Page 284 - Ganit Kaushal

Sol. The unique sums of all the possible combinations of numbers on both dice are –10, – 8, – 6, – 4, – 3,
– 2, – 1, 1, 3, 4, 5, 6, 8, 10, 12. So, the numbers between (–10) and (+12) that are not possible as a sum
of the numbers on the dice are: 0, 2, –5, 7, −7, 9, − 9, 11.
Ex 18. Solve the following: (NCERT)

8 – 13 (–8) – (13) (–13) – (–8) (–13) + (–8)

8 + (–13) (–8) – (–13) (13) – 8 13 – (–8)
Sol. Using Brahmagupta’s rules for addition and subtraction, we get the following:

8 – 13 = –5 (–8) – (13) = –21 (–13) – (–8)= –5 (–13) + (–8) = –21

8 + (–13) = –5 (–8) – (–13) = 5 (13) – 8 = 5 13 – (–8) = 21
Ex 19. The height of all geographical features like mountains, plateaus, and deserts is measured from ‘sea
level’. The height at sea level is taken as 0 m. Look at the following geographical cross-section and
answer the following questions: Height (m)
(a) Fill in the heights of respective points in the 1500 A E
box given. 1000
A B 500 C
Sea G
C D level 0 F

E F –500 B
–1000 D
G
–1500
(b) Which is the highest point in this geographical
cross-section? Which is the lowest point?

(c) Can you write the points A, B, …, G in a sequence of decreasing order of heights? Can you write
the points in a sequence of increasing order of heights? (NCERT)

Sol. (a) A 1400 m B –500 m C 300 m D –1200 m E 1200 m
F –200 m G 100 m

(b) The highest point is A, with a height of 1400 m, and the lowest point is D with a height of –1200 m.
(c) The sequence in decreasing order of heights: A → E → C → G → F → B → D.
The sequence in increasing order of heights: D → B → F → G → C → E → A.
Ex 20. Find the predecessor of the following:
(a) –18 (b) –23 (c) 29 (d) | –15 |

Sol. (a) Predecessor of –18 = –18 – 1= –19 (b) Predecessor of –23 = –23 – 1 = –24
(c) Predecessor of 29 = 29 – 1 = 28
(d) Predecessor of | –15 | = | –15 | – 1 = 15 – 1 = 14 [ | –15 | = 15]

Ex 21. Find the successor of the following.
(a) –18 (b) –23 (c) 29 (d) | –15 |
Sol. (a) Successor of –18 = –18 + 1 = –17 (b) Successor of –23 = –23 + 1 = –22
(c) Successor of 29 = 29 + 1 = 30
(d) Successor of | –15 | = | –15 | + 1 = 15 + 1 = 16 [ | –15 | = 15]

282 Mathematics-6