GATE General Aptitude (GA) Syllabus

Identify and correct the error: 'The committee are divided in its opinion.'

Inconsistent treatment of the collective noun. Either treat 'committee' as singular ('The committee is divided in its opinion') or consistently plural ('The committee are divided in their opinions').

What is a verbal analogy, and how should it be solved?

A verbal analogy presents a pair of words with a logical relationship (A:B) and asks for a matching pair (C:D). Solve it by stating the relationship in a clear sentence (e.g., 'A is a part of B') and applying the same relationship to find D.

In the analogy 'Hand : Glove :: Foot : ?', what is the answer and the relationship?

Answer: Sock (or shoe). Relationship: the second item is the covering worn on the first body part.

What is the relationship type in the analogy 'Hammer : Tool :: Rose : Flower'?

It is a 'type/class' (specific-to-general or member-to-category) relationship: a hammer is a kind of tool, just as a rose is a kind of flower.

What is narrative sequencing in reading comprehension?

Arranging a set of jumbled sentences into a logical, coherent order (para-jumble) using cues such as chronological order, cause-and-effect links, pronoun references, and connecting words to reconstruct the original passage.

What are effective strategies for answering reading-comprehension questions?

Read the passage for the main idea first, identify the author's tone and purpose, locate specific details by scanning, distinguish stated facts from inferences, and avoid answers based on outside knowledge not supported by the text.

How do you convert a fraction to a percentage and a percentage to a decimal?

To convert a fraction to a percentage, multiply by 100: $\frac{a}{b}\times 100\%$. To convert a percentage to a decimal, divide by 100: e.g., $45\% = 0.45$.

What is the formula for percentage increase and percentage decrease?

$\text{Percentage change} = \frac{\text{New value} - \text{Old value}}{\text{Old value}} \times 100\%$. A positive result is an increase; a negative result is a decrease.

If a quantity is increased by $x\%$ and then decreased by $x\%$, what is the net effect?

There is a net decrease of $\frac{x^{2}}{100}\%$. For example, a $10\%$ increase followed by a $10\%$ decrease gives a net decrease of $1\%$.

What is the relationship between a ratio and a proportion?

A ratio $a:b$ compares two quantities by division. A proportion states that two ratios are equal: $\frac{a}{b} = \frac{c}{d}$, which gives the cross-multiplication rule $a \cdot d = b \cdot c$.

If $a:b = 2:3$ and $b:c = 4:5$, what is $a:b:c$?

Make $b$ common: scale the first ratio by 4 and the second by 3 so $b=12$ in both. Then $a:b:c = 8:12:15$.

State the three fundamental laws of exponents for multiplication, division, and powers.

$a^{m}\cdot a^{n} = a^{m+n}$, $\dfrac{a^{m}}{a^{n}} = a^{m-n}$, and $(a^{m})^{n} = a^{mn}$.

What is the value of any nonzero number raised to the power zero, and what does a negative exponent mean?

$a^{0} = 1$ for any $a \neq 0$. A negative exponent denotes a reciprocal: $a^{-n} = \dfrac{1}{a^{n}}$.

What is a surd, and what does it mean to rationalize a denominator?

A surd is an irrational root that cannot be simplified to a rational number, such as $\sqrt{2}$ or $\sqrt[3]{5}$. Rationalizing the denominator means removing the surd from the denominator, e.g., $\dfrac{1}{\sqrt{2}} = \dfrac{\sqrt{2}}{2}$.

How do you rationalize $\dfrac{1}{\sqrt{a}-\sqrt{b}}$?

Multiply numerator and denominator by the conjugate $\sqrt{a}+\sqrt{b}$: $$\frac{1}{\sqrt{a}-\sqrt{b}} = \frac{\sqrt{a}+\sqrt{b}}{a-b}.$$

Express $a^{m/n}$ in radical (surd) form.

$a^{m/n} = \sqrt[n]{a^{m}} = \left(\sqrt[n]{a}\right)^{m}$.

What is the fractional-exponent rule for a root of a power, e.g., $\sqrt[3]{x^{2}}$?

$\sqrt[3]{x^{2}} = x^{2/3}$. In general, $\sqrt[n]{x^{m}} = x^{m/n}$.

What is estimation, and why is it useful in numerical computation?

Estimation is approximating a numerical answer by rounding values to convenient figures to get a quick, close result. It is useful for checking the plausibility of exact answers and for eliminating wrong options quickly in aptitude tests.

Find the next term in the arithmetic series: $3, 7, 11, 15, \ldots$

$19$. It is an arithmetic series with common difference $d = 4$, so each term is the previous term plus 4.

What is the formula for the $n$th term of an arithmetic progression?

$a_{n} = a_{1} + (n-1)d$, where $a_{1}$ is the first term and $d$ is the common difference.

What is the formula for the sum of the first $n$ terms of an arithmetic progression?

$S_{n} = \dfrac{n}{2}\left(2a_{1} + (n-1)d\right) = \dfrac{n}{2}\left(a_{1} + a_{n}\right)$.

What is the formula for the $n$th term of a geometric progression?

$a_{n} = a_{1}\, r^{\,n-1}$, where $a_{1}$ is the first term and $r$ is the common ratio.

Find the next term in the geometric series: $2, 6, 18, 54, \ldots$

$162$. It is a geometric series with common ratio $r = 3$, so each term is the previous term multiplied by 3.

Identify the pattern and next term: $1, 4, 9, 16, 25, \ldots$

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

Identify the pattern and next term: $2, 3, 5, 7, 11, 13, \ldots$

$17$. The series lists consecutive prime numbers, so the next prime after 13 is 17.

Identify the pattern and next term in the Fibonacci-type series: $1, 1, 2, 3, 5, 8, \ldots$

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

What is the formula for the sum of an infinite geometric series, and when does it apply?

$S_{\infty} = \dfrac{a_{1}}{1-r}$, valid only when $|r| < 1$ (the series converges).

In number-series reasoning, what is an 'alternating' series? Give an example.

An alternating series interleaves two independent patterns in odd and even positions. Example: $2, 5, 4, 10, 6, 15, \ldots$ where odd positions go $2,4,6,\ldots$ and even positions go $5,10,15,\ldots$; the next term is $8$.

What is the difference between 'fewer' and 'less', and when is each used?

Use 'fewer' for countable nouns (fewer apples, fewer mistakes) and 'less' for uncountable/mass nouns (less water, less time).

What is the rule for using 'who' vs. 'whom'?

Use 'who' as the subject of a verb ('Who called?') and 'whom' as the object of a verb or preposition ('To whom did you speak?'). Test: if you can replace it with 'he/she', use 'who'; if with 'him/her', use 'whom'.

What is the past tense and past participle of the irregular verbs 'lie' (to recline) and 'lay' (to place)?

'Lie' (recline): lie / lay / lain. 'Lay' (place something): lay / laid / laid. Note the overlap: 'lay' is both the present of the transitive verb and the past tense of the intransitive 'lie'.