Exercise 1.5
1. One night in
Kashmir, the temperature is −5º C. Next day the temperature is 9º C. What is
the increase in temperature?
9°C – (–5°C) = 9°C + 5°C =
14°C
2. An atom can
contain protons which have a positive charge ( +) and electrons which have a
negative charge ( −) . When an electron and a proton pair up, they become
neutral (0) and cancel the charge out. Now, Determine the net charge:
(i) 5 electrons and 3 protons → −5 + 3 = −2 that is 2 electrons
(ii) 6 Protons and 6
electrons →
(iii) 9 protons and
12 electrons →
(iv) 4 protons and 8
electrons →
(v) 7 protons and 6
electrons →
3. Scientists use
the Kelvin Scale (K) as an alternative temperature scale to degrees
Celsius (°C) by the
relation T º C = ( T + 273) K.
Convert the
following to kelvin:
(i) −275° C (ii) 45°
C (iii) −400° C (iv) −273° C
(i) –275° C
(–275 + 273) K = –2° K
(ii) 45°C
(45 + 273) K = 318° K
(iii) –400° C
(–400 +273) K = 127° K
(iv) –273°C
(–273 + 273)K = 0° K
4. Find the amount
that is left in the student’s bank account, if he has made the following
transaction in a month. His initial balance is ₹ 690.
(i) Deposit ( +) of
₹ 485
(ii) Withdrawal ( −)
of ₹ 500
(iii) Withdrawal (
−) of ₹ 350
(iv) Deposit ( +) of
₹ 89
(v) If another ₹ 300
was withdrawn, what would the balance be?
(i) Deposit (+) of ₹
485 ?
₹ 690 + ₹ 485 = ₹ 1175
(ii) Withdrawal (–)
of ₹ 500 ?
₹ 1175 – ₹ 500 = ₹ 675
(iii) Withdrawal (–)
of ₹ 350
₹ 675 – ₹ 350 = ₹ 325
(iv) Deposit of (+)
₹ 89
₹ 325 + ₹ 89 = ₹ 414
(v) If another ₹ 300
was withdrawn, what would the balance be?
₹ 414 – ₹ 300 = ₹ 114
The balance would be = ₹ 114
5. A poet Tamizh
Nambi lost 35 pages of his ‘lyrics’ when his file had got wet in the rain. Use
integers, to determine the following:
(i) If Tamizh Nambi
wrote 5 page per day, how many day’s work did he lose?
35 ÷ 5 = 7 days
(ii) If four pages
contained 1800 characters, (letters) how many characters were lost?
4 pages contained characters = 1800
∴ 35 pages contained characters = [ 1800 × 35 ] / 4 = 15750
15750 characters
were lost
(iii) If Tamizh
Nambi is paid ₹250 for each page produced, how much money did he lose?
Paid money for 1 page = ₹ 250
Paid money for 35 pages = ₹ 250 × 35 = ₹ 8750
He lost = ₹ 8750
(iv) If Kavimaan
helps Tamizh Nambi and they are able to produce 7 pages per day, how many days
will it take to recreate the work lost?
Number of days it will take
to recreate the work lost = 35 ÷ 7 = 5 days
(v) Tamizh Nambi
pays kavimaan ₹ 100 per page for his help. How much money does kavimaan
receive?
Kavimaan receives money = ₹
35 × 100 = ₹ 3500
6. Add 2 to me. Then
multiply by 5 and subtract 10 and divide now by 4 and I will give you 15! Who
am I?
Add 2 to me, multiply by 5 and subtract 10 and divide by 4 = 15
[ (x+2)5 – 10 ] / 4 =
15
5x + 10 – 10 = 60
5x = 60
x = 60 / 5 = 12
The number is 12.
7. Kamatchi, a fruit
vendor sells 30 apples and 50 pomegranates. If she makes a profit of ₹ 8 per
apple and loss ₹ 5 per pomegranate, what will be her overall profit(or)loss?
Number of apples = 30
Profit on apples = ₹ 30 × 8 = ₹240
Number of pomegranates = 50
Loss on pomegranates = ₹ 50 × 5 = ₹ 250
Loss = 250
Profit = ₹ 240
Over all loss = ₹ 10
8. During a drought,
the water level in a dam fell 3 inches per week for 6 consecutive weeks. What
was the change in the water level in the dam at the end of this period?
Water level decrease per week = 3 inches
Water level decrease in 6 weeks = 3 × 6 = 18 inches
Water level decrease 18 inches in 6 weeks
9. Buddha was born
in 563 BC(BCE) and died in 483 BC(BCE). Was he alive in 500 BC(BCE)? and find
his life time. (Source: Compton’s Encylopedia)
Buddha was bom in 563 BC (BCE) died in 483 BC (BCE)
500 BC (BCE) is in
between 563 BC and 483 BC
∴ Yes. He alive in 500 BC (BCE)
Life: 80 year.
10. A young boy has got fever.
The following chart shows how his temperature varies each day in a week. M→up
3° C, T→up 2° C, W→ Down 2° C, Th→ up 2° C, F→ Down 1° C, S→ up 2° C What was
the average daily variation in his temperature?
(Average = Total change in temperature / Number of days)
Total change in temperature = +3 +2 –2 + 2 –1 + 2
= 9 – 3 = 6
Number of days = 6
Average = Total change in temperature / Number of days
= 6 / 6 = 1
Average = 1
ANSWERS
Exercise 1.5
1. 14˚c
2. (i) −2 (ii) 0 (iii) −3 (iv) −4
(v) 1
3. (i) −2 k (ii) 318°k (iii)
−127° k (iv) 0°k
4. (i) ₹1175 (ii) ₹675 (iii) ₹325
(iv) ₹414 (v) ₹114
5. (i) 7 days (ii) 15,750 characters (iii) ₹8750 (iv) 5 days (v) ₹3,500 6. 12
7. Loss of ₹10
8. decrease of 18 inches
9. yes; 80 years
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