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Whole number operations on the number line - class-IX

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State whether the following statement is True or False.
The whole number $13$ lies between $11$ and $12$.

  1. True

  2. False


Correct Option: B
Explanation:

False, $13$ does not lie in between $11$ and $12$.

Rather, $13>12$, $13$ lies to the right of 12 on number line.

Multiplying a negative integer for odd times gives  a _____ result 

  1. negative

  2. $0$

  3. positive

  4. none


Correct Option: A
Explanation:

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

The difference between the greatest and least numbers of  $ \displaystyle \frac{5}{9}  $, $ \displaystyle \frac{1}{9}  $, $ \displaystyle \frac{11}{9}  $ is-

  1. $ \displaystyle \frac{9}{2} $

  2. $ \displaystyle \frac{10}{9} $

  3. $ \displaystyle \frac{3}{8} $

  4. $ \displaystyle \frac{9}{10} $


Correct Option: B
Explanation:

The ascending order of given numbers is  $ \displaystyle  \frac{1}{9} $,$ \displaystyle  \frac{5}{9} $,$ \displaystyle  \frac{11}{9} $


Here denominator is equal, so greater the numerator greater will be the value.

 $ \displaystyle \therefore  $ Required difference 

$ \displaystyle  \frac{11}{9} $-$ \displaystyle  \frac{1}{9} $=$ \displaystyle  \frac{10}{9} $ 

Let $x$ be a real variable, and let $3 < x < 4.$ Which of the following values, $x$ might have?

  1. $-3.1$

  2. $\sqrt{11}$

  3. $\sqrt{\dfrac{10}{11}}$

  4. $4.1$


Correct Option: B
Explanation:

$x$ 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.
Hence, correct answer is option $B=\sqrt11=3.3$.

The rational number $\displaystyle \frac{-18}{5}$ lies between 

  1. $- 2$ and $- 3$

  2. $- 3$ and $- 4$

  3. $- 4$ and $- 5$

  4. $- 5$ and $- 6$


Correct Option: B
Explanation:

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

How many times does the digit $3$ appear while writing the integers from $1$ to $1000$?

  1. $298$

  2. $299$

  3. $300$

  4. $301$


Correct Option: C

The number of whole numbers between the smallest whole number and the greatest 2-digit number is:

  1. $101$

  2. $100$

  3. $99$

  4. $98$


Correct Option: D
Explanation:

The smallest whole number is $0$ and the two-digit greatest whole number is $99$.

So the numbers between $0$ and $99$ are $1,2,....,98$ i.e. there are $98$ whole numbers between $0$ and $99$.

If n is a whole number such that $n + n = n$, then $n =$ ?

  1. 1

  2. 2

  3. 3

  4. None of these


Correct Option: D
Explanation:

$n + n = n$

$2n = n$
Clearly $n = 0$, satisfies 
So $n = 0$ is the final answer.

How many whole numbers are between 437 and 487? 

  1. $50$

  2. $49$

  3. $51$

  4. None of these


Correct Option: B
Explanation:

No. of whole numbers in between

$=(487 - 437) - 1$
$= 50 - 1$
$= 49$

On a vertical number line positive numbers are placed ____ $0$

  1. right side

  2. left side

  3. above

  4. below


Correct Option: C
Explanation:

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

  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


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 $n\in N$

  1. even

  2. odd

  3. prime

  4. none of these


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

  1. $1 \ and \ 2$

  2. $2 \ and \ 3$

  3. $3\  and \ 4$

  4. $11\  and \ 12$


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

  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


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 _______ .

  1. Positive x- axis

  2. Negative x-axis

  3. Positive y-axis

  4. Negative y- axis


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

  1. $^nP _2$

  2. $2^n - 2$

  3. $2^n - 1$

  4. none of these


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 $2^{n}-2$.

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