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 which of the following molecules is the bond order equal to 0?
A.
He2
B.
H2
C.
Li2
D.
Be2
Show solution
Solution
He2 has a bond order of 0, as it has equal bonding and antibonding electrons.
Correct Answer:
A
— He2
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Q. For which of the following molecules is the molecular orbital diagram similar to that of O2?
Show solution
Solution
The molecular orbital diagram of F2 is similar to that of O2, with the same energy level arrangement.
Correct Answer:
B
— F2
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Q. For which of the following pairs of molecules is the bond order the same?
A.
N2 and C2
B.
O2 and F2
C.
B2 and C2
D.
N2 and O2
Show solution
Solution
O2 and F2 both have a bond order of 2.
Correct Answer:
B
— O2 and F2
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Q. For which value of a is the function f(x) = x^2 + ax + 1 differentiable at x = -1?
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Solution
To ensure differentiability at x = -1, we find f'(-1) exists. Setting a = 0 ensures the derivative is defined.
Correct Answer:
B
— 0
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Q. For which value of a is the function f(x) = x^2 + ax + 1 differentiable everywhere?
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Solution
The function is a polynomial and is differentiable for all real numbers, hence any value of a works.
Correct Answer:
B
— 0
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Q. For which value of a is the function f(x) = x^2 - ax + 2 differentiable at x = 1?
Show solution
Solution
Setting the derivative f'(1) = 0 gives a = 1 for differentiability.
Correct Answer:
B
— 1
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Q. For which value of a is the function f(x) = x^2 - ax + 4 differentiable at x = 2?
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Solution
f(x) is a polynomial and is differentiable for all a, hence any value of a works.
Correct Answer:
A
— 0
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Q. For which value of a is the function f(x) = x^3 - 3ax + 2 differentiable at x = 1?
Show solution
Solution
Setting f'(1) = 0 gives a = 1, ensuring differentiability at that point.
Correct Answer:
B
— 1
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Q. For which value of a is the function f(x) = x^3 - 3ax^2 + 3a^2x + 1 differentiable at x = 1?
Show solution
Solution
Setting f'(1) = 0 gives a = 1 for differentiability at x = 1.
Correct Answer:
B
— 1
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Q. For which value of a is the function f(x) = { 2x + a, x < 0; x^2 + 1, x >= 0 continuous at x = 0?
Show solution
Solution
Setting a = 1 gives continuity at x = 0.
Correct Answer:
B
— 0
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Q. For which value of a is the function f(x) = { 3x + a, x < 2; 4x - 1, x >= 2 continuous at x = 2?
Show solution
Solution
Setting 3(2) + a = 4(2) - 1 gives a = 1.
Correct Answer:
A
— -1
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Q. For which value of a is the function f(x) = { ax + 1, x < 0; 2, x = 0; 3x - 1, x > 0 } continuous at x = 0?
Show solution
Solution
Setting ax + 1 = 2 at x = 0 gives a = 2.
Correct Answer:
A
— -1
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Q. For which value of a is the function f(x) = { ax + 1, x < 0; 2x + a, x >= 0 } continuous at x = 0?
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Solution
Setting the two pieces equal at x = 0 gives 1 = a, hence a = 1.
Correct Answer:
A
— -1
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Q. For which value of a is the function f(x) = { ax + 2, x < 1; 3, x >= 1 } continuous at x = 1?
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Solution
Setting ax + 2 = 3 at x = 1 gives a = 1.
Correct Answer:
B
— 2
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Q. For which value of a is the function f(x) = { x^2 + a, x < 1; 3, x >= 1 } continuous at x = 1?
Show solution
Solution
To ensure continuity at x = 1, we set limit as x approaches 1 from left (1 + a) equal to f(1) = 3, thus a = 2.
Correct Answer:
B
— 2
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Q. For which value of a is the function f(x) = { x^2 - a, x < 0; 2x + 1, x >= 0 } continuous at x = 0?
Show solution
Solution
Setting the two pieces equal at x = 0 gives -a = 1, so a = -1.
Correct Answer:
A
— -1
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Q. For which value of a is the function f(x) = { x^2 - a, x < 1; 3x - 2, x >= 1 } continuous at x = 1?
Show solution
Solution
Setting the two pieces equal at x = 1 gives 1 - a = 1. Thus, a = 0.
Correct Answer:
C
— 2
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Q. For which value of a is the function f(x) = { x^2, x < 1; ax + 1, x >= 1 } continuous at x = 1?
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Solution
Setting the two pieces equal at x = 1 gives 1 = a(1) + 1, leading to a = 0.
Correct Answer:
C
— 2
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Q. For which value of b is the function f(x) = { 2x + 1, x < 1; b, x = 1; x^2 + 1, x > 1 continuous at x = 1?
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Solution
Setting the left limit (2(1) + 1 = 3) equal to the right limit (1^2 + 1 = 2), we find b = 3.
Correct Answer:
B
— 2
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Q. For which value of b is the function f(x) = { x^2 - 1, x < 1; b, x = 1; 3x - 2, x > 1 continuous at x = 1?
Show solution
Solution
Setting limit as x approaches 1 gives b = 2 for continuity.
Correct Answer:
C
— 2
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Q. For which value of b is the function f(x) = { x^2 - 4, x < 2; bx + 2, x >= 2 } continuous at x = 2?
Show solution
Solution
Setting the two pieces equal at x = 2 gives us 0 = 2b + 2. Solving for b gives b = -1.
Correct Answer:
B
— 4
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Q. For which value of b is the function f(x) = { x^3 - 3x + b, x < 1; 2x + 1, x >= 1 continuous at x = 1?
Show solution
Solution
Setting 1 - 3 + b = 2 gives b = 4 for continuity.
Correct Answer:
A
— 0
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Q. For which value of c is the function f(x) = { 3x + c, x < 1; 2x^2, x >= 1 continuous at x = 1?
Show solution
Solution
Setting 3(1) + c = 2(1)^2 gives c = -1 for continuity.
Correct Answer:
B
— 0
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Q. For which value of c is the function f(x) = { x^2 - 4, x < c; 3x - 5, x >= c } continuous at x = c?
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Solution
Setting the two pieces equal at x = c: c^2 - 4 = 3c - 5. Solving gives c = 3.
Correct Answer:
C
— 3
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Q. For which value of c is the function f(x) = { x^2 - c, x < 1; 2x + 1, x >= 1 continuous at x = 1?
Show solution
Solution
Setting x^2 - c = 2x + 1 at x = 1 gives c = 2.
Correct Answer:
C
— 2
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Q. For which value of c is the function f(x) = { x^2, x < c; 2x + 1, x >= c continuous at x = c?
Show solution
Solution
Setting x^2 = 2x + 1 at x = c gives c = 2.
Correct Answer:
C
— 2
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Q. For which value of k does the equation x^2 + kx + 16 = 0 have no real roots?
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Solution
The discriminant must be less than zero: k^2 - 4*1*16 < 0 => k^2 < 64 => k < 8 and k > -8.
Correct Answer:
A
— -8
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Q. For which value of k does the equation x^2 + kx + 16 = 0 have real and distinct roots?
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Solution
The discriminant must be positive: k^2 - 4*1*16 > 0 => k^2 > 64 => k > 8 or k < -8. Thus, k = -4 is valid.
Correct Answer:
B
— -4
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Q. For which value of k does the equation x^2 + kx + 4 = 0 have one root equal to 2?
Show solution
Solution
Substituting x = 2 into the equation gives 2^2 + 2k + 4 = 0, leading to k = -4.
Correct Answer:
B
— -2
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Q. For which value of k does the equation x^2 - 4x + k = 0 have roots that differ by 2?
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Solution
Let the roots be r and r+2. Then, r + (r+2) = 4 and r(r+2) = k leads to k = 4.
Correct Answer:
C
— 4
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