Tag: whole number operations on the number line

Questions Related to whole number operations on the number line

The given below input rearranges step-by-step in particular order according to a set of rules. In this case the last step of arranged input is Step V.
Input :  85 16 36 04 19 97 63 09 
Step I :  97 85 16 36 04 19 63 09
Step II : 97 85 63 16 36 04 19 09
Step III : 97 85 63 36 16 04 19 09
Step IV : 97 85 63 36 19 16 04 09
Step V : 97 85 63 36 19 16 09 04
Study the above arrangement carefully and then answer the following question.
Which of the following will be step III for their input below?
Input : 09 25 16 30 32 18 17 06

maths four operations whole number operations on the number line whole numbers on number line introduction to multiples and factors

  1. 32 30 25 09 16 18 17 06

  2. 32 30 09 25 16 18 17 06

  3. 32 09 25 16 30 18 17 06

  4. 32 30 09 25 16 19 17 08

Show answer
Correct Option: A
Explanation:

In every step, the series progresses towards getting its elements arranged in a descending order.
So, in every step, the largest elements of the input come to the front.
Input : 09 25 16 30 32 18 17 06
Step I:32 09 25 16 30 18 17 06
Step II:32 30 09 25 16 18 17 06
Step III:32 30 25 09 16  18 17 06
Hence option A is answer.

$n^2+n+1$ is a or an ______ number for all $n\in N$

maths four operations whole number operations on the number line whole numbers on number line introduction to multiples and factors

  1. even

  2. odd

  3. prime

  4. none of these

Show answer
Correct Option: B
Explanation:

Consider $ {n}^{2} + n = n(n+1) $ 

We know that if $ n $ is a number , then $ n  +1 $ will be its consecutive number

And product of a number and its consecutive number is always even. For example, $ 2 \times 3 = 6 ; 9 \times 10 = 90 $

And as  $ {n}^{2} + n$ is an even number.  Then
$ {n}^{2} + n + 1 $ will be the next consecutive number of the even number , which is an odd number.

Hence, $ {n}^{2} + n + 1 $ will always be an odd number for all natural numbers.

$\displaystyle \frac {11}{4}$ is a number between

maths four operations whole number operations on the number line whole numbers on number line introduction to multiples and factors

  1. $1 \ and \ 2$

  2. $2 \ and \ 3$

  3. $3\  and \ 4$

  4. $11\  and \ 12$

Show answer
Correct Option: B
Explanation:

$\displaystyle \frac {11}{4}\, =\, 2\displaystyle \frac {3}{4}$
So $\displaystyle \frac {11}{4}$ lies between $2$ and $3.$

Select the correct order for defining the following terms:
I - natural number
II - imaginary number
III - rational number
IV - integer

maths four operations whole number operations on the number line whole numbers on number line introduction to multiples and factors

  1. I, IV, III, II

  2. I, II, III, IV

  3. I, III, II, IV

  4. IV, I, III, II

  5. I, IV, II, III

Show answer
Correct Option: A
Explanation:
  • Here natural numbers are subset of integers , integers are subset of rational numbers and rational numbers are subset of imaginary numbers
  • Therefore the correct order of defining them is shown in option $A$

(0 , - 3 ) lies on _______ .

maths four operations whole number operations on the number line whole numbers on number line introduction to multiples and factors

  1. Positive x- axis

  2. Negative x-axis

  3. Positive y-axis

  4. Negative y- axis

Show answer
Correct Option: D
Explanation:

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.

The number of surjections from $A = {1, 2,.....n}, n \leq 2$, onto B = {a, b} is

maths four operations whole number operations on the number line whole numbers on number line introduction to multiples and factors

  1. $^nP _2$

  2. $2^n - 2$

  3. $2^n - 1$

  4. none of these

Show answer
Correct Option: B
Explanation:

A = {1, 2, 3, ........, n}

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