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Engineering and Applied Sciences MCQs
Practice Engineering and Applied Sciences multiple-choice questions for Pakistan Institute of Engineering and Applied Sciences competitive exams. Each question includes the correct answer and a short explanation, and past-paper questions are marked so you can revise both repeated and fresh material in one place.
e^(2x) (2sin(3x) + 3cos(3x))
e^(2x) (3sin(3x) + 2cos(3x))
2e^(2x) * sin(3x) + 3e^(2x) * cos(3x)
e^(2x) (2cos(3x) + 3sin(3x))
وضاحتUsing the product rule (uv)' = u'v + uv', where u=e^(2x) and v=sin(3x), the derivative is 2e^(2x)sin(3x) + 3e^(2x)cos(3x).
4
6
8
10
وضاحتIntegrating (2x + 3) gives x^2 + 3x. Evaluating from 0 to 2: (4 + 6) - (0 + 0) = 10.
It is identity
It is singular
It is invertible
It is symmetric
وضاحتA matrix with a determinant of zero is non-invertible, which is defined as a singular matrix.
0
1
Infinity
-1
وضاحتThis is a standard trigonometric limit result known as the fundamental limit of sine.
1/x
2/x
x^2
2ln(x)
وضاحتUsing the chain rule, d/dx(ln(x^2)) = (1/x^2) * 2x = 2/x.
4
8
12
16
وضاحتThe derivative is y' = 3x^2. Plugging in x = 2 gives 3(4) = 12.
0
1
k
-k
وضاحتBy the right-hand rule and the definition of cross products for unit vectors, i x j = k.
0
1
2
3
وضاحتAn identity matrix is full rank, meaning its rows are linearly independent. For a 3x3 matrix, the rank is 3.
0
1
-1
π/2
وضاحتThe integral of cos(x) is sin(x). Evaluating sin(π/2) - sin(0) gives 1 - 0 = 1.
1/6
1/12
1/36
7/36
وضاحتThere are 6 outcomes that sum to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) out of 36 total outcomes. 6/36 = 1/6.
f(x) = x^3
f(x) = sin(x)
f(x) = x^2 + 1
f(x) = e^x
وضاحتA function is even if f(-x) = f(x). Here, (-x)^2 + 1 = x^2 + 1, which satisfies the condition.
mωr
mω^2r
mωr^2
mω/r
وضاحتThe centripetal force is given by F = ma_c, where a_c = ω^2r, leading to F = mω^2r.
Tesla
Weber
Henry
Gauss
وضاحتThe Weber is the SI derived unit of magnetic flux.
XL > XC
XL < XC
XL = XC
R = 0
وضاحتResonance in an RLC circuit occurs when inductive reactance equals capacitive reactance.
Archimedes' principle
Pascal's law
Bernoulli's principle
Newton's third law
وضاحتBernoulli's principle relates pressure and velocity, explaining lower pressure on the upper surface of a wing.
hf
h/f
f/h
h*c/f
وضاحتThe Planck-Einstein relation states that photon energy E = hf.
8.9 m/s^2
9.8 m/s^2
10.5 m/s^2
12.0 m/s^2
وضاحتStandard acceleration due to gravity on Earth is approximately 9.8 m/s^2.
M
M^2
sqrt(M)
1/M
وضاحتThe escape velocity formula is v = sqrt(2GM/R), where v is directly proportional to the square root of the mass M.
Temperature
Pressure
Entropy
Volume
وضاحتAn adiabatic process is reversible and occurs without the exchange of heat, resulting in no change in entropy.
Reflection
Refraction
Superposition
Polarization
وضاحتInterference occurs when two or more coherent light waves overlap, satisfying the principle of superposition.
h*p
p/h
h/p
h*p^2
وضاحتAccording to the de Broglie hypothesis, wavelength lambda = h/p, where h is Planck's constant.
Photon
Gluon
Graviton
W boson
وضاحتIn Quantum Chromodynamics, gluons are the gauge bosons that mediate the strong nuclear force between quarks.
Queue
Stack
Linked List
Binary Tree
وضاحتA stack follows the LIFO principle where the last element added is the first one to be removed.
Data Link
Network
Transport
Session
وضاحتThe Network layer is responsible for logical addressing (like IP addresses) and routing.
O(n)
O(n log n)
O(log n)
O(1)
وضاحتBinary search repeatedly halves the search space, leading to logarithmic complexity.
RAM
Cache
ROM
Registers
وضاحتROM (Read-Only Memory) retains data even when power is turned off.
static
const
final
virtual
وضاحتThe 'final' specifier prevents a class from being inherited or a virtual function from being overridden.
Clears all data
Removes the table structure
Hides the table
Renames the table
وضاحتDROP TABLE deletes the entire table definition and all its data from the database.
O(n)
O(n log n)
O(n^2)
O(log n)
وضاحتQuickSort's worst case occurs when the pivot is consistently the smallest or largest element, leading to unbalanced partitions.
Immediate
Direct
Indirect
Indexed
وضاحتIn direct addressing, the operand field contains the memory address of the data.
Isolation
Integration
Indexing
Interoperability
وضاحتACID stands for Atomicity, Consistency, Isolation, and Durability.
Application
Network
Host-to-Host
Data Link
وضاحتThe Host-to-Host layer in the TCP/IP suite provides communication between end-user devices, mirroring the Transport layer of OSI.
1110
1100
0110
1011
وضاحتXOR results in 1 where bits are different: 1^0=1, 0^1=1, 1^0=1, 1^1=0, yielding 1110.
3 km
5 km
6 km
8 km
وضاحتLet distance be d. (d/4) - (d/5) = 15 minutes (1/4 hour). d/20 = 1/4, so d = 5 km.
0 degrees
7.5 degrees
15 degrees
22.5 degrees
وضاحتThe minute hand is at 90 degrees. The hour hand moves 0.5 degrees per minute. At 15 mins, it is at (3*30) + (15*0.5) = 97.5 degrees. Difference = 7.5.
PSBOOF
PSBOHF
QSBOOF
PSBOHE
وضاحتEach letter is shifted forward by one position (A->B, P->Q, etc.).
36
40
42
44
وضاحتThe difference between terms is 4, 6, 8, 10. The next difference is 12. 30 + 12 = 42.
$50
$100
$150
$200
وضاحتSimple interest = P * R * T = 1000 * 0.05 * 3 = 150.
5.0
5.6
6.0
6.2
وضاحتThe first five primes are 2, 3, 5, 7, 11. Sum = 28. Average = 28/5 = 5.6.
Fleeting
Permanent
Transitory
Momentary
وضاحتEphemeral means lasting for a very short time; permanent is the direct opposite.
12cm
sqrt(125)cm
15cm
sqrt(50)cm
وضاحتBy Pythagoras, diagonal = sqrt(10^2 + 5^2) = sqrt(100+25) = sqrt(125).
$300
$400
$450
$350
وضاحت20% of 500 is 100. 500 - 100 = 400.
Nurse
Scalpel
Hospital
Medicine
وضاحتA painter uses a brush as a primary tool, just as a surgeon uses a scalpel.
All roses fade quickly
Some roses fade quickly
Some flowers are roses
All flowers are roses
وضاحتSince all roses are flowers, it must be true that some flowers are roses (the set of roses is a subset of flowers).
All Bloops are Lazzies
Some Bloops are Lazzies
Some Lazzies are Razzies
No Bloops are Lazzies
وضاحتSince some Razzies are Lazzies, by symmetry, some Lazzies must be Razzies.
A = C
A > C
C > A
A < B
وضاحتThis follows the property of transitivity in inequalities.
Linear arrangement
Circular arrangement
Selection
Grouping
وضاحتThe items are described as standing in a line, defining a linear arrangement problem.
Some bats are birds
No bats are birds
All birds are bats
Some mammals are birds
وضاحتSince no birds are mammals and all bats are inside the mammals group, no bats can be birds.
X
Y
Z
W
وضاحتThe hierarchy is X > Y > Z > W. W is at the bottom of the list.
No men are honest
Some men are not honest
Some men are honest
All men are dishonest
وضاحتThe negation of a universal affirmative (All A are B) is a particular negative (Some A are not B).
North
Northwest
Northeast
Southwest
وضاحتX is north, Z is east. To get to X from Z, you must move West and North, hence Northwest.
To the left of P
To the right of Q
Opposite to R
To the left of Q
وضاحتIf P is at 12 o'clock, Q is at 6. R is at 3 o'clock (right of P). Therefore, S must be at 9 o'clock, which is opposite R.
Only 1 follows
Only 2 follows
Both follow
Neither follows
وضاحتConclusion 1 is an assumption, not stated. Conclusion 2 is an extreme overgeneralization not supported by the statement.
20-21-5-19-4-1-25
20-21-5-18-4-1-25
19-21-5-19-4-1-25
20-20-5-19-4-1-25
وضاحتEach letter is replaced by its position in the alphabet: T(20), U(21), E(5), S(19), D(4), A(1), Y(25).
5
10
15
20
وضاحتUsing Principle of Inclusion-Exclusion: |T U C| = |T| + |C| - |T n C| = 30 + 20 - 10 = 40. Neither = 50 - 40 = 10.
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Frequently Asked Questions
Are these Engineering and Applied Sciences MCQs free?
Yes. Every Engineering and Applied Sciences MCQ on this page is free to practice, including the correct answer and explanation.
Do these include past-paper questions?
Yes — questions sourced from past papers are clearly marked with a "Past Paper" badge, alongside fresh practice questions.
Which exams do these Engineering and Applied Sciences MCQs help with?
They are aimed at Pakistan Institute of Engineering and Applied Sciences and related Pakistani competitive exams that test Engineering and Applied Sciences.
How should I practice subject-wise MCQs?
Attempt each question first, then reveal the answer and read the explanation. Short, focused sessions on one subject work better than long unstructured reading.