CSIR NET Mathematical Science Part A Syllabus

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'.

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.

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

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

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

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

Find the next term: 2, 6, 12, 20, 30, ? and state the pattern.

$42$. The terms are $n(n+1)$: $1\cdot2, 2\cdot3, 3\cdot4, 4\cdot5, 5\cdot6, 6\cdot7=42$. Differences increase by 2.

Identify the pattern and next term: 1, 4, 9, 16, 25, ?

$36$. These are perfect squares $n^{2}$, so the next is $6^{2}=36$.

Identify the next term in the Fibonacci-type series: 1, 1, 2, 3, 5, 8, ?

$13$. Each term is the sum of the two preceding terms: $5+8=13$.

In blood-relationship problems, what relation is 'my father's only son'?

It refers to the speaker himself (the man speaking), since the father's only son is the speaker.

In blood relations, who is 'the mother of my father's mother' to me?

She is the speaker's great-grandmother (mother of the paternal grandmother).

What does the term 'maternal' versus 'paternal' indicate in family-relationship problems?

Paternal relations come from the father's side of the family; maternal relations come from the mother's side. E.g. maternal uncle = mother's brother.

In seating/arrangement problems, what is the difference between a linear and a circular arrangement?

Linear: people sit in a row, all facing one direction with two ends. Circular: people sit around a table; left/right depend on facing center or outward, and there are no ends.

For $n$ people seated around a circular table, how many distinct circular arrangements are possible?

$$(n-1)!$$ because rotations are considered identical (one position is fixed as reference).

In a circular arrangement where all members face the center, how do left and right relate to a clockwise direction?

When facing the center, a person's right hand points clockwise and left hand points anticlockwise (opposite to when facing outward).

In 'Statements and Conclusions' problems, what must a valid conclusion satisfy?

It must follow logically and necessarily from the given statements alone, without relying on outside assumptions or general knowledge.

In 'Statement and Assumptions', what is an implicit assumption?

Something taken for granted or presupposed in making the statement; it is an unstated idea that must be true for the statement to hold.

What is the purpose of a Data Sufficiency question?

To determine whether the information in the given statements is sufficient to answer a question, rather than to compute the actual answer.

State the standard answer options for a two-statement Data Sufficiency question.

(A) Statement 1 alone sufficient, 2 not; (B) Statement 2 alone sufficient, 1 not; (C) Both together sufficient, neither alone; (D) Each alone sufficient; (E) Both together still insufficient.

In Data Sufficiency, why must each statement first be evaluated independently?

To avoid carrying information from one statement into the other; each must be judged on its own before testing them combined, so you correctly distinguish options A/B/D from C/E.

What is non-verbal reasoning?

Reasoning based on visual/figural information—shapes, patterns, and diagrams—rather than words or numbers; it tests pattern recognition, spatial logic, and figure manipulation.

In non-verbal series, name three common transformations applied to figures.

Rotation (turning by an angle), reflection (mirror image), and addition/deletion or movement of elements within the figure.

What is a mirror image in visual-ability problems, and along which axis is a vertical mirror placed?

A mirror image is the left-right reversed reflection of a figure. A vertical mirror placed to the side reverses left and right while keeping top and bottom fixed.

What is a water image in visual reasoning?

The reflection of a figure as seen in water—an inverted (top-bottom flipped) image about a horizontal axis, keeping left and right unchanged.

In paper-folding/punching (visual ability), what symmetry governs the holes when paper is folded once and punched?

The punched holes appear symmetrically about each fold line when unfolded; one punch through a single fold produces two symmetric holes (doubling per fold).

In graphical analysis, what does the slope of a straight line on a graph represent?

The rate of change of the y-variable with respect to the x-variable: $$\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$

What does the area under a curve typically represent in graphical/data analysis of a rate vs. time graph?

The accumulated total quantity; e.g. the area under a speed-time graph gives the distance travelled, computed as $\int v\, dt$.

In data analysis, how do you compute the percentage change between an old value and a new value?

$$\%\text{ change} = \frac{\text{New} - \text{Old}}{\text{Old}} \times 100$$

In a pie chart used for data analysis, how many degrees correspond to a given percentage of the total?

Each percent equals $3.6^{\circ}$, since $\frac{360^{\circ}}{100} = 3.6^{\circ}$. So a sector of $p\%$ subtends $3.6p$ degrees at the centre.

State the formulas for arithmetic mean, and for the median of an ordered data set of $n$ values.

Mean: $\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_{i}$. Median: the middle value; if $n$ is odd it is the $\frac{n+1}{2}$th value, if $n$ is even it is the average of the $\frac{n}{2}$th and $\frac{n}{2}+1$th values.

In simplification, what is the BODMAS/PEMDAS order of operations?

Brackets, Orders (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right). Equivalent to PEMDAS: Parentheses, Exponents, Multiply/Divide, Add/Subtract.

Simplify using order of operations: $6 + 2 \times (3^{2} - 4) \div 5$.

$8$. Compute brackets: $3^{2}-4 = 5$; then $2 \times 5 = 10$; then $10 \div 5 = 2$; then $6 + 2 = 8$.