Tag: number systems

Questions Related to number systems

$A,B,C$ and $D$ are all different digits between $0$ and $9$. If $AB+DC=7B\ (AB,DC$ and $7B$ are two digit numbers), then the value of $C$ is

maths number systems existence of irrational numbers irrational numbers properties of irrational numbers

  1. $0$

  2. $1$

  3. $2$

  4. $3$

  5. $5$

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Correct Option: A
The value of  $\displaystyle \pi $ upto $50$ decimal places is $:\:314159265358979323846264338327950288419716939937510$
Which are the least occurring digits?
maths number systems existence of irrational numbers irrational numbers properties of irrational numbers

  1. $0$

  2. $1$

  3. $2$

  4. $3$

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Correct Option: A
Explanation:

We will be considering the digits only after the decimal point.


Digit after decimal point frequency
0 2
1 5
2 5
3 8
4 4
5 5
6 4
7 4
8 5
9 8
Total 50

The maximum occurring digits are 3 and 9. 
The least occurring digit is 0.

$0.\overline{35}$ is equal to

maths number systems existence of irrational numbers irrational numbers properties of irrational numbers

  1. $\displaystyle\frac{35}{66}$

  2. $\displaystyle\frac{35}{77}$

  3. $\displaystyle\frac{35}{99}$

  4. none of these

Show answer
Correct Option: C
Explanation:
$X=0.35353535$   -- i
Multiplying equation i with 100,

$100x=35.353535353$   --ii 
Subtracting equation i from ii 

$ 100x-x = 35.3535 - 0.3535 $
$99x=35$
$ x = \dfrac{35}{99}$