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 n=4 and l=2, what is the type of orbital?

A. s
B. p
C. d
D. f

Solution

For l=2, the orbital type is d.

Correct Answer: C — d

Q. If one of the resistors in a Wheatstone bridge is replaced with a variable resistor, what is the effect on the balance condition?

A. It cannot be balanced
B. It can be balanced by adjusting the variable resistor
C. It will always be unbalanced
D. It will short-circuit the bridge

Solution

The variable resistor allows for adjustment to achieve balance in the bridge.

Correct Answer: B — It can be balanced by adjusting the variable resistor

Q. If one root of the equation x^2 - 3x + p = 0 is 2, what is the value of p?

A. 1
B. 2
C. 3
D. 4

Solution

Substituting x = 2 into the equation gives 2^2 - 3*2 + p = 0 => 4 - 6 + p = 0 => p = 2.

Correct Answer: D — 4

Q. If one root of the equation x^2 - 6x + k = 0 is 2, what is the value of k?

A. 4
B. 6
C. 8
D. 10

Solution

Using the root, we substitute: 2^2 - 6*2 + k = 0 => 4 - 12 + k = 0 => k = 8.

Correct Answer: A — 4

Q. If one root of the equation x^2 - 7x + k = 0 is 3, what is the value of k?

A. 6
B. 9
C. 12
D. 15

Solution

Using Vieta's formulas, if one root is 3, the other root is 7 - 3 = 4. Thus, k = 3 * 4 = 12.

Correct Answer: B — 9

Q. If R is a relation defined on set A = {1, 2, 3} such that R = {(1, 2), (2, 3)}, is R a function?

A. Yes
B. No
C. Depends on A
D. Not enough information

Solution

A relation is a function if every element in the domain (set A) maps to exactly one element in the codomain. Here, 1 maps to 2, and 2 maps to 3, but 3 has no mapping, so R is not a function.

Correct Answer: B — No

Q. If R is a relation on set A = {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3)}, is R reflexive?

A. Yes
B. No
C. Depends on A
D. None of the above

Solution

A relation R is reflexive if every element in set A is related to itself. Since R contains (1, 1), (2, 2), and (3, 3), R is reflexive.

Correct Answer: A — Yes

Q. If R is a relation on set A = {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3)}, is R symmetric?

A. Yes
B. No
C. Depends on A
D. None of the above

Solution

A relation is symmetric if for every (a, b) in R, (b, a) is also in R. Since R only contains pairs of the form (a, a), it is symmetric.

Correct Answer: A — Yes

Q. If R is a relation on set A = {1, 2, 3} defined by R = {(1, 2), (2, 3)}, is R transitive?

A. Yes
B. No
C. Not enough information
D. None of the above

Solution

A relation R is transitive if whenever (a, b) ∈ R and (b, c) ∈ R, then (a, c) must also be in R. Here, (1, 2) and (2, 3) are in R, but (1, 3) is not, so R is not transitive.

Correct Answer: B — No

Q. If R is a relation on the set A = {1, 2, 3} defined by R = {(1, 2), (2, 3), (3, 1)}, which of the following properties does R possess?

A. Reflexive
B. Symmetric
C. Transitive
D. All of the above

Solution

R is not reflexive as (1,1), (2,2), (3,3) are not in R. It is symmetric as (2,3) implies (3,2) is not in R. It is transitive as (1,2) and (2,3) implies (1,3) is not in R. Thus, R is not all of the above.

Correct Answer: C — Transitive

Q. If R is a relation on the set {1, 2, 3, 4} defined by R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1)}, what type of relation is R?

A. Reflexive
B. Symmetric
C. Transitive
D. Both reflexive and symmetric

Solution

R is reflexive because it contains all pairs (a, a) and symmetric because (1,2) implies (2,1).

Correct Answer: D — Both reflexive and symmetric

Q. If R is a relation on the set {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3), (1, 2)}, is R a partial order?

A. Yes
B. No
C. Only reflexive
D. Only transitive

Solution

R is not a partial order because it is not transitive; (1,2) and (2,2) do not imply (1,2).

Correct Answer: B — No

Q. If R is a relation on the set {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}, which of the following is true?

A. R is reflexive
B. R is symmetric
C. R is transitive
D. Both 1 and 2

Solution

R is reflexive and symmetric, but not transitive. Thus, both 1 and 2 are true.

Correct Answer: D — Both 1 and 2

Q. If R is a relation on the set {a, b, c} defined by R = {(a, b), (b, c)}, what can be said about R?

A. Reflexive
B. Symmetric
C. Transitive
D. None of the above

Solution

R is neither reflexive, symmetric, nor transitive as it does not satisfy any of the properties.

Correct Answer: D — None of the above

Q. If R is a relation on the set {a, b, c} defined by R = {(a, b), (b, c)}, which property does R NOT have?

A. Reflexive
B. Symmetric
C. Transitive
D. None of the above

Solution

R is not symmetric as (b,c) does not imply (c,b) is in R. It is reflexive and transitive.

Correct Answer: B — Symmetric

Q. If R is a relation on the set {x, y, z} defined by R = {(x, y), (y, z), (z, x)}, what can be said about R?

A. Reflexive
B. Symmetric
C. Transitive
D. None of the above

Solution

R is neither reflexive, symmetric, nor transitive.

Correct Answer: D — None of the above

Q. If R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, what should R4 be for the Wheatstone bridge to be balanced?

A. 7.5Ω
B. 10Ω
C. 12.5Ω
D. 15Ω

Solution

Using the balance condition R1/R2 = R3/R4, we find R4 = (R2 * R3) / R1 = (15 * 5) / 10 = 7.5Ω.

Correct Answer: C — 12.5Ω

Q. If R1 = 10Ω, R2 = 20Ω, and R3 = 30Ω in a Wheatstone bridge, what should R4 be for the bridge to be balanced?

A. 15Ω
B. 20Ω
C. 25Ω
D. 30Ω

Solution

For balance, R1/R2 = R3/R4, thus R4 = (R2 * R3) / R1 = (20 * 30) / 10 = 60Ω.

Correct Answer: B — 20Ω

Q. If R1 = 10Ω, R2 = 20Ω, R3 = 30Ω, and R4 = 60Ω in a Wheatstone bridge, is the bridge balanced?

A. Yes
B. No
C. Depends on the voltage
D. Depends on the current

Solution

The bridge is not balanced because 10/20 ≠ 30/60.

Correct Answer: B — No

Q. If R1 = 2Ω, R2 = 3Ω, and R3 = 6Ω in a Wheatstone bridge, what is the value of R4 for balance?

A. 4Ω
B. 5Ω
C. 6Ω
D. 9Ω

Solution

Using the balance condition R1/R2 = R3/R4, we have 2/3 = 6/R4. Solving gives R4 = 4Ω.

Correct Answer: A — 4Ω

Q. If R1 = 2Ω, R2 = 3Ω, and R3 = 6Ω, what is the value of R4 for the Wheatstone bridge to be balanced?

A. 4Ω
B. 5Ω
C. 6Ω
D. 8Ω

Solution

Using the balance condition R1/R2 = R3/R4, we have 2/3 = 6/R4. Solving gives R4 = 4Ω.

Correct Answer: A — 4Ω

Q. If R1 = 5Ω, R2 = 10Ω, and R3 = 15Ω in a Wheatstone bridge, what is the value of R4 for balance?

A. 7.5Ω
B. 10Ω
C. 15Ω
D. 20Ω

Solution

Using the balance condition R1/R2 = R3/R4, we find R4 = (R2 * R3) / R1 = (10 * 15) / 5 = 30Ω.

Correct Answer: B — 10Ω

Q. If R1 = 5Ω, R2 = 15Ω, R3 = 10Ω, what should R4 be for the Wheatstone bridge to be balanced?

A. 30Ω
B. 10Ω
C. 15Ω
D. 5Ω

Solution

For balance, R4 must be 30Ω since 5/15 = 10/30.

Correct Answer: B — 10Ω

Q. If sec A = 2, what is the value of cos A?

A. 1/2
B. 2
C. √2
D. 1

Solution

Since sec A = 1/cos A, we have cos A = 1/2.

Correct Answer: A — 1/2

Q. If sec θ = 2, what is the value of cos θ?

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

Solution

Since sec θ = 1/cos θ, if sec θ = 2, then cos θ = 1/2.

Correct Answer: A — 1/2

Q. If sec(x) = 2, what is the value of cos(x)?

A. 1/2
B. 2
C. √3/2
D. 1

Solution

sec(x) = 1/cos(x), so cos(x) = 1/2.

Correct Answer: A — 1/2

Q. If sin A = 0.6, what is cos A?

A. 0.8
B. 0.6
C. 0.4
D. 0.2

Solution

Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (0.6)^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.8.

Correct Answer: A — 0.8

Q. If sin A = 0.6, what is the value of cos A?

A. 0.8
B. 0.6
C. 0.4
D. 0.2

Solution

Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (0.6)^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.8.

Correct Answer: A — 0.8

Q. If sin A = 0.6, what is the value of tan A?

A. 0.8
B. 1.2
C. 0.75
D. 1.5

Solution

Using the identity tan A = sin A / cos A, we find cos A = sqrt(1 - (0.6)^2) = 0.8, thus tan A = 0.6 / 0.8 = 0.75.

Correct Answer: B — 1.2

Q. If sin A = 1/2, what are the possible values of A in the range [0°, 360°]?

A. 30°, 150°
B. 45°, 135°
C. 60°, 300°
D. 90°, 270°

Solution

sin A = 1/2 at A = 30° and A = 150°.

Correct Answer: A — 30°, 150°

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