UGC NET Mathematical Reasoning and Aptitude Syllabus

Mathematical Reasoning and Aptitude syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematical Reasoning and Aptitude in UGC NET, not a summary of it.

1. 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. 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. 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. 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. 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)

Mathematical Reasoning and Aptitude flashcards for UGC NET

21 of 50 cards from the Mathematical Reasoning and Aptitude deck — real questions with worked 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.

21. 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].

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