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\ 06-Jan-2025 Surender Singh Routhan Proof-2 Reader’s Sign _______________________ Date __________

−27 81
2. (a) 2401 (b) 32 (c) (d) 729 4. (a) x = –2 (b) x = –1 5.
8 16
–6
(e) 1 (f) 1296 (g) –2 6. (a) 7 × 10 (b) 5.64 × 10 –7
27 7. (a) 0.00000003 (b) 1000100000 (c) 580
 −  9 9  −  1 3 (d) 3614920
3. (a) 1 (b)   (c) 120 (d)   7
 5   33  8. Sun have more diameter than the Earth by 138.725 × 10 m.
9. (a) 1.082 × 10 km (b) 6.0518 × 10 m (c) 5410 hours
8
6
256 1 125 81
4. (a) (b) (c) (d) (d) 360.66 seconds
81 − 3125 − 8 2401
1 Brain Sizzlers
5. (a) − ( 3) 12 (b) 70 2 (c) 5 7 (d) 1 1. Stretching machine = 3456 cm
x 5t () 4 Shrinking machine = 42.67 cm
6. (a) (b) 2 × 5 3 (c) (d) 5 5 2. 4
y 6 2 2
Chapter 12: Direct and Indirect Variations
 y 2 1
2 3
7. (a)   (b) a b c (c)
 x  xy / Let’s Recall
/
23 12
1. Printing of 20 stamp size photos require less area than 8 passport size
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8. (a) −52 9. −5 10. x = 2 photos, so the cost of photographs is less for 20 stamp size photos.
9 13 2
11. (a) x = –2 (b) x = 2 2. 10 : 1 3. 30 times
–2
0
–1
12. (a) 2 × 10 + 3 × 10 + 6 × 10 + 8 × 10 –3 4. Photos Passport Postcard Stamp
–2
–1
1
0
–3
(b) 4 × 10 + 5 × 10 + 2 × 10 + 3 × 10 + 9 × 10 + 4 × 10 –4 Size (in sq. cm) 15.75 150 5
–5
–1
–2
–4
–3
(c) 3 × 10 + 5 × 10 + 9 × 10 + 8 × 10 + 9 × 10 + 8 × 10 –6 Rate per copy (in `) 7.5 75 3
Practice Time 11C Think and Answer
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5
1. (a) 4.7865 × 10 (b) 9.99 × 10 7 (c) 1.00001 × 10 (d) 8.02 × 10 15 2. 9.8 N/kg
2. (a) 700000000000 (b) 5651672 Practice Time 12A
(c) 0.00000000020000002 1. (a) Yes (b) No (c) Yes
–2
11
3. (a) 5 × 10 mm (b) 1 × 10 3
8
–5
(c) 3.84317695 × 10 m (d) 1.275 × 10 m 2. k = 4 , x 1 = 21, y 1 = 48, x 2 = 63, y 2 = 68
4. 1.670910 × 10 –24 g 3. (a) l = km (b) 1 (c) 11 (d) 24
3
8
5. Time for light to travel = 2.7 × 10 seconds 4. 128 5. 155 km 6. (a) 18 km (b) 5.56 hours
Mental Maths 7. 756 words 8. 18 person 9. 3.15 × 10 crystals
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1. 1 2. 1 3. 1 4. 0 10. `12,000 11. 1680 km 12. (a) 9 cm (b) 294 g
3 4 13. 24.9375 m 14. (a) 29 : 20 (b) 232 keys
11
9
5. 5 2 6. 10 7. 1.234 × 10 8. 0.0000503 Practice Time 12B
4 4 1. (a) Inversely (b) Directly (c) Inversely (d) Directly
Maths Fun (e) Inversely (f) Directly (g) Neither of the two
Across (h) Directly
(c) Yes
2. SUM 3. RECIPROCAL 5. NINE 6. DIFFERENCE 2. (a) Yes (b) No 4. 200 5. 36 days
3. m 1 = 40, n 1 = 30, m 2 = 20, n 2 = 60
8. NEGATIVE 9. USUAL
Down 6. (a) 16 hours (b) 60 km/h 7. 448 persons 8. 9 kg
10. 15
9. 1 hour 24 minutes

11. 36
1. ONE THOUSAND TWENTY FOUR 4. ONE 7. POWER 12. 48 machines 13. 27 less horses
Maths Connect 14. 1 extra sweet
Exabyte (EB) = 1000000000000000000 = 10 18 Quick Check
Zettabyte (ZB) = 1000000000000000000000 = 10 21 3
Yottabyte (YB) = 1000000000000000000000000 = 10 24 1. 3 hours 2. (a) 20 days (b) 5 days
7
Puzzle Think and Answer
32 40 hours
Chapter Assessment Practice Time 12C
A. 1. (c) 2. (b) 3. (d) 4. (b) 5. (c) 1. 4 days 2. 3 8 part 3. 37.5 days
6. (d) 7. (b) 8. (d) 4. X → 84.71 days, Y → 62.61 days, Z → 205.71 days
B. 1. (a) 2. (b) 5. 7.67 days 6. 25.71 hours 7. 150 m
1 1 8. (a) 15 seconds (b) 35 seconds 9. 36 seconds 10. 48 seconds
C. 1. –1 2. 3. 64 4.
16 64 Mental Maths
D. 1. T 2. F 3. T 4. F 5. F 1. (a) Directly (b) Neither of the two
E. 1. (a) 5 15 (b) 1 (c) 1 (d) 6 (e) 1 (f) 19 (c) Neither of the two (d) Inversely
5 5 4 64 2. x = 15, 20, 25; y = 21, 28, 35 (Answer may vary)
3. m = 10, 4, 5; n = 12, 30, 24 (Answer may vary) 4. 9.6 km
2. (a) –10 (b) 30
5. 2.25 hours 6. 480 cm 2
3
3. (a) 1 (b)    7 (c) 3 (d) 5 4 Brain Sizzlers
6 4  4 1. `9000 2. 3 : 2 3. 18 cm 2
369 Answers