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

Using distributive formula ,
We can write, $a(b + c) = a \times b + a \times c$
So, $36(8 + 3) = (36 \times 8) + (36 \times 3)$

Here, $x + 12 = 12 + 7.$
But, by commutative of addition,
We have $7 + 12 = 12 + 7$
So, comparing $x + 12 = 12 + 7$ and $7 + 12 = 12 + 7$
We have $x = 7$
Hence, the correct option is $(b).$

The numbers $1, 2, 3, 4, 5, ...$ form the collection of natural numbers.
Thus, $0$ is not a natural number.
Hence, the correct option is $(c).$

$[5 \times (6)] + [5 \times 3] = 5[(6) + 3] (\therefore$ distributive property$)$
$=5[9]$
$=45.$

Zero is called the identity element for addition of rational numbers.
Thus, the sum of $0$ and any rational number is the number itself.

Given Coordinate of Point $P$ are $(0, -3)$
$x - $coordinate $= 0$
$y -$ coordinate $= -3$
$\Rightarrow$ Point $P$ lies of $y -$ axis
Also, As $y -$ coordinate $ < 0$ Point $P (0, -3)$ lies on Negative $y -$ axis.

No. of whole numbers in between
$= (487 - 437) - 1 = 50 -1 = 49$

$\frac{-8}{17}+\text{x}=\frac{-8}{17}​\Rightarrow\text{x}=0$

The successor and predecessor of an odd natural number are both even.
Here, $n = o$ dd. So
Successor of $n = n + 1 ($Even natural number$)$
Predecessor of $n = n - 1 ($Even natural number$)$
Product $= (n + 1) \times (n - 1) =$ even $\times $ even $=$ even
Thus, the product of the successor and predecessor of $n$ is an even number.
Hence, the correct option is $(b).$

$ 16 - 2 ÷ 7 + 6 \times 2$
$=16-\Big(\frac{2}{7}\Big)+6\times2$ [Performing division]
$=16-\Big(\frac{2}{7}\Big)+12$ [performing multiplication]
$=25-\Big(\frac{2}{7}\Big)$ [Performing addition]
$=\frac{28}{1}-\frac{2}{7}=\frac{(196-2)}{7}=\frac{194}{7}=27\frac{5}{7}$ [performing substractrion]

Multiplication is associative for whole numbers.
i.e. $a \times (b \times c) = (a \times b) \times c$
$\therefore 24 \times (6 \times 5) = (24 \times 6) \times 5.$

We have:
$1$ million $= 10,00,000$
Predecessor of $1$ million,
$= 10,00,000 + 1 = 10,00,001$

$= 54 ÷ 3 of 6 + 9$
$= 54 ÷ (3 ÷ 6) + 9$
$= 54 ÷ 18 + 9$
$= 3 + 9 = 12$

Distributive property can bre written as
$a \times (b + c) = a\times b + a \times c$

$a + (b + c) = (a + b) + c$ is associative property of whole numbers.

Given expression:
$32-\Big[48\div\big[36-\big(27-\overline{16-9}\big)\big]\Big]$
$= 32 - [48 ÷ \{36 - (27 - 7)\}] [$Removing bar$]$
$= 32 - [48 ÷ \{36 - 20\}] [$Removing parentheses$]$
$= 32 - [48 ÷ 16] [$Removing braces$]$
$= 32 - 3 [$Removing square brackes$]$
$= 29$

The additive inverse of $36$ is $-36.$
i.e., $36 + (-36) = 0$

Multiplication is associative for whole numbers.
i.e. $a \times (b \times c) = (a \times b) \times c$
$\therefore 25 \times (15 \times 10) = (25 \times 15) \times 10$
$\therefore $ The missing terms are $10, 25.$

Commutative property of addition: Changing the order of addends does not change the sum.
For example, $a + b = b + a$

Multiplication is associative for whole numbers.
i.e. $a \times (b \times c) = (a \times b) \times c$
$\therefore 14 \times (2 \times 10) = (14 \times 2) \times 10$
$\therefore $ The missing terms are $2, 10.$

Divisor $= 46$
Quotient $= 11$
Remainder $= 15$
Dividend $=$ Divisor $\times $ quotient $+$ remainder
$= 46 \times 11 + 15$
$= 506 + 15$
$= 521$

Option $D$ is right.
Number of whole numbers lying between $-5$ and $5$ are $0, 1, 2, 3$ and $4.$

$(147 + 0) + (123 + 0) = 147 + 123$
$= 270$
$( \therefore 147 + 0 = 147, 123 + 0 = 123)$

The counting numbers $1, 2, 3, 4, .....$ are called natural numbers.
The set of natural numbers does not include $0.$

Smallest $3-$digit number $= 100$
Predecessor of $3-$digit number,
$= 100 - 1 = 99$
Hence, the correct option is $(b).$

The number $′0′$ along with the natural numbers gives us the number set $\{0, 1, 2, 3, 4, .....\}$ which is known as set of whole numbers.
Hence, $0, 1, 2, 3, 4....$ are whole numbers.

The smallest even whole number is $2.$
Zero is neither an even number nor an odd number.

Definition of multiplicative identity : an identity element $($such as $1$ in the group of rational numbers without $0)$ that in a given mathematical system leaves unchanged any element by which it is multiplied.
If we multiply $1$ with any number we will get the same number.

The set of whole numbers is $\{0, 1, 2, 3, 4, …\}$
So, the smallest whole number is $0$
Hence, the correct option is $(c).$

The smallest natural number is $1$ and the smallest whole number is $0.$
$\therefore 1 + 0 = 1$

A set of numbers which do not have any other common factor other than $1$ are called co-prime.
The $LCM$ of two co-prime numbers is equal to their product.

$= 13 - (12 - 6 ÷ 3)$
$= 13 - (12 - 2)$
$= 13 - 10 = 3$

 $\dfrac{-18}{5} = -3.6$
Therefore, it lies between $-3$ and $-4.$

 A multiplicative identity is a number which when multiplied with any number, the number is unchanged.
For example: $1 \times 7 = 7, 1 \times 9 = 9, 1 \times 100 = 100$ etc.
Thus, $1$ is multiplicative identity in the set of whole numbers is $1.$
Hence, the correct option is $(c).$

 Given expression:
$27-\Big[18-\big[16-\big(5-\overline{4-1}\big]\Big]$
$= 27 - [18 - \{16 - (5 - 3)\}] [$Removing bar$]$
$= 27 - [18 - \{16 - 2\}] [$Removing parentheses$]$
$= 27 - [18 - 14] [$Removing braces$]$
$= 27 - 4 [$Removing square brackes$]$
$= 23$

 The product of two odd numbers is an odd number.
Example: $5 \times 3 = 15$

$ 80808080 - 1 = 80808079$

Since, $99 = 100 - 1$
Therefore, $47 \times 99 = 47 \times (100 - 1)$
$= 47 \times 100 - 47$
$= 4700 - 47$
$= 4653$
Thus, the value of $47 \times 99$ is $4653.$
Hence, the correct option is $(b).$

 Here, $n$ is an even number.
Successor of $n = n + 1$
Predecessor of $n = n − 1$
Product $= (n + 1) \times (n − 1) = odd \times odd = odd$
Thus, the product of the successor and the predecessor of n is an odd natural number.
Hence, the correct option is $(b).$

$ a + (b + c) = (a + b) + c$ is associative property of whole numbers.

 The sum of $0$ and any rational number is the number itself.
Thus, for any rational number $\frac {\text{a}}{\text{b}}$​
we have $\frac {\text{a}}{\text{b}} + 0 = \frac {\text{a}}{\text{b}}​$

 In the product of two numbers, if one of the numbers (or both) is (are) zero, then the product is zero.
$\therefore0\times0=0$
In a division, if the numerator is zero, then the answer is zero.
$\therefore\frac{0}{2}=0$
Similarly, $\frac{(6-6)}{2}=\frac{0}{2}=0$
Here, $0$ is an additive identity in the set of whole numbers.
$\therefore4 + 0 =4$
Thus, $4 + 0$ is not zero.
Hence, the correct option is $(d).$

Here, $(31 + 15) + x = 31 + (15 + 23).$
But, by associativity of addition,
We have $(31 + 15) + 23 = 31 + (15 + 23)$
So, comparing $(31 + 15) + x = 31 + (15 + 23)$ and $(31 + 15) + 23 = 31 + (15 + 23),$
We have $x = 23$
Hence, the correct option is $(c).$