Question

ਹੇਠ ਲਿਖਿਆਂ ਵਿੱਚੋਂ ਕਿਹੜਾ ਕਥਨ ਗ਼ਲਤ ਹੈ?Which of the following statement is false? * ਕਿਸੇ ਟਾਂਕ ਸੰਖਿਆ ਦਾ ਘਣ ਇੱਕ ਟਾਂਕ ਸੰਖਿਆ ਹੁੰਦੀ ਹੈ।/Cube of any odd number is an odd number. ਇੱਕ ਪੂਰਣ ਘਣ ਦੋ ਸਿਫਰਾਂ 'ਤੇ ਖ਼ਤਮ ਨਹੀਂ ਹੁੰਦਾ।/A perfect cube does not end with two zeros. ਇੱਕ ਅੰਕ ਵਾਲ਼ੀ ਸੰਖਿਆ ਦਾ ਘਣ ਇੱਕ ਅੰਕ ਵਾਲ਼ੀ ਸੰਖਿਆ ਹੋ ਸਕਦੀ ਹੈ।/The cube of a single digit number may be a single digit number. ਇਸ ਤਰ੍ਹਾਂ ਦਾ ਕੋਈ ਪੂਰਨ ਘਣ ਨਹੀਂ ਹੈ ਜੋ 3 'ਤੇ ਖ਼ਤਮ ਹੁੰਦਾ ਹੈ।/There is no perfect cube which ends with 3.​

Answer 1

there is no perfect cube which ends with 3

Answer 2

The required false statement among the four given statements is "There is no perfect cube that ends with 3.​"

Given :

The following four statements are given.

A cube of any odd number is an odd number.

A perfect cube does not end with two zeros.

The cube of a single-digit number may be a single-digit number.

There is no perfect cube that ends with 3.​

To Find :

The false statement among the four given statements

Solution :

We check the validity of the statement "A cube of any odd number is an odd number." in the following way.

We suppose an odd number 2n+1, n=0,1,2...

$(2n+1)^{3}\\ =(2n)^{3}+3\times(2n)^{2}\times1+3\times(2n)\times1^{2}+1^{3}\\=8n^{3}+12n^{2}+6n+1\\=2\times (4n^{3}+6n^{2}+3n)+1\\\\=oddnumber$

Hence, the statement "A cube of any odd number is an odd number." is correct.

We check the validity of the statement 'A perfect cube does not end with two zeros." in the following way.

A perfect cube indicates that the cube root of a perfect cube must be an integer. As such the cube root of a perfect cube that ends with at least three zeroes is an integer that ends with a single zero.

Hence, the statement 'A perfect cube does not end with two zeros." is correct.

We check the validity of the statement "The cube of a single-digit number may be a single-digit number." in the following way.

We know that 3 is a single-digit number and its cube that is equal to 9, is also a single-digit number.

Hence, the statement "The cube of a single-digit number may be a single-digit number." is correct.

We check the validity of the statement "There is no perfect cube that ends with 3.​" in the following way.

We know that the cube of any number that ends with 7 in its unit place, has 3 in its unit place; because $7\times7\times7=343$.

Hence, the statement "There is no perfect cube that ends with 3.​" is false.

The required false statement among the four given statements is "There is no perfect cube that ends with 3.​"

#SPJ2