For an integer $a,$ choose the correct statement.

a^{3}

is always greater than

a^{2}

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a^{3}

is always smaller than

a^{2}

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a^{2}

is always greater than

a^{3}

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None of the above

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Solution

The correct option is D None of the above
False, since the square of 1 is 1 is equal to the cube of 1. In this case $a^{3}$ is not greater than $a^{2}$ .

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Similar questions

Question 67

State whether the following statement is true or false:

For an integer a, $a^{3}$ is always greater than $a^{2}$ .

Question 67

State whether the following statement is true or false:

For an integer a, $a^{3}$ is always greater than $a^{2}$ .

Q. Find the value of

\frac{a_{1}}{a_{1} + 1 -} \frac{a_{2}}{a_{2} + 1 -} \frac{a_{3}}{a_{3} + 1 -} \dots, a_{1}, a_{2}, a_{3}, \dots

being positive and greater than unity.

Write true (T)I or false (f) for the followiong statements:
(i) 392 is a perfect cube.
(ii) 8640 is not a perfect cube.
(iii) No cube can end with exactly two zeros.
(iv) There is no perfect cube which ends in 4.
(v) For an integer $a, a^{3}$ is always greater than $a^{2}$
(vi) if a and b are integers such that $a^{2} > b^{2}, t h e n a^{3} > b^{3}$
(vii) If a adivides b, then $a^{3}$ divides $b^{3}$
(viii) If $a^{2}$ ends in 9 then $a^{3}$ ends in 7.
(ix) If $a^{2}$ ends in 5, then $a^{3}$ ends in 25.
(x) If $a^{2}$ ends in an even number of zeros. than $a^{3}$ ends in an odd number of zeros.

Q. The number of ways in which

10

candidates

A_{1}, A_{2}, A_{3}, \dots, A_{10}

can be ranked so that

A_{1}

is always above

A_{2},

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For an integer a, choose the correct statement.

The correct option is D None of the aboveFalse, since the square of 1 is 1 is equal to the cube of 1. In this case a3 is not greater than a2.

For an integer $a,$ choose the correct statement.

The correct option is D None of the above
False, since the square of 1 is 1 is equal to the cube of 1. In this case $a^{3}$ is not greater than $a^{2}$ .