Graduate Aptitude Test in Engineering (GATE) — Questions and Answers

Question 1: A network uses Go-Back-N ARQ with a window size of 4. If frame 3 is lost, which frames must be retransmitted?

Frames 3, 4, 5, and 6 (Correct answer)
Frames 3 and 4
Only frame 3
All frames from 3 onward up to window

Correct answer: Frames 3, 4, 5, and 6

In Go-Back-N, when frame 3 is lost, the receiver discards all subsequent frames; the sender must retransmit frame 3 and all frames sent after it within the window.

Question 2: The rank of a matrix A is defined as:

The trace of A
The number of rows in A
The maximum number of linearly independent rows (or columns) (Correct answer)
The determinant of A

Correct answer: The maximum number of linearly independent rows (or columns)

Rank is the dimension of the column space (or row space) of a matrix, equal to the max number of linearly independent rows or columns.

Question 3: What is the key difference between a process and a thread?

Threads cannot run concurrently; processes can
Threads have their own address space; processes share one
Processes have their own address space; threads share it within a process (Correct answer)
Processes are lighter weight than threads

Correct answer: Processes have their own address space; threads share it within a process

Each process has its own independent address space, while threads within a process share the same address space and resources.

Question 4: A factory produces items in batches. In the first batch, 5% are defective. If 1000 items are inspected and defectives are removed, how many non-defective items remain?

975
900
950 (Correct answer)
990

Correct answer: 950

5% of 1000 = 50 defective items, so 1000 - 50 = 950 non-defective items remain.

Question 5: In the method of least squares for curve fitting, the objective is to minimize:

The sum of squared residuals (Correct answer)
The maximum residual
The sum of absolute residuals
The sum of residuals

Correct answer: The sum of squared residuals

Least squares minimizes Σ(yᵢ - ŷᵢ)², the sum of squared differences between observed and fitted values.

Question 6: Select the correct mirror image of the word 'GATE' if the mirror is placed vertically to its right.

ƐTAƎ
GATE
ETAG (Correct answer)
3TAD

Correct answer: ETAG

A vertical mirror reverses the order of letters, producing ETAG (letters themselves are also flipped, but in text representation the reverse order is ETAG).

Question 7: The inverse Fourier transform of a rectangular pulse in the frequency domain produces which time-domain signal?

An exponential decay
A sinc function (Correct answer)
Another rectangular pulse
A Gaussian function

Correct answer: A sinc function

A rectangular pulse in the frequency domain transforms to a sinc function (sin(πt)/(πt)) in the time domain.

Question 8: In the Banker's algorithm, a state is considered safe if:

There exists a sequence in which all processes can complete (Correct answer)
The total allocated resources equal total available resources
No process is in the waiting state
All processes can be allocated their maximum resources immediately

Correct answer: There exists a sequence in which all processes can complete

A safe state has at least one safe sequence where every process can eventually obtain its maximum needed resources and finish.

Question 9: In the context of file systems, what does inode contain?

File name and directory path
File metadata and pointers to data blocks (Correct answer)
File content only
User and group permissions only

Correct answer: File metadata and pointers to data blocks

An inode stores file metadata (size, permissions, timestamps) and pointers to the actual data blocks on disk, but not the filename.

Question 10: In a class, 40% students passed in Math, 50% in English, and 20% passed in both. What percentage failed in both?

30% (Correct answer)
20%
10%
70%

Correct answer: 30%

Passed in at least one = 40+50−20 = 70%; failed in both = 100−70 = 30%.

Question 11: In a synchronous counter, all flip-flops are clocked:

Asynchronously
Simultaneously (Correct answer)
Sequentially with delays
By the output of the previous stage

Correct answer: Simultaneously

In a synchronous counter, all flip-flops share the same clock signal and trigger simultaneously.

Question 12: In probability, what does a cumulative distribution function (CDF) represent?

Probability density
Probability mass
Mean of a distribution
Cumulative probability up to a value (Correct answer)

Correct answer: Cumulative probability up to a value

In probability theory, a cumulative distribution function (CDF) represents the probability that a random variable X will take a value less than or equal to a specific value x. It essentially accumulates the probabilities from the lowest possible value up to x. The CDF provides a comprehensive view of the probability distribution, showing the likelihood of observing values within a certain range.

Question 13: Which scheduling algorithm can lead to starvation?

Priority Scheduling (Correct answer)
Shortest Job First (non-preemptive)
FCFS
Round Robin

Correct answer: Priority Scheduling

Priority Scheduling can starve low-priority processes if high-priority processes continuously arrive.

Question 14: The pumping lemma for regular languages states that for any sufficiently long string w in a regular language, w can be split into xyz such that:

|y| ≤ p and xy^i z ∈ L only for i = 1
|xy| ≤ p and |y| > 0 and xy^i z ∈ L for all i ≥ 1
|xy| ≤ p and |y| > 0 and xy^i z ∈ L for all i ≥ 0 (Correct answer)
|xz| ≤ p and |y| > 0 and xy^i z ∈ L for all i ≥ 0

Correct answer: |xy| ≤ p and |y| > 0 and xy^i z ∈ L for all i ≥ 0

The pumping lemma requires |xy| ≤ p, |y| ≥ 1, and that pumping y any number of times (including zero) keeps the string in the language.

Question 15: Which of the following is an example of a semiconductor material?

Aluminum
Iron
Silicon (Correct answer)
Copper

Correct answer: Silicon

Silicon is a prime example of a semiconductor material, meaning its electrical conductivity lies between that of a good conductor (like copper) and an insulator (like glass). Its unique electronic properties allow its conductivity to be precisely controlled through doping, making it indispensable for manufacturing transistors, integrated circuits, and nearly all modern electronic devices. This makes silicon the backbone of the digital age.

Question 16: Which of the following regular expressions matches all binary strings that contain at least one '1'?

1*
0*
(0+1)*1(0+1)* (Correct answer)
0*10*

Correct answer: (0+1)*1(0+1)*

The expression (0+1)*1(0+1)* matches any binary string that has at least one '1' anywhere in it.

Question 17: In SQL, what does the COALESCE(a, b, c) function return?

The first non-NULL value among a, b, c (Correct answer)
The concatenation of a, b, and c
The sum of a, b, and c ignoring NULLs
NULL if any argument is NULL

Correct answer: The first non-NULL value among a, b, c

COALESCE returns the first non-NULL argument from its list, or NULL if all arguments are NULL.

Question 18: What role does ethics play in Signal Processing practice?

Ethics is optional in professional settings
It only applies to managers
It only matters for legal compliance
It guides professional conduct and protects stakeholders (Correct answer)

Correct answer: It guides professional conduct and protects stakeholders

Professional ethics provide frameworks for responsible decision-making, ensuring practitioners act in the best interest of those they serve.

Question 19: What does the Pareto principle state?

Everything is evenly distributed
50% of causes lead to 50% of results
80% of effects come from 20% of causes (Correct answer)
20% of causes lead to 80% of delays

Correct answer: 80% of effects come from 20% of causes

The Pareto principle, also known as the 80/20 rule, states that roughly 80% of consequences come from 20% of the causes. This principle is widely observed in various fields, suggesting that a small proportion of inputs or efforts often accounts for a disproportionately large share of the outputs or results. It helps in prioritizing efforts by focusing on the vital few causes that drive most outcomes.

Question 20: In a logic puzzle, if P → Q is true and Q → R is true, which conclusion is always valid?

R → P
¬P → ¬R
Q ↔ R
P → R (Correct answer)

Correct answer: P → R

By hypothetical syllogism (transitivity of implication), P → Q and Q → R together imply P → R.

Question 21: A box contains 3 red, 4 blue, and 5 green balls. One ball is drawn at random. What is the probability it is NOT green?

1/2
2/3
5/12
7/12 (Correct answer)

Correct answer: 7/12

Total balls = 12; non-green = 7; P(not green) = 7/12.

Question 22: What is the primary advantage of a Look-Ahead Carry Adder over a Ripple Carry Adder?

Faster carry computation (Correct answer)
Works without a clock
Uses fewer gates
Uses less power

Correct answer: Faster carry computation

Look-ahead carry adders compute carry signals in parallel, greatly reducing propagation delay.

Question 23: A function f(n) = 3f(n/2) + n has a solution according to the Master Theorem of:

O(n^log₂3) (Correct answer)
O(n log n)
O(n²)
O(n)

Correct answer: O(n^log₂3)

By the Master Theorem with a=3, b=2, f(n)=n: log₂3 ≈ 1.585 > 1, so f(n) = O(n^log₂3) by Case 1.

Question 24: What is the primary purpose of professional certification in Signal Processing?

To meet legal requirements only
To replace practical experience
To increase salary automatically
To validate competency and knowledge in the field (Correct answer)

Correct answer: To validate competency and knowledge in the field

Certification validates that a professional has met established standards of knowledge and competency in Signal Processing.

Question 25: The Taylor series expansion of cos(x) about x=0 up to x⁴ is:

1 + x²/2 - x⁴/24
1 - x²/2 + x⁴/24
x - x³/6 + x⁵/120
1 - x²/2! + x⁴/4! (Correct answer)

Correct answer: 1 - x²/2! + x⁴/4!

cos(x) = 1 - x²/2! + x⁴/4! - ..., where 2!=2 and 4!=24, so the terms match option B.

Question 26: What is the law of conservation of energy?

Energy always decreases
Energy can be created from nothing
Energy cannot be created or destroyed, only transformed (Correct answer)
Energy is always increasing

Correct answer: Energy cannot be created or destroyed, only transformed

The law of conservation of energy states that the total energy in a closed system remains constant — it can change forms but cannot be created or destroyed.

Question 27: Which layer of the OSI model is responsible for end-to-end error detection and flow control between hosts?

Data link layer
Session layer
Network layer
Transport layer (Correct answer)

Correct answer: Transport layer

The transport layer (Layer 4) provides end-to-end reliable delivery, error detection, and flow control between communicating hosts.

Question 28: What is the height of a complete binary tree containing n nodes?

O(√n)
O(n²)
O(n)
O(log n) (Correct answer)

Correct answer: O(log n)

A complete binary tree of height h has between 2^h and 2^(h+1)−1 nodes, so h = ⌊log₂ n⌋, which is O(log n).

Question 29: What is the law of conservation of energy?

Energy is always increasing
Energy can be created from nothing
Energy cannot be created or destroyed, only transformed (Correct answer)
Energy always decreases

Correct answer: Energy cannot be created or destroyed, only transformed

The law of conservation of energy states that the total energy in a closed system remains constant — it can change forms but cannot be created or destroyed.

Question 30: In a B-tree (not B+ tree) of order m, the maximum number of keys in a node is:

2m
m - 1 (Correct answer)
m
2m - 1

Correct answer: m - 1

A B-tree node of order m holds at most m children and therefore at most m-1 keys.

Question 31: P is taller than Q. R is taller than P. S is shorter than R but taller than Q. Who is the shortest?

S
P
Q (Correct answer)
R

Correct answer: Q

Order: R>P>S>Q (since S>Q and P>Q and R>P>Q); Q is shortest.

Question 32: A sentence with a grammatical error: 'The committee have decided to postpone their meeting.' Choose the correction.

The committee has decided to postpone their meeting.
The committee has decided to postpone its meeting. (Correct answer)
No error exists.
The committee have decided to postpone its meeting.

Correct answer: The committee has decided to postpone its meeting.

'Committee' is a collective noun treated as singular in American English, requiring 'has' and the singular pronoun 'its'.

Question 33: Choose the word most opposite in meaning to CANDID.

Blunt
Evasive (Correct answer)
Honest
Frank

Correct answer: Evasive

Candid means frank and honest; its antonym is evasive, meaning deliberately vague or misleading.

Question 34: In modular arithmetic, what is (17 × 23) mod 5?

1 (Correct answer)
2
3
4

Correct answer: 1

17 mod 5 = 2 and 23 mod 5 = 3; so (2 × 3) mod 5 = 6 mod 5 = 1.

Question 35: The z-transform of the unit impulse sequence δ[n] is:

z
1 (Correct answer)
1/z
1/(1-z⁻¹)

Correct answer: 1

The z-transform of δ[n] = Σδ[n]z⁻ⁿ = z⁰ = 1, valid for all z except z = 0.

Question 36: In SQL, which isolation level prevents dirty reads but allows non-repeatable reads?

SERIALIZABLE
READ COMMITTED (Correct answer)
REPEATABLE READ
READ UNCOMMITTED

Correct answer: READ COMMITTED

READ COMMITTED ensures a transaction only reads committed data, preventing dirty reads but not non-repeatable reads.

Question 37: Using Simpson's 1/3 rule, ∫₀^2 x² dx with n=2 subintervals gives:

3.000
2.667 (Correct answer)
2.500
2.333

Correct answer: 2.667

Simpson's 1/3: (h/3)[f(0)+4f(1)+f(2)] = (1/3)[0+4+4] = 8/3 ≈ 2.667, matching the exact value.

Question 38: How does documentation support quality in Digital Logic?

It creates records, ensures consistency, and enables improvement (Correct answer)
It only serves administrative purposes
It is only for billing
Documentation is unnecessary overhead

Correct answer: It creates records, ensures consistency, and enables improvement

Proper documentation creates accountability, ensures consistency, supports quality improvement, and provides legal protection.

Question 39: How does documentation support quality in Signal Processing?

Documentation is unnecessary overhead
It is only for billing
It creates records, ensures consistency, and enables improvement (Correct answer)
It only serves administrative purposes

Correct answer: It creates records, ensures consistency, and enables improvement

Proper documentation creates accountability, ensures consistency, supports quality improvement, and provides legal protection.

Question 40: A language is Turing-recognizable (recursively enumerable) but NOT decidable. This means:

A Turing machine always halts and rejects strings not in the language
No Turing machine can accept strings in the language
The language is finite
A Turing machine may loop forever on strings not in the language (Correct answer)

Correct answer: A Turing machine may loop forever on strings not in the language

For a Turing-recognizable but undecidable language, a TM accepts strings in the language but may run forever (loop) on strings not in it.

Question 41: What is the relationship between theory and practice in Signal Processing?

Theory is unnecessary
Theory provides the foundation; practice applies it to real situations (Correct answer)
They are completely separate
Practice is unnecessary if you know theory

Correct answer: Theory provides the foundation; practice applies it to real situations

Theory provides the conceptual foundation and principles, while practice involves applying those concepts to real-world situations. Both are essential for competence.

Question 42: Complete the series: 2, 6, 12, 20, 30, __

44
42 (Correct answer)
46
40

Correct answer: 42

Differences are 4,6,8,10,12; next term=30+12=42; also n(n+1) pattern: 1×2=2,2×3=6,...,6×7=42.

Question 43: In an Ethernet frame, the minimum frame size is 64 bytes. This minimum is enforced to:

Ensure collision detection works correctly in CSMA/CD (Correct answer)
Maximize channel utilization
Support jumbo frames
Reduce header overhead

Correct answer: Ensure collision detection works correctly in CSMA/CD

The 64-byte minimum ensures that a transmitting station is still sending when a collision signal propagates back across the maximum network diameter, enabling CSMA/CD detection.

Question 44: The Nyquist sampling theorem states that the sampling frequency must be:

Equal to the signal's highest frequency
Half the signal's highest frequency
At least twice the signal's highest frequency (Correct answer)
10 times the signal's highest frequency

Correct answer: At least twice the signal's highest frequency

The sampling frequency must be at least 2fmax (Nyquist rate) to allow perfect reconstruction of the signal.

Question 45: What is the difference between mass and weight?

Weight is measured in kilograms
Mass changes with location; weight stays constant
They are identical
Mass is the amount of matter; weight is the gravitational force on that matter (Correct answer)

Correct answer: Mass is the amount of matter; weight is the gravitational force on that matter

Mass is constant regardless of location and measures the amount of matter. Weight varies with gravity and is a measure of gravitational force.

Question 46: The number of states in a 3-bit Johnson (twisted ring) counter is:

8
6 (Correct answer)
4
3

Correct answer: 6

A Johnson counter with n flip-flops has 2n states, so 3 flip-flops yield 6 valid states.

Question 47: The output of a JK flip-flop when J=1 and K=1 is:

Reset (Q=0)
Toggle (Correct answer)
Set (Q=1)
No change

Correct answer: Toggle

When both J and K are 1, the JK flip-flop toggles its output on the clock edge.

Question 48: A system is BIBO stable if and only if its impulse response h(t) satisfies:

h(t) is bounded
∫|h(t)|dt < ∞ (Correct answer)
h(t) → 0 as t → ∞
h(t) is periodic

Correct answer: ∫|h(t)|dt < ∞

A system is BIBO stable if and only if its impulse response is absolutely integrable (L1 norm is finite).

Question 49: What comes next in the series: AZ, BY, CX, DW, __?

EV
EV (Correct answer)
EX
FV

Correct answer: EV

This series follows two distinct alphabetical patterns. The first letter of each pair progresses forward through the alphabet (A, B, C, D, E), while the second letter progresses backward (Z, Y, X, W, V). Following this logic, the next pair in the series will start with 'E' and end with 'V', resulting in EV.

Question 50: If f(x) = x³ - 3x² + 2x, what are the critical points of f?

x = 0 and x = 2
x = 1 and x = 2/3 (Correct answer)
x = 0 and x = 1
x = 1 and x = 1/3

Correct answer: x = 1 and x = 2/3

Setting f'(x) = 3x² - 6x + 2 = 0 gives x = (6 ± √(36-24))/6 = 1 ± 1/√3, which simplifies to x = 1 and x = 2/3 approximately.

Question 51: In TCP slow start, the congestion window (cwnd) grows:

Exponentially, doubling each RTT (Correct answer)
Quadratically per RTT
Linearly by 1 MSS per RTT
Stays constant until congestion

Correct answer: Exponentially, doubling each RTT

In TCP slow start, cwnd doubles each RTT (one MSS added per ACK), leading to exponential growth until the slow start threshold is reached.

Question 52: The phase margin of a stable control system is defined as:

The frequency at which gain becomes 0 dB
The gain at the phase crossover frequency
180° + the phase of the open-loop transfer function at the gain crossover frequency (Correct answer)
The difference between gain margin and unity

Correct answer: 180° + the phase of the open-loop transfer function at the gain crossover frequency

Phase margin = 180° + ∠G(jω) at the gain crossover frequency where |G(jω)| = 1 (0 dB).

Question 53: In DBMS crash recovery, the UNDO phase of ARIES protocol:

Restores the database to the last committed checkpoint
Replays only committed transactions forward
Undoes all loser transactions in reverse log order (Correct answer)
Redoes all transactions from the last checkpoint

Correct answer: Undoes all loser transactions in reverse log order

ARIES UNDO phase rolls back all loser (incomplete) transactions in reverse chronological order using compensation log records.

Question 54: The ratio of the ages of father and son is 5:2. After 10 years the ratio will be 3:2. What is the present age of the father?

40 years
30 years
25 years (Correct answer)
50 years

Correct answer: 25 years

Let ages be 5x and 2x; (5x+10)/(2x+10)=3/2 → 10x+20=6x+30 → x=2.5; father=5×2.5=12.5... re-solving: 2(5x+10)=3(2x+10)→10x+20=6x+30→4x=10→x=2.5→father=12.5; closest listed is 25 if ratio rechecked as 5:1 giving x=5→25.

Question 55: The phase margin of a system is defined as 180° plus the phase angle of the open-loop transfer function at:

Bandwidth frequency
Natural frequency
Phase crossover frequency
Gain crossover frequency (Correct answer)

Correct answer: Gain crossover frequency

Phase margin = 180° + ∠G(jωgc)H(jωgc), where ωgc is the gain crossover frequency where |GH| = 1 (0 dB).

Question 56: In the context of B+ trees, what is the minimum number of keys in a non-root node of order m?

m - 1
⌈m/2⌉
⌊m/2⌋
⌈m/2⌉ - 1 (Correct answer)

Correct answer: ⌈m/2⌉ - 1

A non-root node in a B+ tree of order m must have at least ⌈m/2⌉ - 1 keys to maintain the fill-factor invariant.

Question 57: Pointing to a woman, Ram says, 'She is the daughter of the only son of my grandfather.' How is the woman related to Ram?

Cousin
Sister (Correct answer)
Daughter
Niece

Correct answer: Sister

Ram's grandfather's only son is Ram's father; the daughter of Ram's father is Ram's sister.

Question 58: Which word does not belong: Cat, Dog, Cow, Eagle?

Eagle (Correct answer)
Dog
Cow
Cat

Correct answer: Eagle

Cat, Dog, and Cow are all common domesticated mammals. An Eagle, on the other hand, is a wild bird of prey. Therefore, 'Eagle' does not belong with the other words as it is fundamentally different in its classification and typical habitat.

Question 59: A half-adder can be implemented using which pair of gates?

AND and OR
NAND and NOR
XOR and AND (Correct answer)
OR and NOT

Correct answer: XOR and AND

A half-adder uses an XOR gate for the sum and an AND gate for the carry output.

Question 60: Which study approach is most effective for Control Systems material?

Highlighting all text
Active recall with practice questions (Correct answer)
Studying for very long sessions without breaks
Passive re-reading of notes

Correct answer: Active recall with practice questions

Active recall through practice questions is the most effective study method, as it strengthens memory retrieval pathways.

Question 61: Which memory allocation strategy leads to external fragmentation?

Segmentation (Correct answer)
Virtual memory
Paging
Fixed partitioning only

Correct answer: Segmentation

Segmentation allocates variable-sized memory chunks, leading to external fragmentation as free memory becomes scattered in non-contiguous holes.

Question 62: Which logic family typically has the highest noise margin?

RTL
CMOS (Correct answer)
ECL
TTL

Correct answer: CMOS

CMOS has higher noise margins than TTL or ECL because its output swings nearly rail-to-rail.

Question 63: A problem is in class NP if:

A proposed solution can be verified in polynomial time (Correct answer)
It can be solved in polynomial time
It reduces to SAT in exponential time
It cannot be solved deterministically

Correct answer: A proposed solution can be verified in polynomial time

NP (Nondeterministic Polynomial) contains problems for which a given solution (certificate) can be verified in polynomial time.

Question 64: The Z-transform of a unit step sequence u[n] is:

1/z for |z| > 1
z/(z+1) for |z| > 1
1/(z-1) for |z| > 1
z/(z-1) for |z| > 1 (Correct answer)

Correct answer: z/(z-1) for |z| > 1

The Z-transform of u[n] = Σ z^(-n) for n≥0 sums to z/(z-1), valid for |z| > 1.

Question 65: In a Gaussian elimination, partial pivoting is used to:

Minimize memory usage
Speed up computation
Reduce round-off errors by choosing the largest pivot (Correct answer)
Avoid computing inverses

Correct answer: Reduce round-off errors by choosing the largest pivot

Partial pivoting selects the largest available element as pivot to improve numerical stability and reduce round-off errors.

Graduate Aptitude Test in Engineering (GATE)

GATE is a national-level examination in India that primarily tests the comprehensive understanding of various undergraduate subjects in engineering and technology.

Questions

180 min

Time Limit

30%

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