (h) 0 (i). Number of lines of symmetry are : Equilateral triangle ; Square ; Rectangle 2; Isosceles triangle ; Rhombus 2; Circle countless.. (a) Yes; an isosceles triangle. No. Yes; an equilateral triangle. (d) Yes; a scalene triangle. 7. (a) A,H,I,M,O,T,U,V,W,X,Y B, C, D, E, H, I, K, O, X F, G, J, L, N, P, Q, R, S, Z EXERCISE.. Number of lines of symmetry to be marked : (a) 2 (d) 2 (e) (f) 2

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