UGC NET Questions (Paper – 1)

Statements A, B and C correctly describe proper fractions, terminating decimals and the fact that fraction-to-decimal conversion may yield either terminating or repeating expansions. Statement E is also true because comparison techniques such as cross-multiplication allow direct comparison of fractions without converting to decimals. Statement D is false because irrational numbers have non-terminating, non-repeating decimal expansions and cannot be expressed as terminating decimals. Thus, the combination A, B, C and E only is correct.

Option A:
Option A is incomplete as it omits E and therefore does not acknowledge the practical method of comparing fractions directly, which is an important technique in timed aptitude tests.

Option B:
Option B is also incomplete because it excludes C and thus fails to mention that fractions can produce repeating decimals as well, an important conceptual point about rational numbers.

Option C:
Option C is correct since it includes all the true statements and excludes D, which misclassifies irrational numbers. It reflects both the theory and the applied strategies involving fractions and decimals.

Option D:
Option D is wrong because it includes D, the statement that wrongly treats irrational numbers as terminating decimals, and omits B, which accurately characterises the denominators of terminating decimals. This combination cannot be accepted.

To compare the fractions, we can either convert them to decimal form or cross multiply. The fraction 3/5 equals 0.6, 4/7 is approximately 0.571, 5/9 is approximately 0.556 and 6/13 is approximately 0.462. Among these decimal values, 0.6 is the largest. Therefore, 3/5 represents the greatest fraction in the given list.

Option A:
Option A, 3/5, clearly exceeds the others when converted into decimals or compared via cross multiplication with a common denominator. It corresponds to 0.6, which is larger than the approximate decimal values of the remaining fractions.

Option B:
Option B, 4/7, is slightly less than 0.6 and therefore smaller than 3/5, even though it is greater than the other two fractions listed. It cannot be the greatest overall.

Option C:
Option C, 5/9, falls between 0.55 and 0.56, making it smaller than both 3/5 and 4/7, so it is not the maximum value.

Option D:
Option D, 6/13, is noticeably less than 0.5, making it the smallest among the four fractions rather than the largest.