MATHS M.C.Q. [1 Marks Each]

Given that We have to find the value of given expression
$- 7 - (-8)$
we know that $(−) \times (−) = +$
and $(+) \times (−)=−$
$= -7 + 8$
$= 1$
So option $C$ is correct

 If a is an integer, then its successor is $a + 1.$ So
Successor of $-79 = -79 + 1$
$= -(79 - 1)$
$= -78$
Hence, the correct option is $(b).$

$10 × 1 = 10$
$\therefore 10\ INR\ 1$ coins make $INR\ 10.$

Subtract $12$ and $7$ from $64$ and $72$ respectively.
$64 - 12 = 52$
$72 - 7 = 65$
The required number is the $HCF$ of $52$ and $65.$
Now,
$52 = 4 \times 13$
$65 = 5 \times 13$
$\therefore HCF\ 52$ and $65 = 13$
Therefore, the largest number that divides $64$ and $72$ and leave the remainder $12$ and $7$ respectively, is $13.$
Hence, the correct option is $(b)$.

We know that, all the positive integers lie on the right of $0.$
So, integer $5$ is also located to the right of $0.$

Additive inverse of an integer is obtained by changing the sign of the integer.
Therefore, the additive inverse of a negative integer is always positive.
Let a nagative integer be $-5.$ Then, additive inverse of $-5 = -(-5) = 5.$

Let $x$ be the other integer
$x + 30 = -25$
$x = -25 - 30$
$x = -55$

$86 + (-28) + 12 + (-34) = 86 + (-28) - (34 - 12)$
$= 86 + (-28) - 22$
$= (86 - 28) - (34 - 12)$
$= 58 - 22$
$= 36$
Hence, the correct option is $(c).$

For predecessor, we subtract $1$ from the given integer and for successor, we add $1$ to the given integer.
The predecessor of $-50 = -50 -1 = -51$ and the successor of $-51 = -51 + 1 = -50.$

Option $B$ is right.
Every integer less than $0$ has the negative sign.

$(-36) + (+12) = -36 + 12 = -24$

Sum of integers $= -35$
One of the numbers $= 40$
Other number $= (-35) - (40)$
$= -35 - 40$
$= -(35 + 40)$
$= -75$
Therefore, the other number is $-75$
Hence, the correct option is $(b).$

Let the other integer be $xx.$ One of the integer is given that is $-48$Also, it is given that the sum of the two integers is $+62.$ Therefore, we have:
$x + (−48) = + 62$
$\Rightarrow x - 48 - 62$
$\Rightarrow x = 62 + 48$
$\Rightarrow x = 110$
Hence, the other integer is $+110.$

On the number line, $-7$ is to the left of $-5,$ so $-7 < -5.$
Hence, the correct option is $(b).$

Write given integers in addition expression and we get:
$(+5) + (-6)$
Subtract smaller integer $5$ from bigger integer $6$ as follows: $6 − 5 = 1$
Since, the bigger integer $-6$ is a negative integer, so the result should also be negative that is $-1$
Hence, $+ 5 - 6 = -1$

The integers lying between $-10$ and $-15$ are $-11, -12, -13$ and $-14.$
The least integer among these is $-14. [$because with negative sign, greater number is smaller$]$

Firstly, draw a number line and mark all the given pairs of integers on it.

Clearly, we observe that $-3$ is on the right of $-5.$

 In our daily systems, we take zero or ground level as the reference point. If a number is less than $0,$ it will
be negative and if greater, positive. If a level is below the ground level, it is said to be negative.

Smallest positive integer in the given options is obviously $1$ since zero is not considered as positive or
negative integer.

$(+13) - (+12) = +1$

Sum of integers $= -23$
One of the numbers $= 18$
Other number $= (-23) - (18)$
$= -23 - 18$
$= -(23 + 18)$
$= -41$
Therefore, the other number is $− 41.$
Hence, the correct option is $(d).$

The predecessor of a number lies to the left of the number.
$​​-100$ lies to the left of $-​99.$
Hence, $​​-100$ is a predecessor of $-​99.$

Suppose we take two integers one positive $(+1)$ and other negative $-1.$
On adding $1$ to itself, we get $1 + 1 = 2.$
Here, the sum is greater than the integer $(+1).$
Again, adding $-1$ to itself, we get $-1 + (-1) = -1 -1 = -2$
Here, the sum is less than the integer $-1.$
Hence, the given statement is true only when the integer is positive.

If a is an integer, then its predecessor is a$ - 1.$
So Predecessor of $-99 =-99 - 1$
$= -(99 + 1)$
$= -100$
Hence, the correct option is $(b).$

On observing all the options by using a number line, we get that there is only one pair $(-3, -5)$ in which the first integer is not on the left of the other integer.

Greatest $- 8$ digit no $99999999$
Smallest $- 9$ digit no $+ 100000000​$
$199999999​$

If a is an integer, then $a + 0 = 0 + a = a$
Here, $0$ is the additive identity element in the set of integers.
Hence, the correct option is $(c).$

$(+48) + (-53) = 53 − 48 = −5$

$36\div(-9)$
$=\frac{36}{-9}$
$= \frac{36}{9}\times(−1)$
$= -1 \times 4$
$= -4$

The integers lying between $-10$ and $-15$ are$-11, -12, -13$ and $-14.$
The greatest integer among these is $-11.$
with negative sign, smaller number is greater.

We have:$-6 - (-9)$
$= -6 + 9$
$= 3$

Here,$L.H.S. = (-13 + 6)$
$= -7$
$R.H.S. = -25 - (-9)$
$= -25 + 9$
$= -16$
$-7 > -16$
$L.H.S. > R.H.S.$

$(-9) \times 6 + (-9) \times 4$
Using distributive law:$(-9) \times (6 + 4)$
$= (-9) \times (10)$
$= -90$

$(-20) \times (-2) \times (-5) (-35)$
$\Rightarrow 40 \times (−35) [ (-) (-) = (+), (-) \times (+) = (-) ]$
$\Rightarrow -1400$

$6$ more than $-7 = (-7) + 6$
$= -( 7 - 6)$
$= -1$
Hence, the correct option is $(b).$

If x is negative integer, then $|x| = -x$
Here, a is greater than $7$, so $7$ - a is negative.
Therefore, $|7 - a| = -(7 - a) = -7 + a = a - 7$
Hence, the correct option is $(a).$

The successor of $-89$ is ​$-88$. The successor of a number lies towards its right on a number line.
$88$ lies to the right of $-89.$

Every integer less than $0$ has the negative $(-)$ sign.
Note: An integer is positive, if it is greater than zero and negative, if it is less than zero.

Here, the operation $\Delta$ is defined as $\text{a }\Delta\text{ b}=\text{a}-\text{b}-2$.
$7\ \Delta\ (-4)=7-(-4)-2$
$=7+4-2$
$=11-2=9$
Hence, the correct option is $(c).$

Temperature is decreased by $20$.
From the reference level, increase in temperature = +ve and decrease in temperature = −ve.
$\Rightarrow $ Temperature is represented as $−20.$

$x + (-8) = 12$
$\Rightarrow x - 8 = 12$
$\Rightarrow x = 12 + 8$
$\Rightarrow x = 20$

The integers lying between $-1$ and $1$ is $0$, so there is only one integer.

Let $x$ be the other integer$x + 8 = -13$
$x = -13 - 8$
$x = -21$

$-1$ is greatest negative integer.

$0$ is grater than every negativenegative integer.

We know that, one less than a given number, gives a predecessor. Predecessor of the integer $-1 = -1 -1 = -2$ Hence, predecessor of the integer $-1$ is $-2.$

Positive numbers are located above $0$ and negative numbers are located below $0$ on a vertical number line.

Here, $5$ less than $-2 = (-2) - (5) = -2 - 5 = -7.$
Hence, the correct option is $(c).$

Positive numbers are located above $0$ and negative numbers are located below $0$ on a vertical number line.

If a is an integer, then its additive inverse is $- a.$
So, additive inverse of $17 = -17$
Hence, the correct option is $(a).$

Let the number be $x$.Then according to the problem we get, $x + 18 = -34$ or, $x = -34 -18$ or, $x = -52.$

The required number is $(-34) - 18$
Now,
$(-34) - 18 = -(34 + 18)$
$= -52$
Hence, the correct option is $(b).$

$(-7) + (-9) + 12 + (-16)$
$= -7 - 9 + 12 - 16$
$= -20$

$2$ less than $-7$ means the following:$= -7 - 2$
$= -9$

$0 - (-8)$
$= 0 + 8$
$= 8$

$(-16) + 14 - (-13) = (-16) + 14 + 13$ (Additive inverse of $-13$ is $13)$
$= (-16) + 27$
$= 27 - 16$
$= 11$
Hence, the correct option is $(c).$

the possible values of $x$ is $\pm1$

The integer $8$ more than $− 12$ is $(− 12) + 8$
Now,
$(-12) + 8 = -(12 - 8)$
$= -4$
Hence, the correct option is $(b).$

As negative quantity multiplied by negative quantity yeild a positive quantity.
So option $2$ is correct.There is some sign is missing in option $3.$

$-12 - (-28) = (-12) + (+28) =+16$

$1$ is the smallest factor of a multiple and the greatest factor of a multiple is the multiple it self. So, $1$ is a
factor of every multiple.

$-10 - (-30) = (-10) + (+30) = (+20)$

Let the number to be added to $16$ be $x$
$x + 16 = (-31)$
$\Rightarrow x = (-31) - 16$
$\Rightarrow x = -47$

Here, $|-4| = 4$
Therefore, $9 + |-4| = 9 + 4 = 13$
Hence, the correct option is $(c).$

$6 - (-4)$
$= 6 + 4$
$= 10$

Since the Lowest positive integer is $1$. Successor of lowest positive integer will be $2$ as $2$ is the next positive integer number after $1.$

Let x be the other integer$x + (-5) = 20$
$x - 5 = 20$
$x = 25$

Given that We have to find the value of given expression$34 + 67 - 104$
$= (34 + 67) - 104$
$= 101 - 104$

Arya climbed $10$ steps up. Ground being the reference level, upwards direction $= +$ve and downwards direction $= −ve.$
$\Rightarrow $ Position of Arya is $+10$

$1+\omega^\text{n}+\omega^{2\text{n}}$ If n is not a multiple of $31+\omega^\text{n}+\omega^{2\text{n}}=0$
$\because\omega^3=1$ and according to cube-root unity.
$1+\omega^2+\omega=0$

$[15 − \{12 − (7 − \overline{6 − 2)}​\}]$
$=[15−{12−(7−4)}]$
$=[15−{12−(7−4)}]$
$= 15-9$
$=6$
Option $A$ is correct.

$-12 - (-5)$
$= -12 + 5$
$= -7$

$8 + (-8)$
$= 8 - 8$
$= 0$

The integers lying between $-5$ and $5$ are $-4, -3, -2, -1, 0, 1, 2, 3$ and $4.$ Whole numbers are $0, 1, 2, 3$ and $4.$
The number of whole numbers $= 5$ [whole numbers are the group of numbers that consist of the numbers i.e.$ 0, 1, 2, 3, 4, 5,…]$

$49 + (-27)$
$= 49 - 27$
$= 22$

Required number $= -14 - (-7)$
$= -14 + 7$
$= -(14 - 7)$
$= -7$
Hence, the correct option is $(b).$

If a is an integer, then its predecessor is a $- 1.$
So predecessor $-14 = -14 - 1 = -15$
Hence, the correct option is $(a).$

If a is an integer, then its successor is $a + 1.$
So, successor of $-22 = -22 + 1 = -(22 - 1) = -21$
Hence, the correct option is $(b).$

We have:$(-6) \times 9$
$= -(6 \times 9)$
$= -54$

Earning of $Rs. 100$ means we got $Rs. 100.$
Therefore, opposite of earning is spending means we give $Rs. 100$

Here, $0 - (-5) = 0 + 5 = 5$
Therefore, on subtracting $-5$ from $0$, we get $5$
Hence, the correct option is $(b).$

Opposite of rise in temperature by $5^\circ $ is fallin temperature by $5^\circ $

If $x$ is negative integer, then $|x| = -x. So$
$x + |x| = x - x = 0$
$x - |x| = x - (-x) = x + x = 2x$
Hence, the correct option is $(a).$

$2\div7 =\frac{7}{2}$ which is a rational number

$−5$ is an integer number.

$(-23) - (47) = -23 - 47$
$= -(23 + 47)$
$= -70$
Thus, when $47$ is subtracted from $-23$, we get $-70.$
Hence, the correct option is $(d).$

$(-42) + (-35)$
$= -42 - 35$
$= -77$

$4$ more than $-5$ means the following:
$= -5 + 4$
$= -1$

$(-37) + 6$
$= -37 + 6$
$= -31$

$(-35) + (-32) = -(35 + 32) = -67$
$$Hence, the correct option is $(b).$

West direction is denoted towards left. Rushabh walked $3$ units left. His positions co-ordinate on number line $= -3$

The possible values of $x$ is $\pm1$

Sum of two integers $= -26$
One of the two numbers $= 14$
$\therefore$ second number $= -26 - 14$
$= -(26 + 14)$
$= -40$
Hence, the correct option is $(c).$

Given that We have to find the value of given expression $34 + 67 - 104$
$= (34 + 67) - 104$
$= 101 - 104$
$= -3$

$5 - (-8)$
$= 5 + 8$
$= 13$

We know that, if the temperature decreases, the cooling increases.
Given, minimum temperature on a particular at $A = -4^\circ C$ and minimum temperature on a particular at $B = -1^\circ C$ We know that, $-4^\circ C < -1^\circ C.$
So, $A$ is cooler than $6.$
Hence, option $(a)$ is true.

Suppose we take two negative integers $-2$ and $-3.$
We subtract $(-3)$ from $(-2)$ and give a minus sign to get the result. i.e $-2 -(-3) = -2 + 3 = 1.$
Again, we subtract $(-2)$ from $-3$ and give a plus sign to get the result. i.e $-3 - (-2) = -3 + 2 = -1.$
So, the sign of the result depends on the numerical value of the integers..

Greatest eight digit using $4$ digits only then we will choose largest number $6, 7, 8, 9,$
So greatest one $99, 999, 876.$

Write given integers in addition expression and we get:
$(+138) + (-234)$
Subtract smaller integer $138138$ from bigger integer $234$ as follows: $234 - 138 = 96$
Since, the bigger integer $234$ is a negative integer, so the result should also be negative that is $-96$
Hence, $138 - 234 = - 96$

$(-6) + 4 - (-3)$
$= -6 + 4 + 3$
$= -6 + 7$
$= 1$

Withdrawal of $Rs. 200$ means amount $200$ is subtracted from our account.
i.e $Rs. -200$
Option C is correct.

$(+48) + (-53)$
$= 53 - 48$
$= -5$

We know that, negative integer is always less than $0.$

We know that, positive integer is always greater than $0.$

$7 + |-3|$
$= 7 + (+3) $(The absolute value of $-3$ is $3.)$
$= 7 + 3$
$= 10$

$\frac{2}{7}$ = $\frac{2}{7}$ which is a rational number.

Absolute value describes the distance of a number on the number line from $00$ without considering which
direction from zero the number lies.
The absolute value of a number is never negative. Absolute value makes numbers positive.

$2$ less than $-3$ means the following:$= -3 - 2$
$= -5$

$= -4 - 8$
$= -12$

We have:$10 - (-5)$
$= 10 + 5$
$= 15$

$-1$ is greatest negative integer.

If we add the additive inverse of a number to the number, we get $0.$
$-5 + 5 = 0$

Write given integers in addition expression and we get:
$(+22) + (-16)$
Subtract smaller integer $16$ from bigger integer $22$ as follows: $22− 16 = 6$
Since, the bigger integer $22$ is a positive integer, so the result should also be positive that is $+6$ or $6.$
Hence, $-16 + 22 = 6$