Tag: maths

Questions Related to maths

The two numbers formed by subtracting one from $5$ and $10$ are:

maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

  1. 11 and 12

  2. 4 and 10

  3. 4 and 9

  4. 5 and 6

Show answer
Correct Option: C
Explanation:

Let us first subtract one from $5$ as shown below:


$5-1=4$ 

Similarly, subtract one from $10$ as follows:

$10-1=9$ 

Hence, the two numbers formed by subtracting one from $5$ and $10$ are $4$ and $9$.

If a and b are two whole numbers, then commutative law is applicable to subtraction if and only if

maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

  1. $a = b$

  2. a $\neq $ b

  3. $a > b$

  4. $a < b$

Show answer
Correct Option: A
Explanation:
Commutative property : The subtraction of whole numbers is not commutative, that is, if $a$ and $b$ are two whole numbers, then in general $a – b$ is not equal to $(b – a)$.

Verification:

We know that $9 – 5 = 4$ but $5 – 9=-4$ which is not a whole number. Thus, for two whole numbers $a$ and $b$ if $a > b$, then $a – b$ is a whole number but $b – a$ is not possible and if $b > a$, then $b – a$ is a whole number but $a – b$ is not possible.

Now, if $a=b=3$ then, $a-b=3-3=0$ which is also a whole number.

Hence, whole numbers are commutative under subtraction if and only if $a=b$.

Which of the following properties are not applicable to the subtraction of whole numbers?

maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

  1. Closure property

  2. Commutative property

  3. Associative proptery

  4. All the above

Show answer
Correct Option: D
Explanation:

Let us have a look at the properties of whole numbers under subtraction:


(i) Closure property : If $a$ and $b$ are two whole numbers such that $a > b$ or $a = b$, then $a – b$ is a whole number. If $a < b$, then subtraction $a – b$ is not possible in whole numbers. For example: If $a=3$ and $b=5$ then,

$3-5=-2$ which is not a whole number.

Therefore, whole numbers are not closed under subtraction.

(ii) Commutative property : The subtraction of whole numbers is not commutative, that is, if $a$ and $b$ are two whole numbers, then in general $a – b$ is not equal to $(b – a)$.

Verification:

We know that $9 – 5 = 4$ but $5 – 9=-4$ which is not a whole number. Thus, for two whole numbers $a$ and $b$ if $a > b$, then $a – b$ is a whole number but $b – a$ is not possible and if $b > a$, then $b – a$ is a whole number but $a – b$ is not possible.

Therefore, whole numbers are not commutative under subtraction.

(iii) Associative of addition : The subtraction of whole numbers is not associative. That is, if $a, b, c$ are three whole numbers, then in general $a – (b – c)$ is not equal to $(a – b) – c$.

Verification:

We have,

$20 – (15 – 3) = 20 – 12 = 8$,

and, $(20 – 15) – 3 = 5 – 3 = 2$

So, $20 – (15 – 3) ≠ (20 – 15) – 3$.

Therefore, whole numbers are not associative under subtraction.


Hence, all of the properties are not applicable to subtraction of whole numbers.

If $\displaystyle a^{2}-b^{2}=13$ where a and b are natural numbers then value of a is

maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

  1. $6$

  2. $7$

  3. $8$

  4. $9$

Show answer
Correct Option: B
Explanation:

$a^2 - b^2 = 13$
$(a-b)(a +b) = 1 \times 13$
By comparing, $a - b = 1, a + b = 13$
Add both the equations,
$2a = 14$
$a = 7$

Find the value of A and B in the following sum:
$6 A 3$
$\underline {+2 2 B}$
$\underline {B B 1}$

maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

  1. $A=5,B=8$

  2. $A=6,B=8$

  3. $A=5,B=7$

  4. $A=5,B=9$

Show answer
Correct Option: A
Explanation:

Since 3 + B given us 1 in the answer, so B has to be 8 as $3+8=11$.
Now 1 is carried over so, $A+1+2=B$
i.e. $A+1+2=8$. So, A is 5.
Also $6+2=B$ in hundred's place to confirm that B is 8.
The value of A is 5 and B is 8.

If x stands for addition, < for substraction, + stands for division, > for multiplication, - stands for equal to, + for greater than and = stands for less than, state which of the following is true?

maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

  1. $3 \times 2 < 4 \div 16 > 2 + 4$

  2. $5 > 2 + 2 = 10 < 4 \times 2$

  3. $3 \times 4 > 2 - 9 + 3 < 3$

  4. $5 \times 3 < 7 \div 8 + 4 \times 1$

Show answer
Correct Option: B

Two rows of numbers are given The resultant number in each row is to be worked out separately based on the following rules and the question below the rows of numbers is to be answered The operations of numbers progress from left to right
Rules
I. If an odd number is followed by a two-digit even number then they are to be added.
II. If an odd number is followed by a two-digit odd number then the second number is to be subtracted from the first number
III. If an even number is followed by a number which is a perfect square of a number then the second number is to be divided by the first number
IV. If an even number is followed by a two-digit even number then the first number is to be multiplied by the second number
                    8  16  16  14
                   13  11  12  144
What is the difference between the resultant of the first set of numbers and the second set of numbers ?

maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

  1. 106

  2. 118

  3. 210

  4. 222

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Correct Option: A

Savita has Rs. 27 in the form of fifty paise and twenty-five paise coins. She has twice as many twenty-five paise coins as she has 50 paise coins. How many coins of each kind does she have?

maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

  1. 27, 54

  2. 30, 60

  3. 25, 50

  4. 40, 80

Show answer
Correct Option: A
Explanation:

Let the number of 50 paise coins =x
So the number of 25 paise coins=2x
Amount with 50 paise coines=0.5x
Amount with 25 paise coines=0.5x
According to question 
0.5x+0.5x=27
Or x=27
So the number of 50 paise coins=x=27
Or the number of 25 paise coines=2x=54 

$1+5+9+\cdots\cdots+(4n-3)$ is equal to

maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

  1. $n(4n-3)$

  2. $(2n-1)$

  3. $n(2n-1)$

  4. $(4n-3)^2$

Show answer
Correct Option: C
Explanation:

In the given Arithmetic Progression,
First term $ = a  = 1 $
Common difference $ = 5 - 1 = 4 $

Let $ 4n - 3 $ be the $  k $ th term.

Then $ {x} _{n} = a + (n-1)d $
$ => 4n- 3 = 1 + (k-1)4 $
$ => 4n -1 = 1 +4k-4 $
$ => k = n $

So,  $ 4n - 3 $ is the $ n $ th term.

Now, Sum to 'n' terms of an AP $ = \frac {n}{2} (2a+(n-1)d) = \frac {n}{2} (2+(n-1)4) = \frac {n}{2} (4n-2) =n(2n-1) $

The distance between (-4, -5) and (-4, -10) is________units

maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

  1. 15

  2. 10

  3. 5

  4. 2

Show answer
Correct Option: C
Explanation:

Distance between two points $ ({x} _{1}, {y} _{1}) $ and $ ({x} _{2}, {y} _{2}) $ is $ \sqrt {{({x} _{2}-{x} _{1})}^{2} + {{(y} _{2}-{y} _{1})}^{2} } $

So, distance between $ (-4,-5) ; (-4,-10) $ is $ \sqrt {{(-4+4)}^{2} + {(-10+5)}^{2} } = 5 $