First, calculate the exponents: (-3)^3 = -27 (an odd power retains the negative sign) and (-6)^2 = 36 (an even power makes it positive). Multiplying them: -27 × 36 = -972.
57. Which among the following is a correct numeral?
(A) IXX
(B) LXXII
(C) XLX
(D) VXL
Answer:
(B) LXXII
Explanation:
In Roman numerals, LXXII correctly translates to 50 (L) + 10 (X) + 10 (X) + 1 (I) + 1 (I) = 72. The other options violate the standard subtractive and positional rules of Roman numerals.
58. The diagonals of a rectangle always intersect at their:
(A) corners
(B) quadrants
(C) perimeter
(D) midpoints
Answer:
(D) midpoints
Explanation:
A fundamental geometric property of a rectangle is that its two diagonals are equal in length and bisect each other, meaning they intersect exactly at their midpoints.
59. What is the shape of a quadrilateral with all the angles equal to 90°?
(A) Hexagon
(B) Pentagon
(C) Rectangle
(D) Sphere
Answer:
(C) Rectangle
Explanation:
A quadrilateral is a four-sided polygon. If all four of its interior angles are exactly 90 degrees (right angles), the shape is defined as a rectangle.
60. Which among the following is not divisible by 9?
(A) 81
(B) 54
(C) 69
(D) 72
Answer:
(C) 69
Explanation:
The divisibility rule for 9 states that a number is divisible by 9 if the sum of its digits is divisible by 9. For 69, 6+9 = 15, which is not divisible by 9.
