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

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} $
Reveal answer Fill a bubble to check yourself
B Correct answer
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} $ 

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

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. $4.1$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $B=\sqrt11=3.3$.

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

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

  1. $298$
  2. $299$
  3. $300$
  4. $301$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To count the digit 3 from 1 to 1000: in each position (units, tens, hundreds), the digit 3 appears 100 times. For example, in the units place, it appears in 3, 13, 23, ..., 993 (100 times). The same applies to the tens and hundreds places, totaling 300 occurrences.

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

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

  1. $101$
  2. $100$
  3. $99$
  4. $98$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $99$.

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

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.