UGC NET Questions (Paper – 1)

Statements A, B and C give the standard definitions and formulas for GPs. Statement E is also true because phenomena like compound interest and population growth are often modelled using GPs. Statement D is false since a GP does not have constant differences (so it is not an AP). Thus A, B, C and E only are correct.

Option A:
Option A is incomplete since it omits E (applications).

Option B:
Option B is wrong because it includes D (false).

Option C:
Option C is correct because it keeps all true statements and excludes D, which confuses multiplicative and additive patterns.

Option D:
Option D is wrong because it includes D (false) and omits A (definition).

Statements A and B correctly describe arithmetic and geometric series as having constant difference and constant ratio respectively. Statement C is also true because many exam series mix patterns, for example by forming two interleaved sub-sequences. Statement E is correct since checking whether values rise, fall or oscillate helps to guess the right pattern. Statement D is false as some questions deliberately use interleaving or alternating rules. Therefore, the only combination that gathers all true statements and excludes the false one is A, B, C and E only.

Option A:
Option A is incorrect because although A, B and C are all true, the option omits E, which is also a correct and useful principle for analysing series. Since it does not list all the true statements, it cannot be the right answer.

Option B:
Option B is correct because it includes each true statement (A, B, C and E) and excludes D, which wrongly denies the possibility of interleaved or alternating sub-series in exam questions. It therefore matches the complete set of correct statements.

Option C:
Option C is wrong because it includes D, which incorrectly rules out interleaving of sub-series, and at the same time leaves out B, which correctly characterises geometric series. The presence of a false statement and the omission of a true one make this combination invalid.

Option D:
Option D is incorrect because it retains D along with B and E and omits A and C, so it both includes a false restriction about patterns and drops two true statements about arithmetic and mixed series.

Each term is obtained by multiplying the previous term by 2: 5×2 = 10, 10×2 = 20 and 20×2 = 40. This defines a geometric progression with ratio 2. Applying the same rule gives 40×2 = 80. Thus, 80 is the correct next term that preserves the doubling pattern.

Option A:
Option A is 60, which would represent adding 20 to 40 rather than doubling. No earlier transition uses simple addition of a fixed number, so 60 does not fit the rule.

Option B:
Option B is 70, which involves adding 30 to 40 and lacks any basis in the preceding behaviour of the sequence. It fails to keep the constant ratio property. Hence, it is incorrect.

Option C:
Option C equals 80 and results directly from 40×2. The extended series 5, 10, 20, 40, 80 shows a clean geometric pattern. This makes 80 the unique choice that follows the same logic.

Option D:
Option D is 100, which would require a factor of 2.5 from 40. As the sequence has consistently used a ratio of 2, introducing 2.5 is unjustified. Therefore, this option is not valid.

B is the definition of a GP (constant common ratio). C is true for positive terms when r > 1. D is true for positive terms when 0 < r < 1. A is false (that describes an AP), and E is false (a GP is not generally an AP). Therefore B, C and D only are correct. Option A: Option A is incomplete because it omits D, the key decreasing-case when 0 < r < 1. Option B: Option B is incorrect since it includes E, which falsely claims every GP is an AP. Option C: Option C is correct because it includes exactly the true statements (B, C, D) and excludes A and E. Option D: Option D is wrong because it includes A, which incorrectly describes a GP as having a fixed additive difference.

Each term is half of the previous one: 160÷2 = 80, 80÷2 = 40 and 40÷2 = 20. This shows a geometric progression with ratio 1/2. Halving the last term 20 gives 10. Therefore, 10 is the correct next term in the series.

Option A:
Option A is 5, which is half of 10 rather than half of 20. Using 5 directly after 20 would require dividing by 4, not by 2, and thus break the consistent ratio. Hence, 5 is not suitable.

Option B:
Option B is 12, which does not correspond to 20 divided by 2 and would introduce an inconsistent operation. There is no earlier hint of subtracting or adjusting by 8. Therefore, 12 cannot be correct.

Option C:
Option C is 15, which lies between 10 and 20 and does not represent half of the previous term. Choosing 15 would leave the ratio undefined and unclear. Thus, it does not follow the pattern.

Option D:
Option D equals 10, obtained by 20÷2 and preserving the halving process. The extended series 160, 80, 40, 20, 10 keeps the same geometric structure with ratio 1/2. This confirms that 10 is the right continuation.

In a geometric sequence, each term is obtained by multiplying the previous term by a constant factor called the common ratio. Here, 6÷3=2, 12÷6=2 and 24÷12=2, so the ratio between consecutive terms is consistently 2. This confirms that the common ratio is 2. Hence, option B correctly identifies the multiplier generating this sequence.

Option A:
The common ratio is 2, meaning each term is double the previous term. Starting from 3, multiplying by 2 gives 6, then 12, then 24, which matches the sequence given. In mathematical reasoning, recognising this multiplicative pattern helps to predict future terms and solve related problems. Therefore, 2 is the precise value that fits the definition of common ratio in this context.

Option B:
A common ratio of 3 would require that each term be three times the previous term, producing 3, 9, 27, 81 and so on. This does not match the actual sequence where the next term is only double the previous one. Since the ratios 6÷3, 12÷6 and 24÷12 are all 2, not 3, this option is incorrect.

Option C:
A common ratio of 4 would produce 3, 12, 48, 192, which is very different from the given numbers. None of the consecutive quotients in the sequence equals 4. Therefore, 4 cannot describe how the terms are generated, making this option wrong.

Option D:
A common ratio of 1.5 would create terms like 3, 4.5, 6.75, 10.125, which again do not appear in the question. The actual sequence remains strictly integer and doubles each time, unlike the fractional increase implied by 1.5. Hence, 1.5 is not suitable for this pattern.

Each term is three times the previous one: 2×3 = 6, 6×3 = 18 and 18×3 = 54. This defines a geometric progression with common ratio 3. Multiplying the last term 54 by 3 gives 162. Thus, 162 is the next term that keeps the series consistent.

Option A:
Option A suggests 72, which is only 18 more than 54 and does not fit the multiplication-by-three rule. None of the earlier transitions involve adding a fixed number like 18. Therefore, 72 is not appropriate.

Option B:
Option B is 90, which represents 54 plus 36 and again breaks the pure multiplication pattern. The series has never used addition rules, so introducing such a change would be unjustified. Hence, 90 is incorrect.

Option C:
Option C equals 162 and results directly from 54×3, preserving the ratio of 3 between consecutive terms. The extended series 2, 6, 18, 54, 162 shows a clear and consistent geometric pattern. This makes 162 the valid next term.

Option D:
Option D is 180, which does not arise from multiplying 54 by a whole number used earlier in the sequence. Choosing 180 would produce a ratio of 10/3 with the previous term, not 3. Thus, this option does not respect the established rule.

The given series multiplies each term by a constant factor to obtain the next one. Specifically, 9 ÷ 3 = 3, 27 ÷ 9 = 3 and 81 ÷ 27 = 3, so the common ratio is 3. To continue the pattern, we multiply 81 by 3 to obtain the next term. This gives 81 × 3 = 243, which preserves the geometric progression.

Option A:
Option A, 162, arises if someone incorrectly multiplies by 2 instead of 3, giving 81 × 2. However, this contradicts the established common ratio of 3 used in all previous steps.

Option B:
Option B, 200, does not correspond to any simple multiple of 81 consistent with the progression and seems unrelated to the pattern.

Option C:
Option C, 225, is 15² and may be chosen due to familiarity with square numbers, but it does not follow from multiplying 81 by the common ratio 3.

Option D:
Option D maintains the constant ratio of 3 between consecutive terms. By applying 81 × 3, we get 243, which is the only option that respects the geometric structure of the series.

A and B define AP and GP. D is true because the sign of the common difference determines whether an AP increases, decreases, or stays constant. E is true because multiplying by −1 flips a non-zero term’s sign each step, alternating between a and −a. C is false (Fibonacci-type recurrence is generally neither AP nor GP). Hence A, B, D and E only are correct.

Option A:
Option A is incomplete as it omits E, a standard GP special case often tested.

Option B:
Option B is correct because it combines the core definitions with typical behaviour of APs and a specific GP example, and excludes C, which is false.

Option C:
Option C is wrong because it omits A, the definition of an arithmetic sequence.

Option D:
Option D is incorrect because it omits B, the definition of a geometric sequence.

The series is a geometric progression with common ratio 3. Each term is obtained by multiplying the previous term by 3: 2 × 3 = 6, 6 × 3 = 18, 18 × 3 = 54 and 54 × 3 = 162. To continue this pattern, we multiply 162 by 3 to get 162 × 3 = 486. This maintains the constant ratio throughout the sequence.

Option A:
Option A gives 432, which would correspond to multiplying 162 by a factor less than 3 and does not follow the geometric rule. This breaks the constant ratio pattern. Hence, 432 is not correct.

Option B:
Option B offers 450, which is not 162 multiplied by any simple integer ratio used earlier in the series and appears arbitrary. Therefore, 450 cannot be accepted as consistent with the pattern.

Option C:
Option C suggests 480, which again is not equal to 162 × 3 and would require changing the ratio at the end of the series. This disrupts the geometric progression. Thus, 480 is not appropriate.

Option D:
Option D yields 486, which is exactly 162 × 3 and preserves the common ratio of 3. The expanded sequence 2, 6, 18, 54, 162, 486 is a clean geometric progression. Hence, 486 is the correct next term.

Each term in the series is obtained by multiplying the previous term by 2, giving a constant ratio of 2. We have 3×2 = 6, 6×2 = 12 and 12×2 = 24, which confirms the rule. Applying the same operation to the last term gives 24×2 = 48. Thus, 48 is the only term that continues the geometric pattern correctly.

Option A:
Option A suggests 30, which would correspond to adding 6 rather than multiplying by 2. This change in operation does not match any of the earlier transitions in the series. Therefore, 30 does not fit the rule of constant multiplication.

Option B:
Option B maintains the ratio of 2 because 48 ÷ 24 = 2, just as 24 ÷ 12 and 12 ÷ 6 equal 2. The extended sequence 3, 6, 12, 24, 48 clearly follows a doubling rule. This makes 48 the unique correct choice under standard number-series logic.

Option C:
Option C gives 36, corresponding to a factor of 1.5 from 24, which has not appeared anywhere in the series. Introducing this new ratio would destroy the simplicity and consistency of the pattern. Hence, 36 cannot be considered correct.

Option D:
Option D offers 54, which would require multiplying 24 by 2.25. Since none of the previous steps uses such a factor and all use an exact doubling, this option contradicts the established rule. Therefore, it is not the right answer.