1If A:B = 2:3 and B:C = 4:5, then A:C is:
- 2:5
- 8:15
- 6:10
- 3:5
Show answer and explanation
Answer: B. 8:15
Make B equal: A:B:C = 8:12:15.
UGC NET PAPER 1 · CODE 00 · UNIT 05
UGC NET Paper 1 Unit 5: Mathematical Reasoning Notes and MCQs
Mathematical Reasoning uses only school-level arithmetic, so you can score well even if mathematics is not your subject. The questions are short and repeat a small set of patterns. These notes give you the formulas and series patterns to learn, and sample MCQs to practise with.
- 4 syllabus topics
- 600+ free MCQs
- No sign-up
- Updated 11 October 2026
NET Law 058 is an independent study aid, not affiliated with UGC or NTA. Always check the official UGC NET syllabus and the latest official sources for any data.
What Unit 5 covers
Mathematical Reasoning is a speed game on simple arithmetic, so timed daily practice matters more than learning new methods. The official syllabus lists 4 topics for this unit. Each is explained below with the points examiners most often use.
1Types of reasoning
- Deductive reasoning moves from general rules to a specific conclusion that must be true if the premises are true.
- Inductive reasoning moves from specific observations to a general conclusion that is probable, not certain.
- Other types: analogical reasoning (by comparison), verbal reasoning (words) and non-verbal reasoning (figures and patterns).
- Quantitative reasoning solves problems with numbers, and logical reasoning tests the structure of arguments.
2Number series, letter series, codes and relationships
- Number series follow patterns: constant difference, constant ratio, squares, cubes, primes or differences that themselves form a pattern.
- Letter series use alphabet positions (A=1 to Z=26) with fixed jumps or alternating steps. Opposite letters add up to 27.
- Coding-decoding applies a rule such as shifting each letter by a fixed number of places or replacing letters with numbers.
- Blood relation questions need a clear family diagram: for example, a mother's brother is a maternal uncle and his child is a cousin.
3Basic mathematical aptitude: fractions, time and distance, ratio, proportion and percentage
- Percentage: x% of N is N times x over 100. Convert fractions to percentages for quick comparison.
- Speed = distance divided by time. To convert km/h to m/s multiply by 5/18.
- Ratio compares two quantities of the same kind. In A:B and B:C, make the B terms equal to combine them into A:B:C.
- Proportion states that two ratios are equal. In direct proportion both quantities rise together; in inverse proportion one rises as the other falls.
4Profit and loss, interest, averages, discounts and simple calculations
- Profit = SP minus CP and profit percent = profit divided by CP times 100. Loss percent is calculated the same way on CP.
- Simple interest = P x R x T divided by 100. Compound interest amount = P (1 + R/100) to the power T.
- Average = sum of values divided by the number of values. So sum = average times number of values.
- Discount is a reduction on the marked price, and the selling price = marked price minus discount.
Quick reference tables
| Topic | Formula |
|---|---|
| Percentage | x% of N = N x x / 100 |
| Profit percent | (SP - CP) / CP x 100 |
| Loss percent | (CP - SP) / CP x 100 |
| Discount | Marked price - Selling price; Discount percent = Discount / Marked price x 100 |
| Simple interest | SI = P x R x T / 100; Amount = P + SI |
| Compound interest | Amount = P (1 + R/100)^T; CI = Amount - P |
| Average | Sum of values / Number of values |
| Speed, distance, time | Speed = Distance / Time; km/h to m/s: multiply by 5/18 |
| Time and work | If A takes a days and B takes b days, together they take ab / (a + b) days |
| Ratio | A:B and B:C combine to A:B:C by making B equal in both |
| Pattern | Example | Next term |
|---|---|---|
| Add a constant | 3, 7, 11, 15 | 19 |
| Multiply by a constant | 3, 6, 12, 24 | 48 |
| Perfect squares | 1, 4, 9, 16 | 25 |
| Perfect cubes | 1, 8, 27, 64 | 125 |
| Differences increase by 2 | 2, 6, 12, 20, 30 | 42 |
| Prime numbers | 2, 3, 5, 7, 11 | 13 |
| Alternate letters | A, C, E, G | I |
Key terms and facts to remember
Deductive reasoning
General to specific; the conclusion follows necessarily from the premises.
Inductive reasoning
Specific to general; the conclusion is probable.
Alphabet positions
A=1, B=2 up to Z=26. The letter opposite to a given letter has position 27 minus the original.
Percentage
Fraction out of 100; for example 25% equals 1/4 and 20% equals 1/5.
Speed conversion
1 km/h = 5/18 m/s; 1 m/s = 18/5 km/h.
Profit and loss
Always calculated on the cost price unless stated otherwise.
Simple interest
Interest calculated only on the original principal.
Compound interest
Interest calculated on principal plus interest already earned.
Average
Sum divided by number of items; useful to remember sum equals average times count.
Prime numbers
Numbers with exactly two factors; 2 is the only even prime and 1 is not prime.
Clock angles
The minute hand moves 6 degrees per minute and the hour hand 0.5 degrees per minute.
Practise Mathematical Reasoning MCQs topic by topic
Beyond the six samples, all 630 questions for this unit are on their own pages, grouped by syllabus topic, with the answer key on the page.
- Deductive Reasoning (Part 1) (25)
- Deductive Reasoning (Part 2) (25)
- Inductive Reasoning (Part 1) (25)
- Inductive Reasoning (Part 2) (25)
- Abductive Reasoning (Part 1) (19)
- Abductive Reasoning (Part 2) (18)
- Analogical Reasoning (Part 1) (14)
- Analogical Reasoning (Part 2) (14)
- Number Series (Part 1) (22)
- Number Series (Part 2) (22)
- Number Series (Part 3) (22)
- Ratio, Proportion and Partnership (Part 1) (15)
Try 6 sample questions
Tap “Show answer” after you have tried each one. These come from the 600+ MCQs in this unit.
2Next term: 2, 6, 12, 20, 30, ?
- 36
- 40
- 42
- 48
Show answer and explanation
Answer: C. 42
Differences increase by 2: next difference 12.
3An article sold for ₹360 at 10% loss had a cost price of:
- ₹380
- ₹400
- ₹420
- ₹450
Show answer and explanation
Answer: B. ₹400
CP × 0.9 = 360, so CP = 400.
4At 3:15, the angle between the clock hands is:
- 0°
- 7.5°
- 15°
- 30°
Show answer and explanation
Answer: B. 7.5°
Hour hand at 97.5°, minute hand at 90°.
5A can do a work in 10 days and B in 15 days. Together they take:
- 5 days
- 6 days
- 7 days
- 8 days
Show answer and explanation
Answer: B. 6 days
1/10 + 1/15 = 1/6.
6A is B's brother. B is C's sister. C is D's father. A is D's:
- Uncle
- Cousin
- Father
- Brother
Show answer and explanation
Answer: A. Uncle
A is C's brother, hence D's uncle.
How to study this unit
- Learn the formulas table until you can write it in two minutes, then practise ten quick questions a day with a timer.
- For series questions, write the differences and the ratios first. One of the two usually reveals the pattern.
- Check each answer by substitution or an estimate. Many wrong options are the result of a common slip, such as dividing instead of multiplying.
Planning your time? See the UGC NET Law preparation plans for 6 months, 3 months, 1 month or 2 weeks, or check the cut-off trend to set a target score.
Last updated: . Notes are a revision aid. Check official sources for the latest figures. Spotted a mistake? Write to netlawverse@gmail.com.