Engineering & Architecture Admissions MCQ & Objective Questions
Engineering & Architecture Admissions play a crucial role in shaping the future of aspiring students in India. With the increasing competition in entrance exams, mastering MCQs and objective questions is essential for effective exam preparation. Practicing these types of questions not only enhances concept clarity but also boosts confidence, helping students score better in their exams.
What You Will Practise Here
Key concepts in Engineering Mathematics
Fundamentals of Physics relevant to architecture and engineering
Important definitions and terminologies in engineering disciplines
Essential formulas for solving objective questions
Diagrams and illustrations for better understanding
Conceptual theories related to structural engineering
Analysis of previous years' important questions
Exam Relevance
The topics covered under Engineering & Architecture Admissions are highly relevant for various examinations such as CBSE, State Boards, NEET, and JEE. Students can expect to encounter MCQs that test their understanding of core concepts, application of formulas, and analytical skills. Common question patterns include multiple-choice questions that require selecting the correct answer from given options, as well as assertion-reason type questions that assess deeper comprehension.
Common Mistakes Students Make
Misinterpreting the question stem, leading to incorrect answers.
Overlooking units in numerical problems, which can change the outcome.
Confusing similar concepts or terms, especially in definitions.
Neglecting to review diagrams, which are often crucial for solving problems.
Rushing through practice questions without understanding the underlying concepts.
FAQs
Question: What are the best ways to prepare for Engineering & Architecture Admissions MCQs?Answer: Regular practice of objective questions, reviewing key concepts, and taking mock tests can significantly enhance your preparation.
Question: How can I improve my accuracy in solving MCQs?Answer: Focus on understanding the concepts thoroughly, practice regularly, and learn to eliminate incorrect options to improve accuracy.
Start your journey towards success by solving practice MCQs today! Test your understanding and strengthen your knowledge in Engineering & Architecture Admissions to excel in your exams.
Q. For the function f(x) = 2x^3 - 9x^2 + 12x, find the inflection point.
A.
(1, 1)
B.
(2, 2)
C.
(3, 3)
D.
(4, 4)
Show solution
Solution
f''(x) = 12x - 18. Setting f''(x) = 0 gives x = 1.5. The inflection point is (1.5, f(1.5)).
Correct Answer:
B
— (2, 2)
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Q. For the function f(x) = 2x^3 - 9x^2 + 12x, find the intervals where the function is increasing.
A.
(-∞, 1)
B.
(1, 3)
C.
(3, ∞)
D.
(0, 3)
Show solution
Solution
f'(x) = 6x^2 - 18x + 12. Setting f'(x) = 0 gives x = 1 and x = 3. Testing intervals shows f is increasing on (1, 3).
Correct Answer:
B
— (1, 3)
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Q. For the function f(x) = 2x^3 - 9x^2 + 12x, find the local maxima.
A.
(1, 5)
B.
(2, 0)
C.
(3, 0)
D.
(0, 0)
Show solution
Solution
f'(x) = 6x^2 - 18x + 12. Setting f'(x) = 0 gives x = 1 and x = 2. f(1) = 5 is a local maximum.
Correct Answer:
A
— (1, 5)
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Q. For the function f(x) = 3x^2 - 12x + 7, find the coordinates of the vertex.
A.
(2, -5)
B.
(2, -1)
C.
(3, -2)
D.
(1, 1)
Show solution
Solution
The vertex is at x = -b/(2a) = 12/(2*3) = 2. f(2) = 3(2^2) - 12(2) + 7 = -1. So, the vertex is (2, -1).
Correct Answer:
B
— (2, -1)
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Q. For the function f(x) = 3x^3 - 12x^2 + 9, find the x-coordinates of the inflection points.
Show solution
Solution
f''(x) = 18x - 24. Setting f''(x) = 0 gives x = 4/3. This is the inflection point.
Correct Answer:
B
— 2
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Q. For the function f(x) = 3x^3 - 12x^2 + 9x, the number of local maxima and minima is:
Show solution
Solution
Finding f'(x) = 9x^2 - 24x + 9 and solving gives two critical points. The second derivative test confirms one maximum and one minimum.
Correct Answer:
C
— 2
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Q. For the function f(x) = e^x - x^2, the point of inflection occurs at:
A.
x = 0
B.
x = 1
C.
x = 2
D.
x = -1
Show solution
Solution
To find the point of inflection, we compute f''(x) = e^x - 2. Setting f''(x) = 0 gives e^x = 2, leading to x = ln(2). The closest integer is x = 1.
Correct Answer:
B
— x = 1
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Q. For the function f(x) = ln(x), find the point where it is not differentiable.
A.
x = 0
B.
x = 1
C.
x = -1
D.
x = 2
Show solution
Solution
f(x) = ln(x) is not defined for x ≤ 0, hence not differentiable at x = 0.
Correct Answer:
A
— x = 0
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Q. For the function f(x) = sin(x) + cos(x), find the x-coordinate of the maximum point in the interval [0, 2π].
A.
π/4
B.
3π/4
C.
5π/4
D.
7π/4
Show solution
Solution
f'(x) = cos(x) - sin(x). Setting f'(x) = 0 gives tan(x) = 1, so x = π/4 + nπ. In [0, 2π], the maximum occurs at x = 3π/4.
Correct Answer:
B
— 3π/4
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Q. For the function f(x) = x^2 + 2x + 1, what is f'(x)?
A.
2x + 1
B.
2x + 2
C.
2x
D.
x + 1
Show solution
Solution
f'(x) = 2x + 2.
Correct Answer:
B
— 2x + 2
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Q. For the function f(x) = x^2 + 2x + 3, find the point where it is not differentiable.
A.
x = -1
B.
x = 0
C.
x = 1
D.
It is differentiable everywhere
Show solution
Solution
The function is a polynomial and is differentiable everywhere.
Correct Answer:
D
— It is differentiable everywhere
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Q. For the function f(x) = x^2 + kx + 1 to be differentiable at x = -1, what must k be?
Show solution
Solution
Setting the derivative f'(-1) = 0 gives k = 1 for differentiability.
Correct Answer:
C
— 1
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Q. For the function f(x) = x^2 - 2x + 1, find the slope of the tangent line at x = 1.
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Solution
f'(x) = 2x - 2. Thus, f'(1) = 2(1) - 2 = 0.
Correct Answer:
A
— 0
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Q. For the function f(x) = x^2 - 4x + 4, find the point where it is not differentiable.
A.
x = 0
B.
x = 2
C.
x = 4
D.
It is differentiable everywhere
Show solution
Solution
As a polynomial, f(x) is differentiable everywhere, including at x = 2.
Correct Answer:
D
— It is differentiable everywhere
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Q. For the function f(x) = x^2 - 4x + 5, find the minimum value.
Show solution
Solution
The vertex occurs at x = 2. f(2) = 2^2 - 4*2 + 5 = 1, which is the minimum value.
Correct Answer:
B
— 2
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Q. For the function f(x) = x^2 - 4x + 5, find the vertex.
A.
(2, 1)
B.
(2, 5)
C.
(4, 1)
D.
(4, 5)
Show solution
Solution
The vertex is at x = -b/(2a) = 4/2 = 2. f(2) = 2^2 - 4(2) + 5 = 1, so the vertex is (2, 1).
Correct Answer:
A
— (2, 1)
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Q. For the function f(x) = x^2 - 6x + 8, find the x-coordinate of the vertex.
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Solution
The x-coordinate of the vertex is given by x = -b/(2a) = 6/(2*1) = 3.
Correct Answer:
B
— 3
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Q. For the function f(x) = x^3 - 3x^2 + 2, find the points where it is not differentiable.
A.
None
B.
x = 0
C.
x = 1
D.
x = 2
Show solution
Solution
As a polynomial, f(x) is differentiable everywhere, hence no points of non-differentiability.
Correct Answer:
A
— None
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Q. For the function f(x) = x^3 - 3x^2 + 4, find the points where it is not differentiable.
A.
None
B.
x = 0
C.
x = 1
D.
x = 2
Show solution
Solution
The function is a polynomial and is differentiable everywhere, hence there are no points where it is not differentiable.
Correct Answer:
A
— None
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Q. For the function f(x) = x^3 - 3x^2 + 4, find the value of x where f is not differentiable.
Show solution
Solution
The function is a polynomial and is differentiable everywhere, so there is no such x.
Correct Answer:
A
— 0
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Q. For the function f(x) = x^3 - 3x^2 + 4, find the x-coordinate of the point where f is differentiable.
Show solution
Solution
f(x) is a polynomial and is differentiable everywhere. The x-coordinate can be any real number.
Correct Answer:
C
— 1
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Q. For the function f(x) = x^3 - 6x^2 + 9x, find the critical points.
A.
x = 0, 3
B.
x = 1, 2
C.
x = 2, 3
D.
x = 3, 4
Show solution
Solution
First, find f'(x) = 3x^2 - 12x + 9. Setting f'(x) = 0 gives (x - 3)(x - 1) = 0, so critical points are x = 1 and x = 3.
Correct Answer:
A
— x = 0, 3
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Q. For the function f(x) = x^3 - 6x^2 + 9x, find the intervals where the function is increasing.
A.
(-∞, 0)
B.
(0, 3)
C.
(3, ∞)
D.
(0, 6)
Show solution
Solution
f'(x) = 3x^2 - 12x + 9. The critical points are x = 1 and x = 3. The function is increasing on (1, 3) and (3, ∞).
Correct Answer:
B
— (0, 3)
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Q. For the function f(x) = x^4 - 8x^2 + 16, find the coordinates of the inflection point.
A.
(0, 16)
B.
(2, 0)
C.
(4, 0)
D.
(2, 4)
Show solution
Solution
Find f''(x) = 12x^2 - 16. Setting f''(x) = 0 gives x^2 = 4, so x = ±2. f(2) = 0, thus the inflection point is (2, 0).
Correct Answer:
B
— (2, 0)
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Q. For the function f(x) = x^4 - 8x^2 + 16, find the intervals where the function is increasing.
A.
(-∞, -2)
B.
(-2, 2)
C.
(2, ∞)
D.
(-2, ∞)
Show solution
Solution
f'(x) = 4x^3 - 16x. Setting f'(x) = 0 gives x(x^2 - 4) = 0, so x = -2, 0, 2. Test intervals: f' is positive in (-2, ∞).
Correct Answer:
D
— (-2, ∞)
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Q. For the function f(x) = { x^2 + 1, x < 0; 2x + b, x = 0; 3 - x, x > 0 to be continuous at x = 0, what is b?
Show solution
Solution
Setting the left limit (0 + 1 = 1) equal to the right limit (3 - 0 = 3), we find b = 1.
Correct Answer:
B
— 0
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Q. For the function f(x) = { x^2, x < 1; 3, x = 1; 2x, x > 1 }, what is the value of f(1)?
Show solution
Solution
By definition, f(1) = 3, as given in the piecewise function.
Correct Answer:
C
— 3
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Q. For the function f(x) = { x^2, x < 1; kx + 1, x >= 1 }, find k such that f is differentiable at x = 1.
Show solution
Solution
Setting f(1-) = f(1+) and f'(1-) = f'(1+) gives k = 2 for differentiability.
Correct Answer:
B
— 1
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Q. For the function f(x) = { x^2, x < 3; 9, x = 3; 3x, x > 3 } to be continuous at x = 3, the value of f(3) must be:
Show solution
Solution
For continuity, f(3) must equal the limit as x approaches 3, which is 9.
Correct Answer:
B
— 9
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Q. For the function f(x) = |x - 2| + |x + 3|, find the point where it is not differentiable.
Show solution
Solution
The function is not differentiable at x = -3 and x = 2, but the first point of interest is -3.
Correct Answer:
A
— -3
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