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UGC NET Mathematical Reasoning and Aptitude Syllabus

The Mathematical Reasoning and Aptitude syllabus for UGC NET in full: 5 chapters, 20 topics and 8 sub-topics, every one listed below, plus 50 Mathematical Reasoning and Aptitude flashcards with answers.

5Chapters
20Topics
8Sub-topics
50Flashcards

Mathematical Reasoning and Aptitude syllabus: all 5 chapters

Expand any chapter to see its topics and sub-topics.

  1. Number Series and Arithmetic

     4 topics
    • Number series and letter series
    • Codes and relationships
    • Ratio, proportion and percentages
    • Profit, loss, interest and time problems
      • Simple and compound interest
      • Time, speed and distance

  2. Logical Reasoning of Mathematical Type

     4 topics
    • Mathematical aptitude and fraction-based problems
    • Average, mean, median and mode
    • Permutation, combination and probability basics
    • Quantitative comparison problems

  3. Logical Reasoning

     4 topics
    • Understanding the structure of arguments
      • Argument forms and structure of categorical propositions
    • Mood and figure of syllogisms
    • Formal and informal fallacies
    • Uses of language and connotation-denotation

  4. Venn Diagrams and Analogies

     4 topics
    • Venn diagram as a tool of reasoning
    • Establishing relationships through diagrams
    • Analogies and classification
    • Evaluating and distinguishing deductive and inductive reasoning

  5. Indian Logic (Pramanas)

     4 topics
    • Means of knowledge (Pramanas)
      • Pratyaksha (perception)
      • Anumana (inference)
      • Upamana (comparison)
    • Shabda (verbal testimony)
    • Arthapatti (postulation) and Anupalabdhi (non-apprehension)
    • Structure and kinds of inference (Anumana)
      • Vyapti (invariable relation)
      • Hetvabhasa (fallacies)

UGC NET Mathematical Reasoning and Aptitude flashcards — 50 questions with answers

  1. In a number series, what is an arithmetic progression and how do you find the next term?

    An arithmetic progression (AP) has a constant difference between consecutive terms. Find the common difference d, then add it to the last term. nth term = a + (n-1)d.

  2. In a number series, what is a geometric progression and how do you find the next term?

    A geometric progression (GP) has a constant ratio between consecutive terms. Find the common ratio r, then multiply the last term by it. nth term = a x r^(n-1).

  3. What pattern governs the series 2, 6, 12, 20, 30, ...?

    The differences increase by 2 each time (4, 6, 8, 10). The terms follow n(n+1): 1x2, 2x3, 3x4, ... Next term is 42 (6x7).

  4. In letter series, what numeric values are assigned to letters for solving?

    Each letter is given its position in the alphabet: A=1, B=2, ..., Z=26. Patterns are found by tracking the gaps between positions.

  5. In a letter series, what comes next: A, C, E, G, ...?

    I. The pattern skips one letter each time (gap of +2 in position): A(1), C(3), E(5), G(7), I(9).

  6. How do you identify a Fibonacci-type number series?

    Each term equals the sum of the two preceding terms (e.g., 1, 1, 2, 3, 5, 8, 13). Check whether term n = term(n-1) + term(n-2).

  7. What is the EJOTY rule used for in coding-decoding?

    EJOTY gives quick letter positions: E=5, J=10, O=15, T=20, Y=25. It helps rapidly locate any letter's numeric position when decoding letter patterns.

  8. In letter coding, how is a letter usually encoded by a forward/backward shift?

    Each letter is replaced by another a fixed number of positions ahead or behind in the alphabet (e.g., +1: A->B, B->C). Reverse the shift to decode.

  9. In coding, if CAT is written as DBU, what is the coding rule?

    Each letter is shifted +1 position forward (C->D, A->B, T->U). To decode, shift each letter back by 1.

  10. What is the complementary (opposite) letter of a given letter, and how is it found?

    The opposite letter pairs with it summing to 27: position(letter) + position(opposite) = 27. E.g., A(1)<->Z(26), B(2)<->Y(25), M(13)<->N(14).

  11. In blood-relation coding, how do you interpret 'A + B' meaning 'A is the father of B'?

    Treat each symbol as a defined relationship and read the expression left to right, building the family chain. Symbols replace words like father, mother, sister, brother.

  12. What is the formula relating ratio to actual quantities when a:b is given with total T?

    First part = a/(a+b) x T; Second part = b/(a+b) x T. Divide the total in proportion to the ratio terms.

  13. What is a proportion and the key property of four numbers in proportion?

    A proportion states two ratios are equal: a:b = c:d. The product of the means equals the product of the extremes: b x c = a x d (cross multiplication).

  14. How do you convert a fraction or ratio to a percentage?

    Multiply by 100. Percentage = (value/total) x 100. E.g., 3/4 = 0.75 x 100 = 75%.

  15. What is the formula for percentage increase or decrease?

    Percentage change = ((New value - Old value)/Old value) x 100. A positive result is an increase; negative is a decrease.

  16. If a quantity increases by x% then decreases by x%, what is the net change?

    There is a net decrease of (x^2/100)%. Successive equal increase and decrease never cancel out exactly.

  17. What is the formula for the net effect of two successive percentage changes a% and b%?

    Net % change = a + b + (ab/100), using signs (negative for decrease).

  18. What are the formulas for profit, loss, and their percentages?

    Profit = SP - CP; Loss = CP - SP. Profit% = (Profit/CP) x 100; Loss% = (Loss/CP) x 100. All percentages are based on cost price.

  19. How do you find selling price from cost price and profit percentage?

    SP = CP x (100 + Profit%)/100. For a loss, SP = CP x (100 - Loss%)/100.

  20. What is the formula for simple interest?

    Simple Interest (SI) = (P x R x T)/100, where P = principal, R = rate per annum, T = time in years. Amount = P + SI.

Show the other 30 Mathematical Reasoning and Aptitude flashcards

  1. What is the formula for compound interest (annual compounding)?

    Amount = P(1 + R/100)^T; Compound Interest = Amount - P = P[(1 + R/100)^T - 1].

  2. How does the basic work-rate (time and work) relationship work?

    If a person completes a job in n days, their one-day work = 1/n. Combined rate of two workers = 1/a + 1/b, and time together = 1/(1/a + 1/b).

  3. What is the core speed-distance-time relationship and its rearrangements?

    Speed = Distance/Time; Distance = Speed x Time; Time = Distance/Speed.

  4. How do you find the discount and marked price relationship?

    Discount = Marked Price - Selling Price; Discount% = (Discount/Marked Price) x 100. SP = MP x (100 - Discount%)/100.

  5. How do you add or subtract fractions with different denominators?

    Find the least common denominator (LCD), convert each fraction to that denominator, then add or subtract the numerators while keeping the denominator.

  6. How do you multiply and divide fractions?

    Multiply: numerator x numerator over denominator x denominator. Divide: multiply the first fraction by the reciprocal of the second (flip and multiply).

  7. How do you convert a fraction to a decimal and vice versa?

    Fraction to decimal: divide numerator by denominator. Decimal to fraction: write digits over the place-value denominator (e.g., 0.25 = 25/100 = 1/4), then simplify.

  8. What is the formula for the average (arithmetic mean) of a set of numbers?

    Average = (Sum of all observations)/(Number of observations). Sum = Average x Number of observations.

  9. What is the median and how is it determined?

    The median is the middle value of ordered data. For an odd count, it's the middle value; for an even count, it's the average of the two middle values.

  10. What is the mode of a data set?

    The mode is the value that appears most frequently. A data set may have no mode, one mode (unimodal), or more than one mode (bimodal/multimodal).

  11. What is the empirical relationship between mean, median, and mode?

    Mode = 3 x Median - 2 x Mean (approximate relationship for moderately skewed distributions).

  12. How does the average change when a new observation is added to a set?

    New average = (Old sum + new value)/(Old count + 1). Adding a value above the old average raises it; below lowers it.

  13. What is the formula for permutations of n objects taken r at a time?

    nPr = n!/(n-r)!. Permutations count ordered arrangements where order matters.

  14. What is the formula for combinations of n objects taken r at a time?

    nCr = n!/(r!(n-r)!). Combinations count selections where order does not matter.

  15. What is the key difference between a permutation and a combination?

    Permutation counts arrangements where order matters (e.g., rankings, passwords); combination counts selections where order does not matter (e.g., teams, committees).

  16. What is the classical formula for the probability of an event?

    P(E) = (Number of favorable outcomes)/(Total number of possible outcomes). Probability ranges from 0 (impossible) to 1 (certain).

  17. What is the probability of the complement of an event E?

    P(not E) = 1 - P(E). The probabilities of an event and its complement always sum to 1.

  18. What is the addition rule of probability for two events?

    P(A or B) = P(A) + P(B) - P(A and B). For mutually exclusive events, P(A and B) = 0, so P(A or B) = P(A) + P(B).

  19. What is the multiplication rule for independent events?

    For independent events, P(A and B) = P(A) x P(B). Independence means one event's occurrence does not affect the other's probability.

  20. How do you solve a quantitative comparison problem comparing two quantities?

    Compare Quantity A and Quantity B, deciding if A>B, B>A, they are equal, or the relationship cannot be determined. Simplify both, test boundary/extreme values, and avoid assumptions.

  21. What are the essential components of the structure of an argument?

    An argument consists of premises (supporting statements/reasons) and a conclusion (the claim the premises are meant to support). Indicators like 'therefore' signal conclusions; 'because' signals premises.

  22. What is the difference between deductive and inductive arguments?

    In a deductive argument, the conclusion necessarily follows from the premises (valid/invalid). In an inductive argument, premises make the conclusion probable, not certain (strong/weak).

  23. What does it mean for a deductive argument to be valid versus sound?

    Valid: if the premises are true, the conclusion must be true (correct logical form). Sound: the argument is valid AND all its premises are actually true.

  24. What are the four standard categorical (A, E, I, O) propositions in syllogisms?

    A = universal affirmative (All S are P); E = universal negative (No S is P); I = particular affirmative (Some S are P); O = particular negative (Some S are not P).

  25. What is the 'mood' of a categorical syllogism?

    The mood is the sequence of the types (A, E, I, O) of its two premises and conclusion (e.g., AAA, EIO). It identifies the proposition types in order.

  26. What is the 'figure' of a categorical syllogism?

    The figure is determined by the position of the middle term in the two premises. There are four figures based on whether the middle term is subject or predicate in each premise.

  27. What distinguishes a formal fallacy from an informal fallacy?

    A formal fallacy is an error in the logical structure/form of an argument (invalid form regardless of content). An informal fallacy is an error in content, language, or relevance rather than form.

  28. What is the fallacy of 'ad hominem'?

    An informal fallacy that attacks the person making an argument rather than addressing the argument itself, irrelevantly using personal characteristics to reject a claim.

  29. What is the fallacy of 'affirming the consequent'?

    A formal fallacy: from 'If P then Q' and 'Q', wrongly concluding 'P'. The truth of the consequent does not establish the antecedent.

  30. What is the difference between denotation and connotation of a word?

    Denotation is a word's literal, dictionary meaning. Connotation is the emotional, cultural, or implied association a word carries beyond its literal meaning (e.g., 'home' denotes a dwelling but connotes warmth).

UGC NET Mathematical Reasoning and Aptitude FAQ

What is in the UGC NET Mathematical Reasoning and Aptitude syllabus?

UGC NET Mathematical Reasoning and Aptitude is split into 5 chapters: Number Series and Arithmetic, Logical Reasoning of Mathematical Type, Logical Reasoning, Venn Diagrams and Analogies and Indian Logic (Pramanas). Together they contain 20 topics and 8 sub-topics.

How many chapters are in UGC NET Mathematical Reasoning and Aptitude?

5 chapters, containing 20 topics and 8 sub-topics. The largest chapter is Number Series and Arithmetic, with 4 topics.

Are there flashcards for UGC NET Mathematical Reasoning and Aptitude?

Yes — a 50-card Mathematical Reasoning and Aptitude deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.