UGC NET Questions (Paper – 1)

The map scale 4 cm : 10 km means 1 cm represents 10/4 = 2.5 km. If the towns are 7.5 cm apart on the map, the actual distance is 7.5 × 2.5 km. Multiplying gives 18.75 km, so the real distance between the two towns is 18.75 kilometres.

Option A:
Option A is correct because it applies the direct proportion between map distance and real distance consistently. Converting 4 cm to 10 km first and then scaling linearly to 7.5 cm uses a single constant factor of 2.5 km per centimetre, yielding 18.75 km.

Option B:
Option B, 16.5 km, would correspond to using an incorrect scale factor or rounding at an intermediate stage. If 7.5 cm represented 16.5 km, the implied scale would not match 4 cm : 10 km, and the two ratios would conflict. Hence 16.5 km is not accurate.

Option C:
Option C, 20 km, might be guessed by assuming that 8 cm represent 20 km and then approximating 7.5 cm as 8 cm, but such estimation ignores the exact proportional relationship. When we calculate precisely using 2.5 km per centimetre, 20 km is too large.

Option D:
Option D, 22.5 km, would correspond to treating 3 cm as 10 km or some other incorrect mapping. It implies a scale factor different from 2.5 km per centimetre and cannot be derived from 4 cm : 10 km. Therefore, 22.5 km is not consistent with the given scale.

A is correct because time = distance/speed for fixed distance, so time varies inversely with speed. C is true since distance = speed × time at constant speed. D is true because halving speed doubles time for the same distance. B is false because doubling speed at the same time doubles distance, not halves it. E is false; starting time is not forced by speed alone. Therefore A, C and D only are correct.

Option A:
Option A is correct as it captures both inverse and direct proportion relationships along with a key consequence for halving speed.

Option B:
Option B is incomplete because it excludes D, missing an explicit and important inverse-proportion consequence.

Option C:
Option C is wrong since it includes B, which misstates the effect of doubling speed at fixed time.

Option D:
Option D is incorrect because it adds E (false) and omits A (true), so it cannot be correct.

This option is correct because the formula for simple interest is I = PRT/100. When P and R are fixed, the interest I varies directly with T. Doubling the time doubles the interest, and halving the time halves the interest. Therefore, simple interest is directly proportional to the time period.

Option A:
The time period appears as a direct factor in the simple interest formula. If P and R stay constant, any change in T results in a proportional change in I. This shows a clear direct proportionality between interest and time, so this option correctly identifies the varying quantity.

Option B:
Compound amount includes both principal and interest in compound interest problems and is not part of the simple interest formula in this way. Simple interest is not directly proportional to compound amount. Thus, this option is not appropriate.

Option C:
Discount allowed refers to the reduction from the marked price in sales, which belongs to commercial arithmetic. It does not appear in the simple interest formula and is unrelated to the direct proportionality mentioned. Therefore, discount is not the correct answer.

Option D:
Selling price is determined by cost, profit or loss and discount, not directly by simple interest. While interest can affect selling price in some credit contexts, the simple interest formula itself does not express any direct relationship with selling price. Hence, this option is incorrect.