Page 282 - Ganit Kaushal

Ex 3. The greatest integer lying between –10 and –15 is
(a) –10 (b) –11 (c) –15 (d) –14

Sol. (b) [ −10 is the first integer that lies to the right of −11]
Ex 4. The least integer between –10 and –15 is
(a) –10 (b) –11 (c) –15 (d) –14
Sol. (d) [ −15 is the first integer that lies to the left of −14]
Ex 5. The successor of the predecessor of –50 is
(a) –48 (b) –49 (c) –50 (d) –51
Sol. (c) [ The successor of the predecessor of a number is the number itself.]

Ex 6. The additive inverse of a negative integer
(a) is always negative (b) is always positive (c) is the same integer (d) Zero
Sol. (b) [ −(−a) = a]
Ex 7. In which of the following pairs of integers is the first integer not on the left of the second integer on
the number line?
(a) (–1, 10) (b) (–3, –5) (c) (–5, –3) (d) (–6, 0)
Sol. (b) [ −3 is on the right of −5]
Ex 8. Which of the following shows the maximum rise in temperature?
(a) 0°C to 10°C (b) – 4°C to 8°C (c) –15°C to –8°C (d) –7° to 0°C
Sol. (b) [ 8 – (−4) = 12; in all others the difference of temperatures is 10, 7, 7 respectively]
Ex 9. Fill in the blanks with the >, < or = sign.
(a) (–3) + (–6) ____ (–3) – (–6) (b) (–21) – (–10) ____ (–31) + (–11)
(c) 45 – (–11) ____ 57 + (–4) (d) (–25) – (–42) ____ (–42) – (–25)

Sol. (a) < (b) > (c) > (d) >
Ex 10. Fill in the blanks.
(a) (–8) + _____ = 0 (b) 13 + _____ = 0 (c) 12 + (–12) = _____ (d) (–4) + _____ = –12
(e) _____ –15 = –10
Sol. (a) (–8) + (8) = 0 (b) 13 + (–13) = 0 (c) 12 + (–12) = 0 (d) (–4) + (–8) = –12
(e) 5 – 15 = –10
Ex 11. State whether the given statements are True (T) or False (F).
(a) The smallest natural number is zero. (b) All whole numbers are integers.

(c) Every positive integer is larger than every negative integer.
(d) Zero is less than every positive integer. (e) Zero is larger than every negative integer.
(f) Zero is neither positive nor negative. (g) The successor of the integer 1 is 0.
(h) The sum of all integers between –5 and –1 is –6.
(i) Since 5 > 3, therefore, –5 > –3.
Sol. (a) False, since the smallest natural number is 1. (b) True
(c) True (d) True (e) True (f) True
(g) False, since the successor of 1 is 2 not 0.
(h) False, since the integers between –5 and –1 are –4, –3, –2. So, their sum = – 4 – 3 – 2 = –9.
(i) False, since if 5 > 3, then –5 < –3, as in negative numbers, a lesser absolute value is larger.

280 Mathematics-6