Question

There is no perfect cube which ends in 4.
A.True
B.False
C.Ambiguous
D.Data insufficient

Answer 1

Hint: In this question if we get at least one number whose cube ends in 4 then the answer is false if not then the answer is true. This we can check using the hit and trial method.

Complete step-by-step answer:
We know that if we get at least one number whose cube ends in 4 then the given data that there is no perfect cube which ends in 4 will be false.
If we take \[{\left( 3 \right)^3} = 3 \times 3 \times 3 = 27\] which does not end in 4
But for \[{\left( 4 \right)^3} = 4 \times 4 \times 4 = 64\] which ends in 4.
\[ \Rightarrow \] There exists a number which ends in 4.
\[ \Rightarrow \] There is no perfect cube which ends in 4 is false.
Hence, option B. False is the correct answer.

Note: Perfect cube is a number which is equal to the number, multiplied by itself, three times.
Characteristics:
If a number ends in 0, its cube ends in 0.
If a number ends in 1, its cube ends in 1.
If a number ends in 2, its cube ends in 8.
If a number ends in 3, its cube ends in 7.
If a number ends in 4, its cube ends in 4.
If a number ends in 5, its cube ends in 5.
If a number ends in 6, its cube ends in 6.
If a number ends in 7, its cube ends in 3.
If a number ends in 8, its cube ends in 2.
If a number ends in 9, its cube ends in 9.