EXERCISE 1.1 EXERCISE 1.2. (a) 2, 10; [ 2 ( 10) = 8] (b) 6, 1 (c) 1, 2; ( 1 2 = 3) EXERCISE 1.3

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1 ANSWERS 9 ANSWERS EXERCISE.. (a) Lahulspiti: 8 C, Srinagar: C, Shimla: C, Ooty: C, Bangalore: C (b) 0 C (c) 6 C (d) Yes; No.. C; C. 600 m. By a positive integer; Rs 8 6. By a negative integer; 0.. is the magic square 9. (a) < (b) < (c) > (d) s< (e) > 0. (i) jumps jumps (a) = 8 (b) + + = 8 8 in (b) represents going up 8 steps. EXERCISE.. One such pair could be: (a) 0, (b) 6, ; ( 6 = 0) (c),. One such pair could be: (a), 0; [ ( 0) = 8] (b) 6, (c), ; ( = ). Scores of both the teams are same, i.e., 0; Yes. (i) 0 EXERCISE.. (a) (b) (c) 60 (d) 6 (e) 0 (f) 0 (g) 6 (h) 60 (i) (j) 6. (i) a (a) (b) (c) 0. =, = = +, = = +, = = +, = = +, 0 = 0 = + so, ( ) = 0 + =.. (a) 80 (b) 000 (c) 000 (d) 8 (e) 600 (f) 6 (g) 9 (h) C. (i) (a) Loss of Rs 000 (b) 000 bags 9. (a) 9 (b) (c) (d)

2 9 MATHEMATICS EXERCISE.. (a) (b) 0 (c) (d) (e) (f) 0 (g) (h) (i). (a) (b) (c) 06 (d) (e) 8 (f) 8 (g) 0 (h). ( 6, ), (, ), (, ), (9, ), ( 9, ) (There could be many such pairs). 9 p.m.; C 6. (i) 8. hour EXERCISE.. (i) 9 = = (vi) = (vii) 9 = 8 8. (i) 8,, 9,, 0. Yes. 9 = 6 cm. (i) 8 cm 0 cm; Perimeter of ABE is greater cm 0. ; Ritu; 8. Vaibhav; by 6 of an hour. EXERCISE.. (i) (d) (b) (a) (c). (i) (c) (a) (b). (i) 9 (vi) (vii) 6 (viii) 6 (ix) (x) 9. One way of doing this is: (i). (a) (i) (b) (i) 8 (c) (i) (d)(i) 6 8

3 ANSWERS 9 6. (a) (b) (c) (d) (e) 9 (f). (a) (i) 8 9 (b) (i) (i) litres EXERCISE.. (i) (a) 6 (b) 0 (c). (i). (i) (vi) 9 0 (vii) 8 (a) (b) 6 (c) 0 (vi) (vii). (i) of 8 of 6 8. (a) (i) 0. m 6. 0 hours (b) (i) 8 8 EXERCISE.. km. (i) 6. (i). (i). (i) 8 (improper fraction) 8 (improper fraction) (proper fraction) 9 6 (proper fraction) (proper fraction) (vi) 8(whole number) (vii) (whole number) 6 (vii) 8 (viii) (vi) (vi) (vi) 9

4 96 MATHEMATICS EXERCISE.. (i) (vi) (i) ` 0.0 `.0 `. ` 0.0 `.. (i) 0.0m, km. cm, 0.0m, km. (i) 0. kg.0 kg.008 kg. (i) (i) Ones Tens Tenths Hundredths Thousandths. Ayub travelled more by 0.9 km or 900 m 8. Sarala bought more fruits 9..6 km EXERCISE.6. (i) (vi) 8.08 (vii)... cm. (i) (vi) 60 (vii) 6 (viii) 0 (ix) (x) 0.8 (xi) 90 (xii) 0. km. (i) (vi).68 (vii) 0.0 (viii) 0. (ix).00 (x) 0.0 EXERCISE.. (i) (vi).0 (vii) 0.99 (viii) 0.6. (i) (vi) 0.06 (vii) 0.9. (i) (vi) (i) (i) (vi) (vii) 0 (viii) (ix) km. EXERCISE. Marks Tally Marks Frequency

5 ANSWERS (i) (i). = 8 or 9 A 6. (i) Highest marks = 9, Lowest marks = (i) (i) cm 8 cm cm. cm EXERCISE.. Mode = 0, Median = 0, Yes.. Mean = 9, Mode =, Median =, No.. (i) Mode = 8, ; Median = 0 Yes, there are modes.. Mode =, Median =. (i) T F T F EXERCISE.. (a) Cat (b) 8. (i) Maths S. Science Hindi. Cricket Watching sports 6. (i) Jammu Jammu, Bangalore Bangalore and Jaipur or Bangalore and Ahmedabad Mumbai EXERCISE.. (i) Certain to happen Can happen but not certain Imposible Can happen but not certain Can happen but not certain. (i) 6 6. EXERCISE.. (i) No. No Yes No Yes (vi) No (vii) Yes (viii) No (ix) No (x) No (xi) Yes

6 98 MATHEMATICS. (a) No (b) No (c) Yes (d) No (e) No (f) No. (i) p = m = 6. (i) x + = 9 y = 8 0a = 0 t x = (vi) m + = (vii) z (ix) + = 0 b = 6 = (viii) 6y 6 = 60. (i) The sum of p and is subtracted from m is Twice a number m is One-fifth of a number m is Three-fifth of a number m is 6 (vi) Three times a number p when added to gives (vii) subtracted from four times a number p is 8 (viii) Add to half of a number p to get 8 6. (i) m + = y + = 9 l + = 8 b = 80 EXERCISE.. (a) Add to both sides; x = (b) Subtract from both sides; x = (c) Add to both sides; x = 6 (d) Subtract 6 from both sides; x = (e) Add to both sides; y = (f) Add to both sides; y = 8 (g) Subtract from both sides; y = 0 (h) Subtract from both sides; y = 8. (a) Divide both sides by ; l = (b) Multiply both sides by ; b = (c) Multiply both sides by ; p = 8 (d) Divide both sides by ; x = (e) Divide both sides by 8; y = 6 8 (f) Multiply both sides by ; z = (g) Multiply both sides by ; a = (h) Divide both sides by 0; t =. (a) Step : Add to both sides (b) Step : Subtract from both sides Step : Divide both sides by ; n = 6 Step : Divide both sides by ; m = (c) Step : Multiply both sides by (d) Step : Multiply both sides 0 Step : Divide both sides by 0; p = 6 Step : Divide both sides by ; p = 0. (a) p = 0 (b) p = 9 (c) p = 0 (d) p = (e) p = 8 (f) s = (g) s = (h) s = 0 (i) q = (j) q = (k) q = (l) q =

7 ANSWERS 99 EXERCISE.. (a) y = 8 (b) t = 8 (c) a = (d) q = 8 (e) x = (f) x = (g) m = (h) z = (i) l = 9 (j) b =. (a) x = (b) n = (c) n = (d) x = (e) x = 0. (a) p = (b) p = 6 (c) t = (d) p = (e) m =. (a) Possible equations are: 0x + = ; x = ; x = (b) Possible equations are: x = 6; x + = ; x + 0 = EXERCISE.. (a) 8x + = 60; x = (b) x = ; x = (c) y + = ; y = (d) m = ; m = (e) 0 x = 8; x = (f) x +9 = 8; x = (g) n = ; n =. (a) Lowest score = 0 (b) 0 each (c) Sachin: runs, Rahul: 66 runs. (i) 6 years. 0 EXERCISE.. (i) 0. (i) 9 6. (i) supplementary complementary supplementary supplementary complementary (vi) complementary will increase with the same measure as the decrease in.. (i) No No Yes 8. Less than 9. (i) Yes No Yes Yes Yes (vi) COB 0. (i), ;, +, ;,. and are not adjacent angles because their vertex is not common.. (i) x =, y =, z = x =, y = 0, z = 0. (i) supplementary linear pair equal (vi) obtuse angles

8 00 MATHEMATICS. (i) AOD, BOC EOA, AOB EOB, EOD EOA, EOC AOB, AOE; AOE, EOD; EOD, COD EXERCISE.. (i) Corresponding angle property Alternate interior angle property Interior angles on the same side of the transversal are supplementary. (i), ;, 6;, ;, 8, 8;,, ;, 8, ;, ;, ; 6, 8. a = ; b = ; c = ; d = ; e = ; f =. (i) x = 0 x = 00. (i) DGC = 0 DEF = 0 6. (i) l is not parallel to m l is not parallel to m l is parallel to m l is not parallel to m. Altitude, Median, No. EXERCISE 6. EXERCISE 6.. (i) (vi) 90. (i) (vi) 0 EXERCISE 6.. (i) (vi) 0. (i) x = 0, y = 60 x = 0, y = 80 x = 0, y = 0 x = 60, y = 90 x =, y = 90 (vi) x = 60, y = 60 EXERCISE 6.. (i) Not possible Possible Not possible. (i) Yes Yes Yes. Yes. Yes. No 6. Between and EXERCISE cm. cm. 9 m. (i) and. 8m cm cm EXERCISE.. (a) they have the same length (b) 0 (c) m A = m B. A F, B E, C D, AB FE, BC ED, AC FD. (i) C CA A BA

9 ANSWERS 0 EXERCISE.. (a) SSS Congruence criterion (b) SAS Congruence criterion (c) ASA Congruence criterion (d) RHS Congruence criterion. (a) (i) PE EN PN (b) (i) EN AT (c) (i) RAT = EPN ATR = PNE. (i) Given Given Common SAS Congruence criterion. No. WON 6. BTA, TPQ 9. BC = QR, ASA Congruence criterion EXERCISE 8.. (a) 0: (b) 00: (c) 00: (d) 0:. computers. (i) Rajasthan : 90 people ; UP : 80 people Rajasthan EXERCISE 8.. (a).% (b) % (c).% (d) 8 %. (a) 6% (b) 0% (c) % (d) %. (i),% ; 60% ;.% 8. (a). (b) minute or 6 seconds (c) ` 00 (d) 0. kg or 0g. (a) 000 (b) ` 9,000 (c) 0 km (d) 0 minutes (e) 00 litres 6. (a) 0.; (b).; (c) 0.; (d) 0.0; 0. 0% 8. 0%; `, matches EXERCISE 8.. (a) Profit = ` ; Profit % = 0 (b) Profit = ` 00; Profit % =. (c) Profit = ` 00; Profit % = 0 (d) Loss = ` 00; Loss % = 0. (a) %; % (b) 0%, 0%, 0% (c) 0%; 80% (d).%; %; 6.%. %. %. `, ` 6,8. (i) % g 8. `. 9. (a) `,6 (b) ` 8, %. ` 00

10 0 MATHEMATICS. (i). (i). (i). (i),,,,,, = =,, 9 8,,, ,,, ,,, 8 EXERCISE ,,, ,,,,,,0,, 6,,, ,,, ,,, P represents 6.,,, Q represents 8 R represents S represents. (i) (i) < < = > < (vi) = (vii) > 9. (i) 0. (i),, 6,, 9,,

11 ANSWERS 0 EXERCISE 9.. (i) (vi) (vii). (i) (i) (vi). (i) (vi) 9 (vii) EXERCISE.. (i) 0000 m `,00,000, m. 0 m. cm; cm. 0 m 6. cm; Square. cm; 00 cm 8. ` 8 EXERCISE.. (a) 8 cm (b) cm (c) 8. cm (d) cm (e) 8.8 cm. (a) 6 cm (b) 8 cm (c) 6 cm (d) cm. (a). cm (b) 0. cm (c).8 cm (d).0 cm. (a).6 cm (b) 80 cm (c). cm. (a 9. cm (b). cm 6. length of BM = 0cm; length of DL = cm. Area of ABC = 0 cm ; length of AD = 60 cm 8. Area of ABC = cm ; length of CE =. cm EXERCISE.. (a) 88 cm (b) 6 mm (c) cm. (a) 66 mm (b) 886. m (c) 0 cm

12 0 MATHEMATICS.. m; 886. m. m; ` cm 6.. m; ` cm 8. ` 0. (approx.) 9. cm; cm ; cm; circle cm.. cm. cm; 8. cm m. Yes. 9. m; 6.m Times. 9. cm EXERCISE.. 0 m ; 0.6 ha. 6 m. 0 cm. (i) 6 m `,600. (i) 6 m `, ha;. ha. (i) m ` 8,0 8. Yes, 9. m cord is left 9. (i) 0m.6 m.m.6m 0. (i) 0 cm 0 cm ;.66 cm EXERCISE.. (i) y z (x + y) z (vii) 0 yz (viii) ab (a + b) pq x + y (vi) + mn. (i) (a) (b) (c) (d) (e) Expression Terms Factors (a) x + x, x (b) x + y x,x y,y (c) y + y y,y y,y,y (d) xy+x y xy x, y x y, x, x, y, y (e) pq + q pq p, q q q

13 ANSWERS 0 (f).ab.b+.6a.ab.,a,b.b., b.6a.6, a (g) x + x, x (h) 0.p + 0.q 0.p 0., p, p 0.q 0., q, q. Expression Terms Coefficients (i) t t + t + t + t t t t x + xy + y x xy y 00m +000n 00m n 000 p q + pq p q pq (vi).a + 0.8b. a. 0.8 b 0.8 (vii).r.r. (viii) (l + b) l b (ix) 0.y + 0.0y 0.y y 0.0. (a) Expression Terms with x Coefficient of x (i) y x + y y x y y 8yx 8yx 8y x + y + x + z + zx zx z

14 06 MATHEMATICS + x + xy x xy y (vi) xy + xy y (vii) + xy xy y (b) Expression Terms with y Coefficient of y (i) 8 xy xy x y + x y x y xy + y xy x y. (i) binomial monomial trinomial monomial trinomial (vi) binomial (vii) binomial (viii) monomial (ix) trinomial (x) binomial (xi) binomial (xii) trinomial 6. (i) like like unlike like unlike (vi) unlike. (a) xy, xy ; yx, 0x y; 8x, x, 6x ; y, y; 00x, x; yx, xy. (b) 0pq, qp, 8qp; p, 0p; 8q, 00q; p q, q p ;, ; p, 0p ; p q, qp EXERCISE.. (i) 8b z + z 0z p q a + ab 8x y + 8xy x y (vi) y y. (i) mn tz mn a + b + x + (vi) m n mn (vii) 9x y 8xy (viii) pq + 0 (ix) 0 (x) x y. (i) 6y 8xy b a + b ab m 8mn + 8 (vi) x x (vii) 0ab a b (viii) 8p + 8q pq. (a) x + xy y (b) a + b 6. x y xy 6. (a) y + (b) x + EXERCISE.. (i) 0. (i). (i) 9 0

15 ANSWERS 0. (i) 8 0. (i) 0 6. (i) x ; 8x ; x 0; x + ; 9. (i) x+; 0 x + 6; 6 a + 6; 8b + 6; a b 9; 8 8. (i) a + ab + ; 8 EXERCISE.. Symbol Number of Digits Number of Segments (i) n 00 th : 99 n + th : ; 0 th : ; 00 th : 0 n + th : ; 0 th : ; 00 th : 0 n + 0 th : ; 0 th : 90; 00 th : 0 n + th : 6; 0 th : 0 EXERCISE.. (i) (i) 6 t b a (vi) a c d. (i) 9 6. (i) (i) 6. (i) (vi) 6 (vii) (viii) (i) (i). 0 > < 0 EXERCISE.. (i) 6 a x + (vi) (0) (vii) (ab) (viii) (ix) 8 (x) 8 t. (i) 0 or (vi) (vii) (viii) (ix) (a) (x) a 0 (xi) a b (xii) 8

16 08 MATHEMATICS. (i) False; 0 0 = 0 and (00) = 0 False; = 8, = False; 6 = True; 0 =, (000) 0 =. (i) (i) 98 t 8 EXERCISE.. 90 = = = = = (a) 860 (b) 00 (c) 00 (d) (i) (vi) (a) m (b) 0 8 m/s (c).6 0 m (d). 0 9 m (e) 0 (f). 0 0 years (g) 0 0 m (h) (i). 0 9 km (j) EXERCISE. (a) (b) (c) (d) (e) (f)

17 ANSWERS 09 (g) (h) (i) (j) (k) (l). (a) (b) (c) (d) (e). (a) Square (b) Triangle (c) Rhombus

18 0 MATHEMATICS (d) Circle (e) Pentagon (f) Octagon. (a) (b) (c) (d) (e) (f) (g) (h). (a) (b) (c) 0 (d) (e) (f) (g) 0 (h) 0 (i) 6 (j) Infinitely many 8. (a) A, H, I, M, O, T, U, V, W, X, Y (b) B, C, D, E, H, I, O, X (c) O, X, I, H 0. (a) Median (b) Diameter EXERCISE.. (a), (b), (d), (e), (f). (a) (b) (c) (d) (e) (f) (g) 6 (h) EXERCISE.. Yes. Square 6. 0, 80, 0, 00, 60. (i) Yes No EXERCISE.. Nets in,,, (vi) form cubes.

19 ANSWERS No, because one pair of opposite faces will have and on them whose total is not, and another pair of opposite faces will have and 6 on them whose total is also not.. Three faces. (a) (b) (c) (d) (i) BRAIN-TEASERS. Solve the number riddles: (i) Tell me who I am! Who I am! Take away from me the number eight, Divide further by a dozen to come up with A full team for a game of cricket! Add four to six times a number, To get exactly sixty four! Perfect credit is yours to ask for If you instantly tell the score!. Solve the teasers: (i) There was in the forest an old Peepal tree The grand tree had branches ten and three On each branch there lived birds fourteen Sparrows brown, crows black and parrots green! Twice as many as the parrots were the crows And twice as many as the crows were the sparrows! We wonder how many birds of each kind Aren t you going to help us find?

20 MATHEMATICS I have some five-rupee coins and some two-rupee coins. The number of two-rupee coins is twice the number of five-rupee coins. The total money I have is 08 rupees. So how many five-rupee coins do I have? And how many two-rupee coins?. I have vats each containing mats. cats sat on each of the mats. Each cat wore funny old hats. On each hat lay thin rats. On each rat perched black bats. How many things are in my vats?. Twenty-seven small cubes are glued together to make a big cube. The exterior of the big cube is painted yellow in colour. How many among each of the small cubes would have been painted yellow on (i) only one of its faces? two of its faces? three of its faces?. Rahul wanted to find the height of a tree in his garden. He checked the ratio of his height to his shadow s length. It was :. He then measured the shadow of the tree. It was feet. So what was the height of the tree? 6. A woodcutter took minutes to make pieces of a block of wood. How much time would be needed to make such pieces?. A cloth shrinks 0.% when washed. What fraction is this? 8. Smita s mother is years old. Two years from now mother s age will be times Smita s present age. What is Smita s present age? 9. Maya, Madhura and Mohsina are friends studying in the same class. In a class test in geography, Maya got 6 out of. Madhura got 0. Their average score was 9. How much did Mohsina score? Answers. (i) 0 0. (i) Sparrows: 0, crows:, Parrots: 6 Number of ` coins =, Number of ` coins =.. (i) feet 6. minutes years 9.