CSS General Science and Ability General Ability Syllabus

What is the formula for the volume of a cylinder?

V = πr^2 h, where r = radius of the base and h = height.

What is the formula for the volume of a sphere?

V = (4/3)πr^3, where r is the radius.

Define complementary and supplementary angles.

Complementary angles add up to 90°; supplementary angles add up to 180°.

In statistics, define mean, median, and mode.

Mean = average (sum/count); Median = middle value when data is ordered; Mode = the most frequently occurring value.

What is the range of a data set, and how is it calculated?

The range is a measure of spread equal to the maximum value minus the minimum value.

Define standard deviation in basic statistics.

A measure of how spread out the data is from the mean; it is the square root of the variance (the average of the squared deviations from the mean).

What is random sampling, and why is it used?

A sampling method where every member of the population has an equal chance of being selected. It reduces bias and makes the sample representative of the population.

Distinguish between a population and a sample.

A population is the entire set of items/individuals under study; a sample is a smaller subset drawn from the population to make inferences about it.

What is the difference between deductive and inductive reasoning?

Deductive reasoning moves from general premises to a specific, certain conclusion (top-down). Inductive reasoning moves from specific observations to a general, probable conclusion (bottom-up).

What is a syllogism in deductive reasoning?

A logical argument with two premises and a conclusion, e.g., 'All A are B; All B are C; therefore all A are C.'

In a number series, identify the next term: 2, 6, 12, 20, 30, ?

42. The differences increase by 2 each time (4, 6, 8, 10, 12); 30 + 12 = 42. (Pattern: n(n+1).)

What is the rule for a geometric (multiplicative) number series, and give an example?

Each term is multiplied by a constant ratio. Example: 3, 6, 12, 24, 48 (each term × 2).

In letter series, what is the next letter: A, C, E, G, ?

I. The series skips one letter each time (gap of 2 positions in the alphabet).

What is coding-decoding in reasoning tests?

A technique where letters/numbers are substituted by other letters/numbers/symbols by a rule; you must decode the rule to translate a new word or message.

If in a code language CAT is written as DBU, what is the coding rule?

Each letter is shifted forward by one position in the alphabet (+1): C→D, A→B, T→U.

What is the alphabet position trick used in coding-decoding (EJOTY)?

E=5, J=10, O=15, T=20, Y=25 — memorized reference points to quickly find any letter's position in the alphabet.

What is meant by 'problem visualization' in general ability tests?

The ability to mentally picture and manipulate a problem (figures, arrangements, or spatial relationships) to understand its structure and arrive at a solution.

In logical deduction from given information, what is the key approach?

Treat the given statements as true regardless of real-world facts, then derive only conclusions that necessarily follow from those statements.

In a circular seating arrangement, how do directions (left/right) work when people face the centre?

When all face the centre, a person's left is the clockwise direction and their right is the anticlockwise direction (opposite to facing outward).

What is the first step in solving a seating arrangement puzzle?

Identify fixed/definite clues first (absolute positions), place those, then use the conditional clues to fill remaining positions.

In cause-and-effect reasoning, what is the difference between a cause and an effect?

A cause is the event/factor that produces a result; the effect is the result or consequence that follows from the cause. The cause precedes the effect in time.

What does 'decision making' assessment in general ability typically evaluate?

The ability to choose the best course of action from alternatives by analyzing given conditions, criteria, and consequences logically.

In verbal ability, define synonyms and antonyms.

Synonyms are words with the same or similar meaning (e.g., big/large); antonyms are words with opposite meanings (e.g., hot/cold).

What is an analogy in verbal ability tests?

A relationship between a pair of words that must be matched by another pair, e.g., 'Hand : Glove :: Foot : Sock' (item to its covering).

What is a homophone? Give an example.

Words that sound the same but differ in spelling and meaning, e.g., 'their / there / they're' or 'to / too / two'.

What does numerical ability primarily test?

The ability to work quickly and accurately with numbers — arithmetic operations, percentages, ratios, fractions, and basic data interpretation.

What does mechanical ability (mechanical reasoning) assess?

Understanding of physical and mechanical principles — levers, pulleys, gears, forces, and how simple machines and tools work.

In a system of gears, how does the direction of rotation of two meshed gears compare?

Two directly meshed (interlocking) gears rotate in opposite directions; a smaller gear turns faster than a larger one it meshes with.

What is the principle of a lever, and what gives mechanical advantage?

A lever pivots on a fulcrum; load and effort balance per the law of the lever (effort × effort arm = load × load arm). A longer effort arm relative to the load arm gives greater mechanical advantage.

What does 'social ability' assess in a general ability context?

The capacity to understand social situations, interpersonal relationships, etiquette, cooperation, and appropriate behaviour/judgement in dealings with people.