AIIMS NORCET General Aptitude Syllabus

In algebra, what is the identity for (a + b)²?

(a + b)² = a² + 2ab + b².

What is the algebraic identity for (a − b)²?

(a − b)² = a² − 2ab + b².

What is the identity for a² − b²?

a² − b² = (a + b)(a − b).

What is the expansion of (a + b)³?

(a + b)³ = a³ + 3a²b + 3ab² + b³ = a³ + b³ + 3ab(a + b).

What is the identity for a³ + b³?

a³ + b³ = (a + b)(a² − ab + b²).

What is the identity for a³ − b³?

a³ − b³ = (a − b)(a² + ab + b²).

What is the quadratic formula for solving ax² + bx + c = 0?

x = [−b ± √(b² − 4ac)] / 2a, where (b² − 4ac) is the discriminant.

What does the discriminant of a quadratic equation tell you about its roots?

If b²−4ac > 0, roots are real and distinct; if = 0, roots are real and equal; if < 0, roots are imaginary (complex).

For a quadratic ax² + bx + c = 0, what are the sum and product of the roots?

Sum of roots = −b/a; Product of roots = c/a.

What is the identity for (a + b + c)²?

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.

In analogy reasoning, what is the basic approach to solve 'A : B :: C : ?'

Identify the relationship between A and B, then apply the same relationship to C to find the missing term. Example: Hand : Glove :: Foot : Sock.

Give an example of a 'tool and worker' analogy relationship.

Doctor : Stethoscope :: Carpenter : Hammer — each pairs a worker with the tool they use.

What type of analogy is 'Hot : Cold :: Big : Small'?

An opposite (antonym) analogy, where each pair consists of words with opposite meanings.

What relationship defines the analogy 'CAT : ANIMAL :: ROSE : ?'

A 'category/classification' relationship — the answer is FLOWER, because a cat is a type of animal and a rose is a type of flower.

In a number series, how do you identify an arithmetic progression?

In an arithmetic progression the difference between consecutive terms is constant (common difference d). Example: 2, 5, 8, 11 (d = 3).

What is the nth term of an arithmetic progression?

nth term = a + (n − 1)d, where a is the first term and d is the common difference.

What is the nth term of a geometric progression?

nth term = a × r^(n−1), where a is the first term and r is the common ratio.

Identify the pattern: 1, 4, 9, 16, 25, ...

These are perfect squares of consecutive natural numbers (1², 2², 3², 4², 5²); the next term is 36.

Identify the pattern: 2, 6, 12, 20, 30, ...

The differences increase by 2 (4, 6, 8, 10); equivalently n(n+1): 1×2, 2×3, 3×4...; the next term is 42.

What is the Fibonacci series and its rule?

The Fibonacci series is 0, 1, 1, 2, 3, 5, 8, 13, ... where each term is the sum of the two preceding terms.

In puzzle solving (seating arrangement), what does 'facing the centre' imply for left and right?

When people face the centre of a circle, their left and right are opposite to the observer's; the left of a person is in the clockwise direction and right is counter-clockwise.

In blood relation puzzles, who is 'the son of my father's only son' to me?

My father's only son is myself, so 'the son of my father's only son' is my own son.

What is the systematic method to solve a logical puzzle with multiple conditions?

Create a grid/table listing all variables, fill in definite clues first, eliminate impossible options using each condition, then deduce the remaining placements.

In direction-sense puzzles, if you face North and turn 90° clockwise, which direction do you face?

East. (North → East → South → West for each successive 90° clockwise turn.)

What is a bar graph and what is it best used for?

A bar graph uses rectangular bars of lengths proportional to the values they represent; it is best for comparing quantities across discrete categories.

In a bar graph, how do you read the value represented by a bar?

Match the top (height) of the bar to the value on the measured axis (usually the vertical/Y-axis) using the scale provided.

What is the key difference between a bar graph and a histogram?

A bar graph compares discrete categories with gaps between bars; a histogram shows the frequency distribution of continuous data with no gaps between bars.

In a pie chart, how many degrees does the whole circle represent and how is each sector's angle found?

The whole circle is 360°. Each sector's angle = (Value of category / Total value) × 360°.

In a pie chart, how do you convert a sector angle into a percentage?

Percentage = (Sector angle / 360°) × 100. For example, a 90° sector represents 25%.

What is a key advantage of a table over a graph for presenting data?

A table presents exact numerical values in rows and columns, allowing precise reading and easy cross-comparison, whereas graphs show trends and comparisons visually but approximately.