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. At what temperature does a reaction become spontaneous if ΔH = 50 kJ and ΔS = 0.1 kJ/K?
A.
500 K
B.
250 K
C.
1000 K
D.
200 K
Show solution
Solution
Set ΔG = 0: 0 = ΔH - TΔS; T = ΔH/ΔS = 50 kJ / 0.1 kJ/K = 500 K.
Correct Answer:
A
— 500 K
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Q. At what temperature does the Gibbs Free Energy change from negative to positive?
A.
At absolute zero
B.
At the melting point
C.
At the boiling point
D.
At the transition temperature
Show solution
Solution
The Gibbs Free Energy changes from negative to positive at the transition temperature, where the system shifts from one phase to another.
Correct Answer:
D
— At the transition temperature
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Q. At what temperature does the volume of a gas become zero according to Charles's Law?
A.
0 K
B.
-273.15 °C
C.
273.15 K
D.
None of the above
Show solution
Solution
According to Charles's Law, the volume of a gas approaches zero at absolute zero, which is -273.15 °C.
Correct Answer:
B
— -273.15 °C
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Q. At what temperature does the volume of a gas theoretically become zero?
A.
0°C
B.
0 K
C.
273 K
D.
100 K
Show solution
Solution
According to Charles's Law, the volume of a gas approaches zero at absolute zero, which is 0 K.
Correct Answer:
B
— 0 K
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Q. At what temperature will the RMS speed of a gas be 1000 m/s if its molar mass is 0.044 kg/mol? (R = 8.314 J/(mol K))
A.
500 K
B.
600 K
C.
700 K
D.
800 K
Show solution
Solution
Using v_rms = sqrt(3RT/M), we solve for T: T = (v_rms^2 * M) / (3R) = (1000^2 * 0.044) / (3 * 8.314) = 700 K.
Correct Answer:
C
— 700 K
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Q. At what temperature will the RMS speed of a gas be 1000 m/s if its molar mass is 0.044 kg/mol?
A.
300 K
B.
400 K
C.
500 K
D.
600 K
Show solution
Solution
Using v_rms = sqrt(3RT/M), we rearrange to find T = (v_rms^2 * M) / (3R). Plugging in values gives T approximately 500 K.
Correct Answer:
C
— 500 K
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Q. At what temperature will the RMS speed of a gas be 300 m/s if its molar mass is 28 g/mol?
A.
300 K
B.
600 K
C.
900 K
D.
1200 K
Show solution
Solution
Using the formula v_rms = sqrt((3RT)/M), we can rearrange to find T. Setting v_rms = 300 m/s and M = 28 g/mol, we find T = (M * v_rms^2)/(3R) = 600 K.
Correct Answer:
B
— 600 K
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Q. At what temperature will the RMS speed of a gas be 500 m/s if its molar mass is 0.02 kg/mol? (2000)
A.
250 K
B.
500 K
C.
1000 K
D.
2000 K
Show solution
Solution
Using v_rms = sqrt(3RT/M), rearranging gives T = (v_rms^2 * M) / (3R). Substituting values gives T = 500 K.
Correct Answer:
B
— 500 K
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Q. At what temperature will the RMS speed of a gas be 600 m/s if its molar mass is 0.02 kg/mol?
A.
300 K
B.
600 K
C.
900 K
D.
1200 K
Show solution
Solution
Using v_rms = sqrt(3RT/M), we can rearrange to find T = (v_rms^2 * M) / (3R). Plugging in values gives T = (600^2 * 0.02) / (3 * 8.314) = 900 K.
Correct Answer:
C
— 900 K
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Q. Calculate the area between the curves y = x and y = x^2 from x = 0 to x = 1.
A.
0.25
B.
0.5
C.
0.75
D.
1
Show solution
Solution
The area is given by the integral from 0 to 1 of (x - x^2) dx. This evaluates to [x^2/2 - x^3/3] from 0 to 1 = (1/2 - 1/3) = 1/6 = 0.5.
Correct Answer:
B
— 0.5
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Q. Calculate the area between the curves y = x^2 and y = 2x from x = 0 to x = 2.
Show solution
Solution
The area is given by the integral from 0 to 2 of (2x - x^2) dx. This evaluates to [x^2 - x^3/3] from 0 to 2 = (4 - 8/3) = 4/3.
Correct Answer:
A
— 2
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Q. Calculate the area between the curves y = x^2 and y = 4 from x = 0 to x = 2.
Show solution
Solution
The area is given by the integral from 0 to 2 of (4 - x^2) dx. This evaluates to [4x - x^3/3] from 0 to 2 = (8 - 8/3) = 16/3.
Correct Answer:
A
— 4
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Q. Calculate the area under the curve y = cos(x) from x = 0 to x = π/2.
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Solution
The area under the curve y = cos(x) from x = 0 to x = π/2 is given by ∫(from 0 to π/2) cos(x) dx = [sin(x)] from 0 to π/2 = 1 - 0 = 1.
Correct Answer:
A
— 1
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Q. Calculate the area under the curve y = x^2 + 2x from x = 0 to x = 2.
Show solution
Solution
The area under the curve is given by ∫(from 0 to 2) (x^2 + 2x) dx = [x^3/3 + x^2] from 0 to 2 = (8/3 + 4) = 20/3.
Correct Answer:
B
— 6
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Q. Calculate the area under the curve y = x^4 from x = 0 to x = 2.
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Solution
The area under the curve y = x^4 from x = 0 to x = 2 is given by ∫(from 0 to 2) x^4 dx = [x^5/5] from 0 to 2 = (32/5) - 0 = 32/5.
Correct Answer:
B
— 8
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Q. Calculate the derivative of f(x) = e^(2x).
A.
2e^(2x)
B.
e^(2x)
C.
2xe^(2x)
D.
e^(x)
Show solution
Solution
Using the chain rule, f'(x) = d/dx(e^(2x)) = 2e^(2x).
Correct Answer:
A
— 2e^(2x)
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Q. Calculate the derivative of f(x) = x^2 * e^x.
A.
(2x + x^2)e^x
B.
2xe^x
C.
x^2e^x
D.
(x^2 + 2x)e^x
Show solution
Solution
Using the product rule, f'(x) = d/dx(x^2 * e^x) = (x^2 + 2x)e^x.
Correct Answer:
D
— (x^2 + 2x)e^x
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Q. Calculate the determinant of the matrix [[1, 2], [3, 4]].
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Solution
Determinant = (1*4) - (2*3) = 4 - 6 = -2.
Correct Answer:
A
— -2
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Q. Calculate the determinant of the matrix \( B = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \).
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Solution
The determinant is calculated as \( 2*7 - 3*5 = 14 - 15 = -1 \).
Correct Answer:
D
— 10
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Q. Calculate the determinant of the matrix \( G = \begin{pmatrix} 2 & 1 & 3 \\ 1 & 0 & 1 \\ 3 & 1 & 2 \end{pmatrix} \).
Show solution
Solution
The determinant is calculated as \( 2(0*2 - 1*1) - 1(1*2 - 3*1) + 3(1*1 - 3*0) = 0 \).
Correct Answer:
A
— -1
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Q. Calculate the determinant of the matrix \( \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \).
Show solution
Solution
The determinant is calculated as \( 2*4 - 3*1 = 8 - 3 = 5 \).
Correct Answer:
A
— 5
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Q. Calculate the determinant of the matrix \( \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \).
Show solution
Solution
The determinant is calculated as (2*7) - (3*5) = 14 - 15 = -1.
Correct Answer:
A
— 1
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Q. Calculate the determinant of the matrix: | 1 1 1 | | 2 2 2 | | 3 3 3 |
Show solution
Solution
The rows are linearly dependent, hence the determinant is 0.
Correct Answer:
A
— 0
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Q. Calculate the determinant \( \begin{vmatrix} 1 & 2 & 1 \\ 2 & 3 & 1 \\ 3 & 4 & 1 \end{vmatrix} \).
Show solution
Solution
The determinant is 0 because the rows are linearly dependent.
Correct Answer:
A
— 0
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Q. Calculate the determinant \( \begin{vmatrix} 2 & 3 \\ 5 & 7 \end{vmatrix} \)
Show solution
Solution
The determinant is \( 2*7 - 3*5 = 14 - 15 = -1 \).
Correct Answer:
A
— 1
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Q. Calculate the determinant \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \)
A.
ad - bc
B.
ab + cd
C.
ac - bd
D.
bc - ad
Show solution
Solution
The determinant is calculated as \( ad - bc \).
Correct Answer:
A
— ad - bc
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Q. Calculate the determinant | 1 0 0 | | 0 1 0 | | 0 0 1 |.
Show solution
Solution
The determinant of the identity matrix is 1.
Correct Answer:
B
— 1
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Q. Calculate the determinant | 2 3 | | 4 5 | + | 1 1 | | 1 1 |.
Show solution
Solution
The first determinant is -2 and the second is 0, so the total is -2 + 0 = -2.
Correct Answer:
B
— 1
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Q. Calculate the determinant: | 2 3 1 | | 1 0 2 | | 0 1 3 |.
Show solution
Solution
The determinant evaluates to 0 as the rows are linearly dependent.
Correct Answer:
A
— -1
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Q. Calculate the determinant: | 2 3 1 | | 1 0 4 | | 0 5 2 |.
Show solution
Solution
Using the determinant formula, we find that the determinant evaluates to 0.
Correct Answer:
A
— -1
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