SQUARES AND CUBES OF NUMBERS

NOTE : In Q. 1 & Q. 2, (a-b){2} means, square of (a-b), likewise, follow other statements also...

1) a and b are negative integers such that b > a. Which of the following statements(s) is/are true?

I. (a - b){2} > 0
II. (a – b){3} > 0
III. (a – b){3} < 0
IV. (a + b){3} > 0
V. (a + b){3) < 0

1] I and II only.
2] II and III only.
3] I, III and V only.
4] I, III and IV only.

2) If x < 0, y > 0 then, which of the following relations is necessarily true?

1] y/x{2} > 0
2] y/x{6} > x{3}/y
3] y{2} + x{2} > x{3} + y{4}
4] xy/x{2}y > 1

3) Which of the following is true?

I. Sum of two squares can not end in 2 and 8.

II. Sum of two cubes can not end in 3 and 9.

III. Sum of a cube and a square can not end in 0.

1] I only.
2] II only.
3] III only.
4] None of these.

4) Which of the following operations will make the number 847 a perfect square?

I. Add 53 to the number.
II. Multiply the number by 7.
III. Divide the number by 11.
IV. Divide the number by 7.
V. Subtract 6 from the number.

1] I, II, III, IV.
2] I, II, IV, V.
3] I, II, III, V.
4] I, II, III, IV, V.