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

 The smallest prime number is $2$
So, Successor of $2 = 2 + 1 = 3$

$ 100$ million $= 100,000,000100,000,000$
$= 10,00,00,000 = 10 = 10,00,00,000 = 10$ crore

 We know that natural numbers start from $1, 2, 3, ...$
So, the smallest natural number $=1$

 Using distributive law of multiplication over subtraction, we get
$1735 \times 1232 - 1735 \times 232 = 1735 (1232 - 232)$
$= 1735 \times 1000$
$= 1735000$
Hence, the correct option is $(c).$

$ (-1) \times (-1) \times (-1).......$odd times $=$ Negative sign.

 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.
The $HCF$ of two co-prime numbers is $1.$

$\Rightarrow $ The smallest $4 −$ digit number $= 1000.$
$\Rightarrow $ The greatest $4 −$ digit number $= 9999.$
$\Rightarrow $ Total $4 −$ digit numbers $= (9999 - 1000) + 1$
$= 8999 + 1$
$= 9000$
So, we say that we have $9000$ four - digit numbers.

$67 + 33 = 33 + 67$ is an example of​ commutative property of addition.

Closure property in whole number states that if we do the operation between two whole number we should get a whole number. $2, 5$ are
whole number. $2 - 5 = (-3)$ is not a whole number. $\frac{2}{5} ​= 0.4$ is not a whole number.
Closure property is not satisfied w.r.t. subtraction and division in whole numbers.

$4 \times 538 \times 25$
$= 100 \times 538$
$= 53800$

The multiplicative identity property states that any time you multiply a number by $1,$ the result, or product, is that original number.
So it is clear that multiplicative property is given by

The additive identity element is $0.$ We know that the sum of $0$ and any number is the number itself.
Let the number be $x.$
$\therefore x + 0 = 0$
$\Rightarrow x = 0$

The sum of two odd numbers is an even number.
Example: $5 + 3 = 8$

Here, the given number is $28.$
Additive inverse of a given number is a number which when added to the given number gives zero.
Now $28 + (-28) = 0$
Thus, $-28$ is the additive inverse of $28.$
Hence, the correct option is $(c).$

 Whole numbers are not closed under subtraction operation because when any two whole numbers are considered and from them one is subtracted from the other, the difference so obtained is not necessarily a whole number.
Eg. $2 - 5 = -3.$

$\frac{4}{-17}+\frac{0}{-17} =\frac{4}{-17}$
$\frac{4}{-17}-\frac{0}{-17}= \frac{4}{-17}$
Therefore we use both $+$ or $-$

Natural numbers set is $1, 2, 3, ......$
Whole numbers set is $0, 1, 2, 3, .....$
Clearly every natural number is a whole number.

The natural numbers along with $0$ form the collection of whole numbers.
So, the numbers $0, 1, 2, 3, 4, …$ form the collection of whole numbers.
A natural number which is not divisible by $2$ is called an odd whole number.
So, in the collection $“0, 1, 2, 3, 4, …”, 1$ is the smallest odd whole number.
Hence, the correct option is $(b).$

The product of the multiplicative identity of whole number i.e.,
$1$ and a whole number we get the number itself.

$A = \{1, 2, 3, ........, n\} $
$B = \{a, b\}$
A has $n$ elements. $B$ has $2$ elements.
$\therefore$ No. of surjection is $ 2^{\text{n}}-2$

Whole numbers are not closed under subtraction operation because when any two whole numbers are considered and from them one is subtracted from the other,
the difference so obtained is not necessarily a whole number.
Eg. $2 - 5 = −3.$

 If we write natural numbers from $1$ to $100,$ the number of times the digit $5$ has been written is $20.$

The numbers $0, 1, 2, 3, 4, ….$ form the collection of whole numbers.
The smallest whole number is $0.$
So, $0$ does not have a predecessor.
Hence, the correct option is $(b).$

$x$ can have any values between $3$ and $4$ so it can be rational or irrational.
option $c = 0.9$ and options $A$ and $D$ are outside the given range.

Distributive property say that multiplication an division can be distributed over parenthesis.
$a \times (b + c) = a \times b + a \times c$

Natural numbers are the set of whole numbers $($except $0).$
The numbers $1,2,3,4,5.......$ are called natural numbers.

The Distributive Property is easy to remember if you recall that "multiplication distributes over addition".
Formally, they write this property as $"a(b + c) = ab + ac".$
$14 \times 6 + 14 \times 4$
$= 14 \times (6 + 4) ($distributive property$)$
$= 14 \times 10$
$= 140.$

$x(y + z) = (x \times y) + (x \times z)$ shows the distributive property of multiplication over addition.

Number of whole numbers $= (1203 - 1018) - 1$
$= 185 - 1$
$= 184$

$587 \times 99$
$= 587 \times (100 - 1)$
$= 587 \times 100 - 587 \times 1$
$= 58700 - 587$
$= 58113$

By using the distributive property, we have:
$24679 \times 92 + 24679 \times 8$
$= 24679 \times (92 + 8)$
$= 24679 \times 100$
$= 2467900$

We know that, the sum of $0$ and any rational number is the number itself.
Thus, $0$ is the additive identity for rational numbers.

$LCM$ of $15, 20, 24$ and $32$ is given by
$15 = 3 \times 5 = 3^1 \times 5^1$
$20 = 2 \times 2 \times 5 = 2^2 \times 5^1$
$24 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3^1$
$32 = 2 \times 2 \times 2 \times 2 \times 2 = 2^5$
$LCM = 2^5 \times 3^1 \times 5^1 = 480$

Smallest whole number $= 0$
Greatest $2-$digit whole number $= 99$
The whole numbers between $0$ and $99$ are $1, 2, 3, 4 …… 97, 98.$
To find the number of whole numbers between $0$ and $99,$
Subtract $1$ from the difference of $0$ and $99.$
Therefore, Number of whole numbers between $0$ and $99 = (99 - 0) - 1$
$= 99 - 1$
$= 98$
Hence, the correct option is $(d).$

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

An additive identity is a number which when added to any number, the number is unchanged.
For example: $0 + 7 = 7, 0 + 9 = 9, 0 + (- 11) = -11$ etc.
Thus, $0$ is the additive identity in the set of whole numbers.
Hence, the correct option is $(a).$