UGC NET Questions (Paper – 1)

The third proportional c to numbers a and b is defined by a:b = b:c. For a = 5 and b = 20, we have 5:20 = 20:c. Writing this as a fraction gives 5/20 = 20/c, so c = (20 × 20)/5 = 400/5 = 80. Thus, 80 is the third proportional to 5 and 20.

Option A:
Option A, 40, produces the ratio 20:40 = 1:2, whereas 5:20 = 1:4. Since these ratios are not equal, 40 cannot be the third proportional under the definition a:b = b:c.

Option B:
Option B, 64, might emerge from mistakenly squaring only part of a fraction or choosing a convenient number, but 5:20 = 1:4 and 20:64 = 5:16, which do not match. Therefore, 64 does not satisfy the required proportional relationship.

Option C:
Option C is correct because with c = 80 we get 5:20 = 1:4 and 20:80 = 1:4. The equality of these ratios confirms that 80 is the valid third proportional to 5 and 20.

Option D:
Option D, 100, yields 20:100 = 1:5, which differs from 1:4, the simplified form of 5:20. While 100 is a round number, it does not preserve the proportional structure defined in the question.