2 Marks Questions

Question 12 Marks

Write five integers which are less than $-100$ but greater than $-150.$

Answer

All the integers lying between $-100$ and $-150$ are less than $-100$ and greater than $-150.$
So, $-101, -102, -103, -104$ and $-105$ are such five integers.
Note: There can be many answers of this question.

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Question 22 Marks

Temperature of a place at $12:00$ noon was $+5^\circ C.$ Temperature increased by $3^\circ C$ in first hour and decreased by $1^\circ C$ in the second hour. What was the temperature at $2:00\ pm?$

Answer

Temperature at $12:00$ noon $= +5^\circ C.$
It is given that temperature increased by $3^\circ C$ in first hour.
So, temperature at $1:00\ pm = 5^\circ C + 3^\circ C = 8^\circ C$
Also, temperature decreased by $1 ^\circ C$ in second hour.
So, the temperature at $2:00\ pm = 8^\circ C - 1^\circ C = 7^\circ C$
Hence, the temperature at $2:00\ pm$ is $7^\circ C.$

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Question 32 Marks

The sum of two integers is $30.$ If one of the integers is $-42,$ then find the other.

Answer

Given, sum of two integers $= 30$ and one integer $= -42$ The other integer $=$ Sum of two integers $-$ One integer $= 30 - (-42) = 30 + 42 = 72.$
Hence, the other integer is $72.$

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Question 42 Marks

Arrange the following integers in the ascending order: $-2, 1, 0, -3, +4, -5$

Answer

For arranging the given integers in ascending order, we have to arrange them from smaller to larger. $-5 < -3 < -2 < 0 < 1 < 4.$

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Question 52 Marks

Observe the following: $1 + 2 - 3 + 4 + 5 - 6 - 7 + 8 - 9 = -5$ Change one $‘–’$ sign as $‘+’$ sign to get the sum $9.$

Answer

$LHS = 1 + 2 - 3 + 4 + 5 - 6 - 7 + 8 - 9 = (3 - 3) + (9 - 9) - 6 - 7 + 8 = 0 + 0 - 6 - 7 + 8 = 2 - 7$
Now, we have to get the sum $9,$
so replace the sign of $(-)$ into $(+)$ before $7.$
$LHS = 2 + 7 = 9.$

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Question 62 Marks

Write the integer which is $2$ less than its additive inverse.

Answer

Firstly, draw a number line.
Let $-1$ be an integer and its additive inverse is $+1.$
From the number line, we see that $-1$ is $2 $ less than its additive inverse.
Hence, the required integer is $-1.$

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Question 72 Marks

Arrange the following integers in the descending order: $-3, 0, -1, -4, -3, -6$

Answer

For arranging the given integers in descending order, we have to arrange them from larger to smaller. $0 > -1 > -2 > -3 > -4 > -6.$

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Question 82 Marks

Write the digits $0, 1, 2, 3, ..., 9$ in this order and insert $‘+’$ or $‘–’$ between them to get the result $3.$

Answer

Given digits are $0, 1, 2, 3, 4, 5, 6, 7, 8$ and $9.$ To get sum $3, 0 + 1 + 2 + 3 - 4 + 5 + 6 + 7 - 8 - 9 = 1 + 2 + 3 + 5 + 6 + 7 - (4 + 8 + 9) = 24 - 21 = 3.$

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Question 92 Marks

Write two integers whose sum is less than both the integers.

Answer

For the required integers, we can take any two negative integers.Let $-5$ and $-7$ be two negative integers.
$(-5) + (-7) = -5 -7 = -12$ Clearly, $-12$ is less than both $-5$ and $-7.$
Note: Any two negative integers can be taken.

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Question 102 Marks

Sum of two integers is $-80.$ If one of the integers is $-90,$ then find the other.

Answer

Given, sum of two integers $= -80.$ and one integer $= -90.$
The other integer $=$ Sum of two integers $-$ One integer $= (-80) - (-90) = -80 + 90 = 10.$
Hence, the other integer is $10.$

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Question 112 Marks

Write two integers whose sum is $6$ and difference is also $6.$

Answer

We know that, on adding zero to an integers, the sum is the integer itself, e.g. $6 + 0 = 6$
Also, if we subtract zero from an integer, the difference is the integer itself, e.g. $6 - 0 = 6.$
Hence, the required two integers are $0$ and $6.$

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Question 122 Marks

Subtract $-5308$ from the sum $[(-2100) + (-2001)]$

Answer

Firstly, we find the sum: $[(-2100) + (-2001)] = [-2100- 2001] = -4101$
Now, subtract $- 5308$ from $- 4101. $
$-4101 - (-5308) = -4101 + 5308 = 1207.$

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Question 132 Marks

Write the integer which is $4$ more than its additive inverse.

Answer

Firstly, draw a number line.

Let $+1$ be an integer and its additive inverse is $-1.$ From the number line, we see that $+1$ is $2$ more than its additive inverse. So, we reject this integer. Again, let $+ 2$ be an integer and its additive inverse is $-2.$ From the number line, we see that $+2$ is $4$ more than its additive inverse. Hence, the required integer is $2.$

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