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

Question 1: A subnet mask of 255.255.255.192 means the subnet has how many usable host addresses?

62 (Correct answer)
30
254
126

Correct answer: 62

255.255.255.192 = /26, giving 2^6 = 64 addresses; subtracting network and broadcast gives 62 usable hosts.

Question 2: What is the primary purpose of professional certification in Signal Processing?

To replace practical experience
To meet legal requirements only
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 3: The Laplace transform of t·e^(at) is:

s/(s-a)²
1/(s+a)
1/(s-a)
1/(s-a)² (Correct answer)

Correct answer: 1/(s-a)²

Using the first shifting theorem and L{t} = 1/s², L{t·e^(at)} = 1/(s-a)².

Question 4: A system is said to be observable if:

The initial state can be determined from the output over a finite time interval (Correct answer)
All eigenvalues are in the left half-plane
All states can be driven to zero by a suitable input
The transfer function has no RHP zeros

Correct answer: The initial state can be determined from the output over a finite time interval

Observability means the initial state x(0) can be uniquely determined from the output y(t) over a finite time interval [0, T].

Question 5: If f(x) = x³ - 3x² + 2x, what are the critical points of f?

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

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 6: A salesperson visits 5 cities. The number of distinct routes visiting each city exactly once and returning to the starting city is:

24
120
60
12 (Correct answer)

Correct answer: 12

For n cities in TSP, the number of distinct tours (fixing start) is (n-1)!/2 = 4!/2 = 24/2 = 12.

Question 7: Which of the following sorting algorithms has the best average-case time complexity?

Bubble Sort
Insertion Sort
Merge Sort (Correct answer)
Selection Sort

Correct answer: Merge Sort

Merge Sort has O(n log n) average-case complexity, which is optimal for comparison-based sorting.

Question 8: Which of the following is NOT a property of transactions guaranteed by ACID?

Atomicity
Consistency
Isolation
Distribution (Correct answer)

Correct answer: Distribution

ACID stands for Atomicity, Consistency, Isolation, and Durability — Distribution is not part of ACID.

Question 9: How does documentation support quality in Digital Logic?

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

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

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

Question 10: Choose the word closest in meaning to VERBOSE.

Silent
Brief
Wordy (Correct answer)
Precise

Correct answer: Wordy

Verbose means using more words than necessary; its synonym is wordy.

Question 11: Which of the following is a decidable problem for context-free grammars?

Ambiguity of a CFG
Intersection of two CFLs being context-free
Equivalence of two CFGs
Membership: does string w belong to L(G)? (Correct answer)

Correct answer: Membership: does string w belong to L(G)?

The membership problem for CFLs — whether a given string belongs to the language of a given grammar — is decidable using CYK or Earley parsing.

Question 12: If 6 men can complete a job in 8 days working 10 hours a day, how many days will 4 men take working 12 hours a day?

15 days
10 days (Correct answer)
12 days
8 days

Correct answer: 10 days

Total man-hours=6×8×10=480; new scenario: 480/(4×12)=10 days.

Question 13: In a randomly constructed Binary Search Tree (BST), what is the average-case time complexity for a search operation?

O(log n) (Correct answer)
O(n log n)
O(n)
O(1)

Correct answer: O(log n)

A randomly constructed BST has an expected height of O(log n), so search visits at most O(log n) nodes on average.

Question 14: The halting problem is:

Undecidable in general (Correct answer)
Decidable if the input is a regular language
Decidable for all Turing machines
Decidable only for deterministic Turing machines

Correct answer: Undecidable in general

Turing proved that no general algorithm can determine whether an arbitrary Turing machine will halt on a given input.

Question 15: Which normal form ensures that a context-free grammar has no unit productions and no ε-productions (except possibly S → ε)?

Wirth Syntax Notation
Chomsky Normal Form (CNF) (Correct answer)
Greibach Normal Form (GNF)
Backus-Naur Form

Correct answer: Chomsky Normal Form (CNF)

Chomsky Normal Form requires all productions to be of the form A → BC or A → a, eliminating unit productions and ε-productions.

Question 16: 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?

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

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 17: Find the odd one out: Apple, Banana, Carrot, Mango.

Mango
Carrot (Correct answer)
Banana
Apple

Correct answer: Carrot

Apple, Banana, and Mango are all types of fruits. Carrot, however, is a root vegetable. Therefore, 'Carrot' is the odd one out because it belongs to a different botanical category than the other items in the list.

Question 18: If 20% of a number is 80, what is 35% of that number?

140 (Correct answer)
130
150
120

Correct answer: 140

Number = 80/0.20 = 400; 35% of 400 = 140.

Question 19: Which of the following sorting algorithms is both stable and guarantees O(n log n) worst-case time complexity?

HeapSort
Merge Sort (Correct answer)
QuickSort
Selection Sort

Correct answer: Merge Sort

Merge Sort preserves the relative order of equal elements (stable) and always runs in O(n log n); HeapSort is O(n log n) but not stable, and QuickSort degrades to O(n²) worst case.

Question 20: How many minterms does the Boolean function of 3 variables have?

8 (Correct answer)
4
16
6

Correct answer: 8

A function of n variables has 2^n minterms; for n=3, that is 2^3 = 8.

Question 21: What is the difference between mass and weight?

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

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 22: Which of the following is a universal gate?

AND
OR
NAND (Correct answer)
XOR

Correct answer: NAND

NAND (and NOR) are universal gates because any Boolean function can be implemented using only NAND gates.

Question 23: In SQL, which isolation level prevents dirty reads but allows non-repeatable reads?

READ UNCOMMITTED
SERIALIZABLE
REPEATABLE READ
READ COMMITTED (Correct answer)

Correct answer: READ COMMITTED

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

Question 24: A function f(n) = 3f(n/2) + n has a solution according to the Master Theorem of:

O(n)
O(n²)
O(n^log₂3) (Correct answer)
O(n log 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 25: The rank of a matrix A is defined as:

The trace of A
The maximum number of linearly independent rows (or columns) (Correct answer)
The number of rows in A
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 26: Using the trapezoidal rule with n equal intervals of width h, the error is of order:

O(h)
O(h²) (Correct answer)
O(h³)
O(h⁴)

Correct answer: O(h²)

The global truncation error of the trapezoidal rule is O(h²), making it a second-order method.

Question 27: In a row of 40 students, Priya is 15th from the left. What is her position from the right?

24th
27th
25th
26th (Correct answer)

Correct answer: 26th

Position from right = 40−15+1 = 26th.

Question 28: The Mason's gain formula is used to find:

Transfer function from a signal flow graph (Correct answer)
Characteristic roots of a system
Controllability of a state-space system
Stability margins from a Bode plot

Correct answer: Transfer function from a signal flow graph

Mason's gain formula computes the overall transfer function of a signal flow graph using forward paths, loops, and cofactors.

Question 29: What is root cause analysis?

Identifying the primary reason for a problem (Correct answer)
Creating new problems
Guessing the issue
Addressing symptoms only

Correct answer: Identifying the primary reason for a problem

Root cause analysis (RCA) is a systematic process for identifying the underlying, fundamental causes of a problem or undesirable event, rather than just addressing its symptoms. The goal of RCA is to implement solutions that prevent recurrence by eliminating the root cause. This leads to more effective and lasting problem resolution.

Question 30: What is the difference between an element and a compound?

An element is a pure substance; a compound is two or more elements chemically combined (Correct answer)
An element contains multiple types of atoms
They are the same thing
A compound is simpler than an element

Correct answer: An element is a pure substance; a compound is two or more elements chemically combined

Elements consist of one type of atom (e.g., oxygen), while compounds are substances formed by chemical combination of two or more different elements (e.g., water = H₂O).

Question 31: Read the passage: 'All employees who joined before 2010 are eligible for a pension. John joined in 2008.' Which conclusion is valid?

John joined after 2010
John is not eligible for a pension
Nothing can be concluded
John is eligible for a pension (Correct answer)

Correct answer: John is eligible for a pension

John joined in 2008, which is before 2010, so he meets the condition for pension eligibility.

Question 32: If A is an n×n invertible matrix, which statement is FALSE?

det(A) ≠ 0
The system Ax=0 has only the trivial solution
Rank(A) = n
A has n linearly independent eigenvectors (Correct answer)

Correct answer: A has n linearly independent eigenvectors

An invertible matrix need not have n linearly independent eigenvectors; defective matrices are invertible but not diagonalizable.

Question 33: What is the relationship between theory and practice in Control Systems?

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

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

Sequentially with delays
Asynchronously
Simultaneously (Correct answer)
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 35: Which matrix operation results in a change in the determinant's sign?

Scaling a row
Swapping two rows (Correct answer)
Adding a row to another
Multiplying a row by 0

Correct answer: Swapping two rows

When two rows (or columns) of a matrix are swapped, the determinant of the resulting matrix changes its sign. For instance, if the original determinant was D, performing a single row swap will yield a new determinant of -D. This is a fundamental property of determinants in linear algebra, crucial for understanding matrix transformations.

Question 36: A system is BIBO stable if and only if its impulse response h(t) satisfies:

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

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 37: What does Bernoulli’s principle describe?

Fluid dynamics (Correct answer)
Nuclear fission
Electrical conduction
Thermal expansion

Correct answer: Fluid dynamics

Bernoulli's principle is a fundamental concept in fluid dynamics, which is the study of fluids in motion. It describes the inverse relationship between the speed of a fluid and its pressure or potential energy. Specifically, it states that an increase in fluid speed occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy, explaining phenomena like aerodynamic lift.

Question 38: What role does ethics play in Signal Processing practice?

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

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 39: What is the worst-case time complexity of Merge Sort on an array of n elements?

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

Correct answer: O(n log n)

Merge Sort satisfies the recurrence T(n) = 2T(n/2) + O(n), which by the Master Theorem resolves to O(n log n) in all cases.

Question 40: Which of the following conditions is NECESSARY for a system to be minimum-phase?

All poles and zeros in the left half-plane
Damping ratio greater than 1
All poles in the left half-plane
All zeros in the left half-plane (Correct answer)

Correct answer: All zeros in the left half-plane

A minimum-phase system has all its zeros (and poles for stability) in the left half-plane, giving the minimum possible phase lag.

Question 41: What is the key difference between a process and a thread?

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

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 42: The general solution of the second-order ODE y'' - 4y = 0 is:

y = (C₁+C₂x)e^(2x)
y = C₁e^(4x) + C₂
y = C₁e^(2x) + C₂e^(-2x) (Correct answer)
y = C₁cos(2x) + C₂sin(2x)

Correct answer: y = C₁e^(2x) + C₂e^(-2x)

The characteristic equation r² - 4 = 0 gives r = ±2, leading to y = C₁e^(2x) + C₂e^(-2x).

Question 43: Which of the following is an example of a real-time operating system (RTOS)?

Windows 10
macOS Monterey
Ubuntu Linux
VxWorks (Correct answer)

Correct answer: VxWorks

VxWorks is a widely-used real-time operating system designed for embedded systems where deterministic timing guarantees are critical.

Question 44: A leaky bucket algorithm with a bucket size of 10 packets and output rate of 2 packets/second receives a burst of 10 packets instantly. How long until the bucket drains?

20 seconds
2 seconds
5 seconds (Correct answer)
10 seconds

Correct answer: 5 seconds

At 2 packets/second, draining 10 packets takes 10/2 = 5 seconds.

Question 45: 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?

990
975
900
950 (Correct answer)

Correct answer: 950

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

Question 46: Why is continuing education important in Digital Logic?

To stay current with evolving standards and practices (Correct answer)
It is not important after certification
To network only
Only for re-certification requirements

Correct answer: To stay current with evolving standards and practices

Continuing education keeps professionals updated with the latest developments, standards, and best practices in their field.

Question 47: The 0/1 Knapsack problem with n items and capacity W, solved using dynamic programming, has time complexity:

O(n log W)
O(2ⁿ)
O(n + W)
O(n × W) (Correct answer)

Correct answer: O(n × W)

The DP table has n rows and W+1 columns, and each of the n×W cells is filled in O(1) time, giving O(n × W) total.

Question 48: How does documentation support quality in Signal Processing?

It is only for billing
It only serves administrative purposes
It creates records, ensures consistency, and enables improvement (Correct answer)
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 49: The eigenvalues of a real symmetric matrix are always:

Complex conjugates
Purely imaginary
Zero
Real (Correct answer)

Correct answer: Real

Real symmetric matrices always have real eigenvalues, a fundamental result in linear algebra.

Question 50: In CSMA/CD, after the k-th collision, a station waits a random number of slot times chosen from [0, 2^k - 1]. This is called:

Fibonacci backoff
Binary exponential backoff (Correct answer)
Exponential backoff
Linear backoff

Correct answer: Binary exponential backoff

Binary exponential backoff doubles the contention window after each successive collision, reducing the probability of repeated collisions.

Question 51: Which of the following is NOT a property of a Poisson distribution?

Events occur independently
Describes rare event counts in a fixed interval
Mean equals variance
The distribution is symmetric about the mean (Correct answer)

Correct answer: The distribution is symmetric about the mean

Poisson distributions are right-skewed (not symmetric), though they approach symmetry as λ → ∞.

Question 52: Which routing algorithm guarantees the shortest path by exploring nodes in order of their cumulative distance from the source?

Dijkstra's algorithm (Correct answer)
DFS-based routing
Bellman-Ford
Floyd-Warshall

Correct answer: Dijkstra's algorithm

Dijkstra's algorithm uses a greedy approach with a priority queue to always expand the closest unvisited node, guaranteeing shortest paths in graphs with non-negative weights.

Question 53: A shopkeeper marks his goods at 25% above cost price and allows a 10% discount. What is his profit percentage?

17.5%
10%
12.5% (Correct answer)
15%

Correct answer: 12.5%

SP = CP×1.25×0.90 = 1.125×CP; profit = 12.5%.

Question 54: In a network where a router has the routing table entry '192.168.10.0/24 via 10.0.0.1', what does '10.0.0.1' represent?

The next-hop router (Correct answer)
The subnet mask
The destination network
The outgoing interface IP

Correct answer: The next-hop router

In a routing table, 'via X.X.X.X' denotes the next-hop IP address — the address of the next router toward the destination.

Question 55: What is a firewall?

A fire-resistant building component
A password manager
An antivirus program
A security device that monitors and controls network traffic based on rules (Correct answer)

Correct answer: A security device that monitors and controls network traffic based on rules

Firewalls filter incoming and outgoing network traffic based on security rules, creating a barrier between trusted and untrusted networks.

Question 56: Which memory allocation strategy leads to external fragmentation?

Paging
Segmentation (Correct answer)
Fixed partitioning only
Virtual memory

Correct answer: Segmentation

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

Question 57: What does the Pareto principle state?

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

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 58: What is the main advantage of multilevel feedback queue scheduling?

It guarantees no starvation
It is simple to implement
It adapts to process behavior dynamically (Correct answer)
It requires no context switching

Correct answer: It adapts to process behavior dynamically

Multilevel feedback queues promote or demote processes based on their CPU burst behavior, adapting dynamically to workload characteristics.

Question 59: What role does ethics play in Signal Processing practice?

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

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 60: Which of the following problems can be solved in polynomial time and is therefore in class P (not NP-complete)?

Vertex Cover
3-SAT
Minimum Spanning Tree (Correct answer)
Hamiltonian Cycle

Correct answer: Minimum Spanning Tree

Minimum Spanning Tree is solvable in polynomial time by Kruskal's or Prim's algorithm, whereas 3-SAT, Hamiltonian Cycle, and Vertex Cover are all NP-complete.

Question 61: A train travels 60 miles in 1.5 hours. What is its average speed?

40 mph (Correct answer)
30 mph
45 mph
50 mph

Correct answer: 40 mph

To find the average speed, you divide the total distance traveled by the total time taken. In this case, the train travels 60 miles in 1.5 hours. Therefore, the average speed is calculated as 60 miles / 1.5 hours = 40 miles per hour (mph).

Question 62: What comes next in the series: AZ, BY, CX, DW, __?

FV
EX
EV
EV (Correct answer)

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 63: Which of the following is the correct order of SQL query logical execution?

WHERE → FROM → GROUP BY → SELECT → HAVING
FROM → WHERE → GROUP BY → HAVING → SELECT (Correct answer)
SELECT → FROM → WHERE → GROUP BY → HAVING
FROM → SELECT → WHERE → GROUP BY → HAVING

Correct answer: FROM → WHERE → GROUP BY → HAVING → SELECT

SQL logical execution order is FROM, WHERE, GROUP BY, HAVING, SELECT (then ORDER BY), regardless of written order.

Question 64: The minimum number of NAND gates required to implement the function F = A·B + C is:

3 (Correct answer)
4
5
2

Correct answer: 3

F = A·B + C can be realized with 3 NAND gates: NAND(A,B), NAND(C,C), and NAND of their outputs.

Question 65: The transfer function representation of a system is LESS general than the state-space representation because:

Transfer functions require time-domain analysis
Transfer functions are only valid for nonlinear systems
Transfer functions assume zero initial conditions (Correct answer)
Transfer functions cannot represent MIMO systems

Correct answer: Transfer functions assume zero initial conditions

Transfer functions are defined under zero initial conditions, so they only capture the forced response, whereas state-space handles arbitrary initial conditions.

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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