Questions & Answers

Question

Answers

$

{\text{a}}{\text{. 10345}} \\

{\text{b}}{\text{. 10453}} \\

{\text{c}}{\text{. 10543}} \\

{\text{d}}{\text{. 10534}} \\

$

Answer
Verified

Hint: - First place cannot be filled with digit zero.

As there are a total 5 numbers so we have to make a smallest five digit odd number.

For an odd number the last digit should be odd.

So from given digits odd numbers are $\left( {1,3,5} \right)$

As we see there is a digit zero in given numbers but we have to make a smallest 5 digit odd number, so numbers cannot start with zero.

After zero the smallest number is 1, so the number is starting from 1.

And the second place of the number should be zero because we have to make a smallest number.

Now the remaining digits are $3,4{\text{ and }}5$, so the last digit is filled with 5 because it is an odd number and the greatest number among these numbers, greatest numbers should be at oneâ€™s place because we have to make a smallest number.

Now the remaining digits for ${3^{rd}}{\text{ and }}{4^{th}}$ place are $3{\text{ and }}4$.

Similarly fourth place is filled with second highest number and third place is filled with third highest number.

Therefore fourth place is filled with digit 4.

And the third place is filled with digit 3.

So, the required number is 10345.

Hence option (a) is correct.

Note: - In such types of question, if in given digits there is digit 0, then the number cannot start with zero, because if we start with zero, it become a four digit number which is not the required case, so for smallest number start with lowest digit after that apply digit 0 so that number become smallest then apply the digits using the method which is written above we will get the required answer. If there is only one odd number in the given digits and we have to make an odd number then this digit always comes at last place, remaining 4 digits will follow the same procedure.

As there are a total 5 numbers so we have to make a smallest five digit odd number.

For an odd number the last digit should be odd.

So from given digits odd numbers are $\left( {1,3,5} \right)$

As we see there is a digit zero in given numbers but we have to make a smallest 5 digit odd number, so numbers cannot start with zero.

After zero the smallest number is 1, so the number is starting from 1.

And the second place of the number should be zero because we have to make a smallest number.

Now the remaining digits are $3,4{\text{ and }}5$, so the last digit is filled with 5 because it is an odd number and the greatest number among these numbers, greatest numbers should be at oneâ€™s place because we have to make a smallest number.

Now the remaining digits for ${3^{rd}}{\text{ and }}{4^{th}}$ place are $3{\text{ and }}4$.

Similarly fourth place is filled with second highest number and third place is filled with third highest number.

Therefore fourth place is filled with digit 4.

And the third place is filled with digit 3.

So, the required number is 10345.

Hence option (a) is correct.

Note: - In such types of question, if in given digits there is digit 0, then the number cannot start with zero, because if we start with zero, it become a four digit number which is not the required case, so for smallest number start with lowest digit after that apply digit 0 so that number become smallest then apply the digits using the method which is written above we will get the required answer. If there is only one odd number in the given digits and we have to make an odd number then this digit always comes at last place, remaining 4 digits will follow the same procedure.

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