Engineering & Architecture Admissions - Exam Prep Guide

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Engineering & Architecture Admissions

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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.

JEE Main

Q. If the true value of a measurement is 50.0 units and the measured value is 48.0 units, what is the percentage error?

A. 4.0%
B. 2.0%
C. 5.0%
D. 3.0%

Solution

Percentage error = |(True value - Measured value) / True value| * 100 = |(50.0 - 48.0) / 50.0| * 100 = 4.0%.

Correct Answer: A — 4.0%

Q. If the true value of a quantity is 100 and the measured value is 98, what is the percentage error?

A. 2%
B. 1%
C. 3%
D. 0.5%

Solution

Percentage error = (|True value - Measured value| / True value) * 100 = (|100 - 98| / 100) * 100 = 2%.

Correct Answer: A — 2%

Q. If the true value of a quantity is 200 and the measured value is 198, what is the percentage error?

A. 1%
B. 0.5%
C. 2%
D. 0.25%

Solution

Percentage error = (|True value - Measured value| / True value) * 100 = (|200 - 198| / 200) * 100 = 1%.

Correct Answer: A — 1%

Q. If the universal set U = {1, 2, 3, 4, 5} and A = {1, 2}, what is A'?

A. {3, 4, 5}
B. {1, 2}
C. {1, 2, 3}
D. {2, 3, 4, 5}

Solution

The complement of A, denoted A', includes all elements in U that are not in A. Thus, A' = {3, 4, 5}.

Correct Answer: A — {3, 4, 5}

Q. If the value of one of the resistances in a Wheatstone bridge is doubled, what effect does it have on the balance condition?

A. It remains balanced
B. It becomes unbalanced
C. It depends on other resistances
D. It cannot be determined

Solution

Doubling one resistance will change the ratio, thus making the bridge unbalanced.

Correct Answer: B — It becomes unbalanced

Q. If the value of one of the resistances in a Wheatstone bridge is increased, what effect does it have on the balance of the bridge?

A. It remains balanced
B. It becomes unbalanced
C. It depends on the other resistances
D. It becomes short-circuited

Solution

Increasing one resistance will generally cause the bridge to become unbalanced.

Correct Answer: B — It becomes unbalanced

Q. If the vapor pressure of a pure solvent is 80 mmHg and a non-volatile solute is added, resulting in a vapor pressure of 60 mmHg, what is the mole fraction of the solvent in the solution?

A. 0.75
B. 0.50
C. 0.25
D. 0.80

Solution

Using Raoult's Law, P_solution = X_solvent * P_pure_solvent; 60 mmHg = X_solvent * 80 mmHg; X_solvent = 60/80 = 0.75.

Correct Answer: A — 0.75

Q. If the vapor pressure of a solution is 80 mmHg and the vapor pressure of the pure solvent is 120 mmHg, what is the mole fraction of the solvent in the solution?

A. 0.67
B. 0.33
C. 0.50
D. 0.75

Solution

Using Raoult's Law, P_solution = X_solvent * P_solvent^0; 80 = X_solvent * 120; X_solvent = 80/120 = 0.67.

Correct Answer: A — 0.67

Q. If the vapor pressure of pure solvent A is 100 mmHg, and the mole fraction of A in the solution is 0.6, what is the vapor pressure of the solution according to Raoult's Law?

A. 60 mmHg
B. 100 mmHg
C. 40 mmHg
D. 80 mmHg

Solution

Using Raoult's Law, P_solution = X_A * P_A^0 = 0.6 * 100 mmHg = 60 mmHg.

Correct Answer: A — 60 mmHg

Q. If the vapor pressure of pure solvent A is 100 mmHg, and the mole fraction of A in the solution is 0.5, what is the vapor pressure of the solution according to Raoult's Law?

A. 50 mmHg
B. 100 mmHg
C. 150 mmHg
D. 200 mmHg

Solution

According to Raoult's Law, P_solution = X_A * P_A^0 = 0.5 * 100 mmHg = 50 mmHg.

Correct Answer: A — 50 mmHg

Q. If the vapor pressure of pure solvent A is 100 mmHg, what is the vapor pressure of a solution containing 0.5 mole fraction of A?

A. 50 mmHg
B. 100 mmHg
C. 75 mmHg
D. 25 mmHg

Solution

According to Raoult's Law, the vapor pressure of the solution is 0.5 * 100 mmHg = 50 mmHg.

Correct Answer: A — 50 mmHg

Q. If the vapor pressure of pure solvent is 120 mmHg, what will be the vapor pressure of a solution containing 0.2 moles of solute in 1 mole of solvent?

A. 100 mmHg
B. 110 mmHg
C. 120 mmHg
D. 80 mmHg

Solution

Using Raoult's Law, the vapor pressure of the solution is P_solution = P_solvent * X_solvent = 120 * (1/(1+0.2)) = 120 * (1/1.2) = 100 mmHg.

Correct Answer: B — 110 mmHg

Q. If the vapor pressure of pure solvent is 80 mmHg and the mole fraction of the solvent in the solution is 0.75, what is the vapor pressure of the solution?

A. 60 mmHg
B. 80 mmHg
C. 75 mmHg
D. 20 mmHg

Solution

Using Raoult's Law, P_solution = X_solvent * P_solvent^0 = 0.75 * 80 mmHg = 60 mmHg.

Correct Answer: A — 60 mmHg

Q. If the vapor pressure of pure water is 23.8 mmHg at 25°C, what is the vapor pressure of a solution containing 1 mole of NaCl in 1 kg of water?

A. 20.0 mmHg
B. 22.0 mmHg
C. 23.0 mmHg
D. 23.8 mmHg

Solution

Using Raoult's law, the vapor pressure lowering is calculated considering the van 't Hoff factor for NaCl.

Correct Answer: B — 22.0 mmHg

Q. If the variance of a data set is 16, what is the standard deviation?

A. 4
B. 8
C. 16
D. 2

Solution

Standard deviation = √variance = √16 = 4.

Correct Answer: A — 4

Q. If the vector A = (1, 2) and B = (2, 1), what is the angle between them?

A. 0 degrees
B. 90 degrees
C. 45 degrees
D. 180 degrees

Solution

Cosine of angle = (A · B) / (|A| |B|) = (1*2 + 2*1) / (√5 * √5) = 4/5, angle = cos^(-1)(4/5).

Correct Answer: C — 45 degrees

Q. If the vector a = (1, 2) and b = (3, 4), find the angle between them using the dot product.

A. 0 degrees
B. 90 degrees
C. 45 degrees
D. 60 degrees

Solution

cos(θ) = (a · b) / (|a| |b|). a · b = 1*3 + 2*4 = 11, |a| = √(1^2 + 2^2) = √5, |b| = √(3^2 + 4^2) = 5. Thus, cos(θ) = 11 / (√5 * 5) = 11 / (5√5), θ = 60 degrees.

Correct Answer: D — 60 degrees

Q. If the vector a = (2, -1) and b = (1, 3), what is a + b?

A. (3, 2)
B. (1, 2)
C. (2, 2)
D. (3, 1)

Solution

a + b = (2 + 1, -1 + 3) = (3, 2)

Correct Answer: A — (3, 2)

Q. If the vector a = (2, -1) and b = (1, 3), what is the cross product a × b?

A. 5
B. 7
C. 1
D. 0

Solution

Cross product in 2D = a1*b2 - a2*b1 = 2*3 - (-1)*1 = 6 + 1 = 7

Correct Answer: A — 5

Q. If the vector a = (2, 2) and b = (2, -2), what is the angle between them?

A. 90 degrees
B. 45 degrees
C. 0 degrees
D. 180 degrees

Solution

Angle = cos⁻¹((a·b) / (|a||b|)) = cos⁻¹(0) = 90 degrees

Correct Answer: A — 90 degrees

Q. If the vector a = (2, 2) is scaled by a factor of 3, what is the resulting vector?

A. (6, 6)
B. (3, 3)
C. (2, 2)
D. (1, 1)

Solution

Scaled vector = 3 * a = 3 * (2, 2) = (6, 6)

Correct Answer: A — (6, 6)

Q. If the vector a = (2, 3) and b = (4, 1), what is the cross product a × b?

A. -10
B. 10
C. 0
D. 5

Solution

Cross product a × b = 2*1 - 3*4 = 2 - 12 = -10.

Correct Answer: A — -10

Q. If the vector a = (2, 3) and b = (4, 1), what is the resultant vector a + b?

A. (6, 4)
B. (2, 4)
C. (4, 2)
D. (6, 2)

Solution

Resultant vector a + b = (2+4, 3+1) = (6, 4).

Correct Answer: A — (6, 4)

Q. If the vector A = (2, 3) is multiplied by 2, what is the resulting vector?

A. (4, 6)
B. (2, 3)
C. (1, 1.5)
D. (0, 0)

Solution

Resulting vector = 2 * A = 2 * (2, 3) = (4, 6).

Correct Answer: A — (4, 6)

Q. If the vector A = (2, 3) is reflected across the line y = x, what is the resulting vector?

A. (3, 2)
B. (2, 3)
C. (0, 0)
D. (1, 1)

Solution

Reflection across y = x gives vector (3, 2).

Correct Answer: A — (3, 2)

Q. If the vector A = (2, 3) is scaled by a factor of 2, what is the resulting vector?

A. (4, 6)
B. (2, 3)
C. (1, 1.5)
D. (0, 0)

Solution

Scaled vector = 2 * A = 2 * (2, 3) = (4, 6).

Correct Answer: A — (4, 6)

Q. If the vector a = (2, 3, 4) and b = (1, 0, -1), what is a + b?

A. (3, 3, 3)
B. (1, 3, 3)
C. (2, 3, 3)
D. (2, 3, 5)

Solution

a + b = (2+1, 3+0, 4-1) = (3, 3, 3).

Correct Answer: A — (3, 3, 3)

Q. If the vector a = (2, 3, 4) and b = (1, 0, -1), what is the scalar triple product a · (b × a)?

A. 0
B. 1
C. 2
D. 3

Solution

The scalar triple product is 0 because a · (b × a) = 0.

Correct Answer: A — 0

Q. If the vector a = (2, 3, 4) is scaled by a factor of 2, what is the resulting vector?

A. (4, 6, 8)
B. (2, 3, 4)
C. (1, 1.5, 2)
D. (0, 0, 0)

Solution

Scaling the vector a by 2 gives (2*2, 2*3, 2*4) = (4, 6, 8).

Correct Answer: A — (4, 6, 8)

Q. If the vector a = (3, 4) and b = (1, 2), find the cross product a × b.

A. -2
B. 2
C. 0
D. 1

Solution

In 2D, a × b = a1*b2 - a2*b1 = 3*2 - 4*1 = 6 - 4 = 2.

Correct Answer: A — -2

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