UGC NET Questions (Paper – 1)

Statements A, B, C and E correctly describe fundamental ideas of ratio and proportion. Ratios compare quantities by division, proportions equate two ratios and ad = bc is the standard cross-multiplication rule. It is also true that meaningful ratios compare quantities in the same units. Statement D is false because there is no requirement that a + c equals b + d in a valid proportion. Hence the combination including A, B, C and E but excluding D is the only fully correct set.

Option A:
Option A is correct because it includes all true statements and excludes D, which imposes a wrong condition on proportions. It provides a complete and accurate summary of the key properties tested in NET-level questions on ratio and proportion.

Option B:
Option B is incomplete since it omits E and therefore ignores the practical requirement about same units, which is important for interpreting real-life ratio problems. This omission makes the set of statements only partially correct.

Option C:
Option C is wrong because it includes D, the incorrect condition about sums of antecedents and consequents, even though it also contains some true statements. The presence of D makes the overall combination incorrect.

Option D:
Option D is wrong because it omits A (the basic definition of ratio) and also includes E while missing other true statements; it does not match the complete set of correct statements.

The relation 4:6 = 10:x can be expressed as 4/6 = 10/x. Cross-multiplying gives 4x = 60, so x = 60/4 = 15. Therefore, 15 is the fourth proportional to 4, 6 and 10, making the two ratios 4:6 and 10:15 equal.

Option A:
Option A, 12, would give 10:12 = 5:6, while 4:6 simplifies to 2:3. Since 2:3 ≠ 5:6, the equality of ratios is not preserved, and 12 cannot be the correct fourth proportional.

Option B:
Option B is correct because substituting x = 15 yields 10:15 = 2:3, which matches 4:6 = 2:3. This confirms that the proportionality 4:6 = 10:15 holds perfectly, satisfying the definition of fourth proportional.

Option C:
Option C, 18, leads to 10:18 = 5:9, which again does not equal 2:3 and therefore fails the test of proportion. Even though 18 is larger than 15, it does not maintain the required ratio.

Option D:
Option D, 20, produces 10:20 = 1:2, while 4:6 = 2:3, so the two ratios differ markedly. As a result, 20 is not consistent with the proportional relationship given in the question.