Question 12 Marks
Write two integers which are greater than $-10$ but their sum is smaller than $-10$
AnswerFor two integers which are greater than $-10$ but their sum is smaller than $-10$
Let first integer $= -4$ and
second integer $= -7 [\because -4 > (-10)$ and $-7 > -10]$
Sum $= – 4 + (-7)= -11 < -10$
View full question & answer→Question 22 Marks
A green grocer had a profit of $Rs. 47$ on Monday, a loss of $Rs. 12$ on Tuesday and loss of $Rs. 8$ on Wednesday. Find his net profit or loss in $3$ days.
AnswerAs per the given information,
Profit on Monday $= Rs. 47$ and
loss on Tuesday $= Rs. 12$ and
loss on Wednesday $= Rs. 8$
$\therefore$ Net profit $=$ Total profit – Total loss
Now,total profit $= Rs. 47$ and total loss $= 12 + 8 = 20$
$\therefore$ Net profit $= 47 - 20 = Rs. 27$
View full question & answer→Question 32 Marks
Social Studies Application: Remembering that $1AD$ came immediately after $1BC,$ while solving these problems take $1BC$ as $-1$ and $1AD$ as $+1.$ Bhaskaracharya was born in the year $1114AD$ and died in the year $1185AD.$ What was his age when he died$?$
AnswerAge, when Bhaskaracharya died $=$ year in which he died-year in which he born $= (1185AD) - (1114AD) = (+ 1185) - (+ 1114) = 1185 - 1114 = 71$ year
Hence, Bhaskaracharya was died in the age of $71$ year.
View full question & answer→Question 42 Marks
From given integers in Column $I$ match an integer of Column $II$ so that their product lies between $-19$ and $-6$
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Column I
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Column II
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$-5$
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$1$
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$6$
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$-1$
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$-7$
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$3$
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$8$
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$-2$
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Answer$-5 \times 3 = (-15)$ which lies between -19 and $-6$
$6 \times (-2) = (-12)$ which lies between -19 and $-6$
$-7 \times 1 = (-7)$ which lies between -19 and $-6$
$8 \times (-1) = (-8)$ which lies between -19and $-6$
View full question & answer→Question 52 Marks
Social Studies Application: Remembering that $1AD$ came immediately after $1BC,$ while solving these problems take $1BC$ as $-1$ and $1AD$ as $+1.$ The Greeco-Roman era, when Greece and Rome ruled Egypt started in the year $330BC$ and ended in the year $395AD.$ How long did this era last$?$
AnswerTotal duration of the era $=$ End year - start year $= (395AD) - (330BC) = +395 - (-330) 395 + 330 = 725$ year Hence, total duraction of this era was $725$ year.
View full question & answer→Question 62 Marks
The table shows the lowest recorded temperatures for each continent. Write the continents in order from the lowest recorded temperature to the highest recorded temperature.
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The Lowest Recorded Temperatures
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Continent
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Temperature (in Fahrenheit)
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Africa
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$-11^\circ $
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Antarctica
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$-129^\circ $
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Asia
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$-90^\circ $
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Australia
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$-9^\circ $
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Europe
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$-67^\circ $
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North America
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$-81^\circ $
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South America
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$-27^\circ $
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AnswerLowest to heights (ascending order) in a negative number, the number that has greater value of actually smaller and vice-versa. So, accordingly, we arrange them in ascending order. $\text{Antarctica}<\text{Asia}<\text{North America}<\text{Europe}<\text{Sourh America}<\text{Africa}<\text{Australia}\\ (-129^\circ)\ \ \ \ \ \ \ (-90^\circ)\ \ \ \ \ \ \ \ \ \ (-81^\circ)\ \ \ \ \ \ \ \ \ \ \ \ \ (-67^\circ)\ \ \ \ \ \ \ \ \ \ \ \ (-27^\circ)\ \ \ \ \ \ \ \ \ \ \ \ \ (-11^\circ)\ \ \ \ \ \ \ (-9^\circ)$
View full question & answer→Question 72 Marks
Sana and Fatima participated in an apple race. The race was conducted in $6$ parts. In the first part, Sana won by $10$ seconds. In the second part she lost by $1$ minute, then won by $20$ seconds in the third part and lost by $25$ seconds in the fourth part, she lost by $37$ seconds in the fifth part and won by $12$ seconds in the last part. Who won the race finally$?$
AnswerLet difference in time denoted by positive, when Sana wins the race and negative, when Sana loses the race.
Total difference in time taken by Sana in all the six parts $= 10 - 60 + 20 - 25 - 37 + 12 = -80s$ $ [\because 1\ min = 60s]$
Hence, Fatima won the race by $80s.$
View full question & answer→Question 82 Marks
Write a positive integer and a negative integer whose difference is a negative integer.
AnswerA number of solutions can be possible. e.g.
Let first integer
$= (-7)$ and second integer
$= 2$ Difference
$= (-7 - 2) = (-9) [$negative integer$]$
View full question & answer→Question 92 Marks
Evaluate the following, using distributive property.
$(-85) \times 43 + 43 \times (-15)$
Answer$(-85) \times 43 + 43 \times (-15)$
Taking $43$ as common
$= 43 \times (-85 - 15)$
$[\because a \times b + a \times c = a (b + c)]$
$= 43 \times (-100) = -4300$
View full question & answer→Question 102 Marks
In a test, $+3$ marks are given for every correct answer and $-1$ mark are given for every incorrect answer. Sona attempted all the questions and scored $+20$ marks though she got $10$ correct answers. How many incorrect answers has she attempted$?$
AnswerLet $x$ be the correct answers and $y$ be the incorrect answers, given by Sona.
It is given that, if she gives $10$ correct answers and her score is $20.$
Since, for every correct answer, $+3$ is given and for every incorrect answer, $-1.$ is given.
Hence, $3 \times ($Correct answer$) + (-1) \times ($Incorrect anwser$) =$ Total score
$\Rightarrow 3 \times 10 + (-1) \times y = 20$
$\Rightarrow 30 - y = 20$
$\Rightarrow 30 - 20 = y$
$\Rightarrow y = 10.$
View full question & answer→Question 112 Marks
Social Studies Application: Remembering that $1AD$ came immediately after $1BC,$ while solving these problems take $1BC$ as $-1$ and $1AD$ as $+1.$ Turks ruled Egypt in the year $1517AD$ and Queen Nefertis ruled Egypt about $2900$ years before the Turks ruled. In what year did she rule$?$
AnswerYear in which Queen Nefertis ruled $=$ year in which turks ruled $-\ 2900$ year
$= (1517AD) -2900 = (+1517) -2900 = -1383 = 1383BC$
Hence, Queen Nefertis ruled in the year $1383BC.$
View full question & answer→Question 122 Marks
Write two integers which are smaller than $-6$ but their difference is greater than $-6$
AnswerFor two integers which are smaller than $-6$ but their difference is greater than $-6$
Let first integer $= (-8)$ and
second integer $= (-9) [\because -8 < -6 $ and $-9 < -6]$
Difference $= -8 - (-9) = -8 + 9 = 1 > (-6)$
View full question & answer→Question 132 Marks
Write two integers whose product is smaller than both the integers.
AnswerA number of solutions can be possible. e.g.
Let first integer $= -3$ and second integer $= 5$
Product $= -3 × 5 = -15 [\because -15 < -3$ and $-15 < 5]$
View full question & answer→Question 142 Marks
If $*$ is an operation such that for integers $a$ and $b$ we have $a × b = a × b + (a × a + b × b)$ then find. $(-3) * (-5)$
AnswerWe have, $a * b = a × b +(a × a+b × b)$ Now, put $a = (-3)$ and $b = (-5) (-3) * (-5) = (- 3) × (-5) + [(-3) × (-3) + (-5) × (-5)] = 15 + (9 + 25) = 15 + 34 = 49$
View full question & answer→Question 152 Marks
If $*$ is an operation such that for integers a and b we have $a \times b = a \times b + (a \times a + b \times b)$ then find. $(-6) * 2$
AnswerNow, put $a = -6$ and $b = 2$
$(-6)*2 = (-6 \times 2) + \{(-6) \times (-6) + 2 \times 2\} $
$= -6 \times 2 + (36 + 4)$
$= -12 + 40 = 28$
View full question & answer→Question 162 Marks
Write a positive integer and a negative integer whose sum is a positive integer.
AnswerA number of solutions can be possible. e.g.
Let first integer $= 8$ and second integer $= -2$
Sum$= 8 + (-2) = 6 [$positive integer$]$
View full question & answer→Question 172 Marks
You are at an elevation $380m$ above sea level as you start a motor ride. During the ride, your elevation changes by the following metres: $540m, -268m, 116m, -152m, 490m, -844m, 94m.$ What is your elevation relative to the sea level at the end of the ride$?$
AnswerAs per the given information, initial position of motor was 380m.
During the ride, change in elevation was $540m,$
$-268m, 116m, -152m, 490m, -844m$ and $94m.$
Net change in position
$= 540 + (-268) + (116) + (-152) + (490) + (-844) + 94$
$= -24m$ Initial position was $380m.$ So,
at the end of the ride the position would be
$= 380 + (-24)$
$= 356m.$
View full question & answer→Question 182 Marks
Write a positive integer and a negative integer whose difference is a positive integer.
AnswerA number of solutions can be possible. e.g.
Let first integer $= 4$ and
second integer $= (-3) [$positive integer$]$
View full question & answer→Question 192 Marks
Write two integers such that one is smaller than $-11$, and other is greater than $-11$ but their difference is $-11.$
AnswerFor two integers, such that one is smaller than $-11$ and other is greater than $-11$.
Let first integer
$= -20$ and second integer
$= -9$
$[\because -20 < -11$ and $-9 > -11]$
Difference
$= - 20 - (-9) = (-11)$
View full question & answer→Question 202 Marks
Evaluate the following, using distributive property.
$-39 \times 99$
Answer$-39 \times 99 = (-40 + 1) \times (100 - 1)$
$= 40 \times (100 - 1) + 1 \times (100 - 1)$
Now, using distributive propert,
$= (-40 \times 100) + (-1 \times -40) + (1 \times 100) + (1 \times -1)$
$[\because a \times (b + c) = a \times b + a \times c]$
$= -400 + 40 + 100 - 1 = -3861$
View full question & answer→Question 212 Marks
Evaluate the following, using distributive property. $68 \times (-17) + (-68) \times 3$
Answer$68 \times (-17) + (-68) \times 3$
$= 68 \times (-17) -68 \times 3$
Taking $68$ as common, $68 \times (-17) -68 \times 3 [\because a \times b + a \times c = a \times (b + c)]$
i.e using Disteibutrive proprty $= 68 \times (-20) = -1360$
View full question & answer→Question 222 Marks
Write a positive integer and a negative integer whose sum is a negative integer.
AnswerA number of solutions can be possible. e.g.
Let first integer $= 4$ and second integer $= (-6)$
Sum $= 4 + (-6) = -2 [$negative integer$]$
View full question & answer→Question 232 Marks
The highest point measured above sea level is the summit of Mt. Everest which is $8,848\ m$ above sea level and the lowest point is challenger Deep at the bottom of Mariana Trench which is $10911\ m$ below sea level. What is the vertical distance between these two points?
AnswerAs per the given information, we can draw the diagram,
Let $A$ be the point above the sea level and $B$ be the point below the sea level.
Vertical distance between points $A$ and
$B =$ Distance between point $A$ and sea level $+$ Distance between point $B$ and
sea level $= AO + OB = 8848 + 10911 = 19759m.$ View full question & answer→Question 242 Marks
In a true$-$false test containing $50$ questions, a student is to be awarded $2$ marks for every correct answer and $-2$ for every incorrect answer and $0$ for not supplying any answer. If Yash secured $94$ marks in a test, what are the possibilities of his marking correct or wrong answer$?$
AnswerSince, Yash scored $94$ marks.
So, minimum correct answer $=\frac{\text{Total marks}}{\text{Marks for 1 correct answer}}$
$=\frac{94}{2}$
$=47$
Hence, there are two possibilities:
$i. 47$ correct answers and $3$ unattempted.
$ii. 48$ correct answers, $1$ unattempted and $1$ wrong answer.
View full question & answer→Question 252 Marks
Evaluate the following, using distributive property. $53 \times (-9) - (-109) \times 53$
Answer$53 \times (-9) - (-1.9) \times 53$
Taking $53$ as common, $= 53 \times (-9 + 109)$
$ [\because a \times b + a \times c = a \times (b + c)]$
$= 53 \times 100 = 5300$
View full question & answer→Question 262 Marks
Write two integers which are greater than $-4$ but their difference is smaller than $-4$
AnswerFor two integers which are greater than $-4$ but their difference is smaller than $-4$
Let first integer $= (-1)$ and
second integer $= 4[\because -1 > -4$ and $4 > -4]$
Difference $= -1 - 4 = -5 < (-4)$
View full question & answer→Question 272 Marks
Write a pair of integers whose product is $-36$ and whose difference is $15$
AnswerFor a pair of integers, whose product is $-36$ and difference is $15,$
one possible solution is $(-3, 12)$
So, first integer $= -3$ and second integer $= 12$
Their product $= (-3) \times 12 = -(3 \times 12) = -36$ and
the difference between these two integers is $12 -(-3) = 15$
View full question & answer→Question 282 Marks
Write two integers whose product is greater than both the integers.
AnswerA number of solutions can be possible. e.g.
Let first integer $= 4$ and
second integer $= 6$
Product $= 6 \times 4 = 24$
$[\because -24 > 6$ and $24 > 4]$
View full question & answer→Question 292 Marks
Taking today as zero on the number line, if the day before yesterday is $17$ January, what is the date $3$ days after tomorrow$?$
Answer
If we take today as zero, then two days before today is $17$ January.
Hence, $3$ days after tomorrow will be at $4th$ place from zero on the number line.
So, required date will be $(17 + 6)$ January $= 23$ January. View full question & answer→Question 302 Marks
Write two negative integers whose difference is $7$
AnswerA number of solutions can be possible. e.g.
Let first integer
$= (-3)$ and second integer
$= (-10)$
Difference $= -3 - (-10) = 7$
View full question & answer→Question 312 Marks
Write two integers which are smaller than $-5$ but their difference is $-5$
AnswerFor two integers, which are smaller than $-5$ but their difference is $-5$
Let first integer $= -11$ and
second integer $= (-6) [\because -11 < (-5)$ and $-6 < (-5)]$
Difference $= -11 -(-6) = -11 + 6 = (-5)$
View full question & answer→