Q. 235.0( 2 Votes )

# Write true (T) or false (F) for the following 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}, then a^{3}>b^{3}.

(vii) If a divides 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 an even number of zeros, then a^{3} ends in 25.

(x) If a^{2} ends in an even number of zeros, then a^{3} ends in an odd number of zeros.

Answer :

(i) 392 is a perfect cube.

False.

Prime factors of 392 = 2 × 2 × 2 × 7 × 7 = 2^{3} × 7^{2}

(ii) 8640 is not a perfect cube.

True

Prime factors of 8640 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 = 2^{3} × 2^{3} × 3^{3} × 5

(iii) No cube can end with exactly two zeros.

True

Beause a perfect cube always have zeros in multiple of 3.

(iv) There is no perfect cube which ends in 4.

False

64 is a perfect cube = 4 × 4 × 4 and it ends with 4.

(v) For an integer a, a^{3} is always greater than a^{2}.

False

In case of negative integers ,

=

(vi) If a and b are integers such that a^{2}>b^{2}, then a^{3}>b^{3}.

False

In case of negative integers,

=

But ,

(vii) If a divides b, then a^{3} divides b^{3}.

True

If a divides b =

=

For each value of b and a its true.

(viii) If a^{2} ends in 9, then a^{3} ends in 7.

False

Let a = 7

7^{2} = 49 and 7^{3} = 343

(ix) If a^{2} ends in an even number of zeros, then a^{3} ends in 25.

False

Let a = 20

= a^{2} = 20^{2} = 400 and a^{3} = 8000

(x) If a^{2} ends in an even number of zeros, then a^{3} ends in an odd number of zeros.

False

Let a = 100

= a^{2} = 100^{2} = 10000 and a^{3} = 100^{3} = 1000000

Rate this question :

Which of the following numbers are not perfect cubes?

(i) 64

(ii) 216

(iii) 243

(iv) 1728

RD Sharma - Mathematics