CSIR NET Mathematical Science Part A Syllabus

Part A syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Part A in CSIR NET Mathematical Science, not a summary of it.

1. 1

   Analytical Reasoning

   14 topics

   • Syllogisms
   • Analogies
   • Directions
   • Coding-Decoding
   • Classification
   • Alphabet Series
   • Symbols and Notations
   • Similarities and Differences
   • Number Series
   • Blood Relationships
   • Arrangements
   • Statements
   • Data Sufficiency
   • Non-verbal Reasoning
     • Visual Ability
     • Graphical Analysis
     • Data Analysis
2. 2

   Quantitative Aptitude

   13 topics

   • Simplifications
   • Number System
   • Average
   • Algebra
   • PercentageTime & Work
   • Simple & Compound Interest
   • Time & Speed
   • HCF, LCM Problems
   • Area
   • Profit & Loss
   • Bar Graph, Pictorial Graph, Pie Chart
   • Ratio & Proportion
   • Permutation & Combination
3. 3

   Data Interpretation & Graphical Analysis

   5 topics

   • Mean
   • Median
   • Mode
   • Measures of Dispersion
   • Graphical Analysis
     • Bar Graph
     • Line Graph
     • Pie-Chart
     • Tabulation

Part A flashcards for CSIR NET Mathematical Science

24 of 50 cards from the Part A deck — real questions with worked answers.

1. In logical reasoning, what is a syllogism?

   A form of deductive reasoning consisting of two premises (a major and a minor statement) from which a logically necessary conclusion is drawn. Example: All A are B; All B are C; therefore All A are C.

2. In syllogism problems, what does the 'possibility' rule allow you to conclude from the statements 'Some A are B' and 'Some B are C'?

   Nothing definite can be concluded; no relation between A and C is established. Only possibility conclusions (e.g. 'Some A may be C') hold, never a definite one.

3. State the four standard categorical (proposition) types used in syllogisms.

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

4. What is the rule for distributing the negative term in syllogisms (conversion of 'No A is B')?

   'No A is B' converts to a valid definite conclusion 'No B is A' (E-type converts to E). Both terms are distributed, so the negative relation is symmetric.

5. In a verbal analogy, what is the core task the solver must identify?

   The specific relationship (logical, functional, causal, part-whole, etc.) between the first pair, then apply the identical relationship to complete the second pair.

6. Identify the relationship type in the analogy: Doctor : Hospital :: Teacher : ____

   Worker-to-workplace relationship; the answer is School.

7. In a number analogy such as $7 : 49 :: 9 : ?$, what is the answer and the relationship?

   $81$. The relationship is squaring: $7^{2}=49$ and $9^{2}=81$.

8. In direction-sense problems, what are the four cardinal and four ordinal (intercardinal) directions?

   Cardinal: North, South, East, West. Ordinal: North-East, North-West, South-East, South-West (each at $45^{\circ}$ between two cardinals).

9. In a direction test, if you face North and turn $90^{\circ}$ clockwise, then $180^{\circ}$, which direction do you finally face?

   Turning $90^{\circ}$ clockwise from North gives East; a further $180^{\circ}$ turn gives West.

10. What formula gives the shortest distance between start and end points after movements forming a right angle?

    The Pythagorean theorem: if horizontal displacement is $a$ and vertical is $b$, the shortest distance is $d=\sqrt{a^{2}+b^{2}}$.

11. What is coding-decoding in reasoning, and name the common types.

    Encrypting a word/message by a rule and decoding it back. Common types: letter coding, number coding, substitution coding, symbol coding, and matrix/conditional coding.

12. In letter-shift coding, if 'CAT' is coded as 'DBU', what is the rule and how would 'DOG' be coded?

    Each letter is shifted $+1$ in the alphabet. So 'DOG' becomes 'EPH'.

13. What is the positional value of letters A through Z, and the reverse (opposite) value of a letter?

    A=1, B=2, ..., Z=26 forward. The opposite value is given by $27 - (\text{forward position})$; e.g. A's opposite is Z (=26), since $27-1=26$.

14. In classification (odd-one-out) problems, what is the objective?

    To identify the one item in a group that does not share the common property/category that all the others possess.

15. Find the odd one out: 3, 5, 11, 14, 17, 23. What is it and why?

    $14$. All the others are prime numbers, but $14 = 2 \times 7$ is composite.

16. In an alphabet series, what is the standard forward gap pattern called when letters skip by a fixed number?

    An arithmetic letter series, where each term advances by a constant number of positions (e.g. +2: A, C, E, G, ...).

17. Complete the alphabet series: B, D, G, K, P, ? (state the pattern).

    $V$. The gaps increase by one each step: $+2, +3, +4, +5, +6$. From P (16) add 6 to reach 22 = V.

18. What is the middle letter of the English alphabet, and how is it found?

    There is no single middle letter for 26 letters; the two central letters are the 13th and 14th, M and N. (The midpoint between positions is $13.5$.)

19. In 'Symbols and Notations' problems, what does it mean when symbols are redefined (e.g. $+$ means $\times$)?

    You must substitute the redefined operations and then evaluate following the standard order of operations (BODMAS/PEMDAS) with the new meanings.

20. Using the substitution where $+$ means $\div$, $-$ means $\times$, $\times$ means $+$, $\div$ means $-$, evaluate $12 + 6 - 2$.

    Substitute: $12 \div 6 \times 2 = 2 \times 2 = 4$.

21. In notation problems, what is the meaning of inequality symbols $a \geq b$ and $a \leq b$?

    $a \geq b$ means 'a is greater than or equal to b'; $a \leq b$ means 'a is less than or equal to b'.

22. In 'Similarities and Differences' reasoning, what distinguishes the two tasks?

    Similarity = finding the common shared property/relationship among items; Difference = isolating the distinguishing feature that sets one item apart from the rest.

23. What is the general term formula for an arithmetic number series with first term $a$ and common difference $d$?

    $$a_{n} = a + (n-1)d$$

24. What is the general term formula for a geometric number series with first term $a$ and common ratio $r$?

    $$a_{n} = a \cdot r^{\,n-1}$$

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