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. If the roots of the equation x^2 + 3x + k = 0 are real and distinct, what is the range of k?
A.
k < 9
B.
k > 9
C.
k < 0
D.
k > 0
Show solution
Solution
For real and distinct roots, the discriminant must be positive: 3^2 - 4*1*k > 0 => 9 - 4k > 0 => k < 9.
Correct Answer:
A
— k < 9
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Q. If the roots of the equation x^2 + 4x + k = 0 are real and distinct, what is the condition on k?
A.
k < 16
B.
k > 16
C.
k = 16
D.
k <= 16
Show solution
Solution
The discriminant must be greater than zero: 4^2 - 4*1*k > 0 => 16 - 4k > 0 => k < 4.
Correct Answer:
A
— k < 16
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Q. If the roots of the equation x^2 + 4x + k = 0 are real and equal, what is the minimum value of k?
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Solution
For real and equal roots, the discriminant must be zero: 16 - 4k = 0, thus k = 4.
Correct Answer:
B
— -4
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Q. If the roots of the equation x^2 + 5x + 6 = 0 are a and b, what is the value of a + b?
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Solution
Using Vieta's formulas, the sum of the roots is -b/a = -5/1 = -5.
Correct Answer:
A
— 5
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Q. If the roots of the equation x^2 + 5x + k = 0 are -2 and -3, find k.
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Solution
Using Vieta's formulas, k = (-2)(-3) = 6.
Correct Answer:
B
— 6
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Q. If the roots of the equation x^2 + 6x + k = 0 are -2 and -4, what is the value of k?
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Solution
Using the sum and product of roots: -2 + -4 = -6 and -2*-4 = k => k = 8.
Correct Answer:
C
— 10
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Q. If the roots of the equation x^2 + mx + n = 0 are -2 and -3, what is the value of m + n?
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Solution
The sum of the roots is -(-2 - 3) = 5, so m = 5. The product of the roots is (-2)(-3) = 6, so n = 6. Thus, m + n = 5 + 6 = 11.
Correct Answer:
C
— -7
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Q. If the roots of the equation x^2 + px + q = 0 are -2 and -3, what is the value of p + q?
Show solution
Solution
Using Vieta's formulas, p = -(-2 - 3) = 5 and q = (-2)(-3) = 6. Therefore, p + q = 5 + 6 = 11.
Correct Answer:
C
— -7
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Q. If the roots of the equation x^2 + px + q = 0 are -2 and -3, what is the value of p?
Show solution
Solution
Using Vieta's formulas, p = -(-2 - 3) = 5.
Correct Answer:
A
— 5
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Q. If the roots of the equation x^2 + px + q = 0 are 1 and -1, what is the value of p?
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Solution
The sum of the roots is 0, hence p = -sum = 0.
Correct Answer:
A
— 0
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Q. If the roots of the equation x^2 + px + q = 0 are equal, what is the relationship between p and q?
A.
p^2 = 4q
B.
p^2 > 4q
C.
p^2 < 4q
D.
p + q = 0
Show solution
Solution
For equal roots, the discriminant must be zero: p^2 - 4q = 0, hence p^2 = 4q.
Correct Answer:
A
— p^2 = 4q
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Q. If the roots of the equation x^2 - 5x + k = 0 are equal, what is the value of k?
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Solution
For the roots to be equal, the discriminant must be zero. Thus, b^2 - 4ac = 0 => 25 - 4k = 0 => k = 25.
Correct Answer:
C
— 6
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Q. If the roots of the equation x^2 - 5x + k = 0 are real and equal, what is the minimum value of k?
Show solution
Solution
The minimum value of k is 6, as the discriminant must be zero.
Correct Answer:
C
— 6
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Q. If the roots of the equation x^2 - 5x + k = 0 are real and equal, what is the value of k?
Show solution
Solution
For real and equal roots, the discriminant must be zero: 25 - 4k = 0, thus k = 6.
Correct Answer:
C
— 6
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Q. If the roots of the equation x^2 - 6x + k = 0 are 2 and 4, find the value of k.
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Solution
Using Vieta's formulas, k = 2 * 4 = 8.
Correct Answer:
B
— 10
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Q. If the roots of the equation x^2 - 7x + p = 0 are 3 and 4, what is the value of p?
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Solution
Using Vieta's formulas, the sum of the roots is 7 and the product is p. Thus, 3 * 4 = p, so p = 12.
Correct Answer:
C
— 16
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Q. If the roots of the equation x^2 - 7x + p = 0 are in the ratio 3:4, what is the value of p?
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Solution
Let the roots be 3k and 4k. Then, 3k + 4k = 7 => 7k = 7 => k = 1. The product of the roots is 3k * 4k = 12k^2 = p => p = 12.
Correct Answer:
C
— 20
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Q. If the roots of the equation x^2 - kx + 8 = 0 are equal, what is the value of k?
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Solution
For equal roots, the discriminant must be zero: k^2 - 4*1*8 = 0, solving gives k = 4.
Correct Answer:
A
— 4
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Q. If the roots of the quadratic equation ax^2 + bx + c = 0 are 3 and -2, what is the value of c if a = 1 and b = -1?
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Solution
Using the product of the roots, c = 3 * (-2) = -6.
Correct Answer:
A
— -6
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Q. If the roots of the quadratic equation ax^2 + bx + c = 0 are equal, what is the condition on a, b, and c?
A.
b^2 - 4ac > 0
B.
b^2 - 4ac = 0
C.
b^2 - 4ac < 0
D.
a + b + c = 0
Show solution
Solution
The condition for equal roots is given by the discriminant b^2 - 4ac = 0.
Correct Answer:
B
— b^2 - 4ac = 0
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Q. If the roots of the quadratic equation x^2 + mx + n = 0 are 3 and 4, what is the value of m?
Show solution
Solution
The sum of the roots is 3 + 4 = 7, hence m = -7.
Correct Answer:
A
— 7
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Q. If the roots of the quadratic equation x^2 + px + q = 0 are equal, what is the relationship between p and q?
A.
p^2 = 4q
B.
p^2 > 4q
C.
p^2 < 4q
D.
p + q = 0
Show solution
Solution
For equal roots, the discriminant must be zero: p^2 - 4q = 0, hence p^2 = 4q.
Correct Answer:
A
— p^2 = 4q
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Q. If the roots of the quadratic equation x^2 - 3x + p = 0 are 1 and 2, what is the value of p?
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Solution
Using Vieta's formulas, sum of roots = 1 + 2 = 3 and product of roots = 1*2 = 2. Thus, p = 2.
Correct Answer:
D
— 6
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Q. If the scalar product of two vectors A and B is 0, what can be said about the vectors?
A.
They are parallel
B.
They are orthogonal
C.
They are equal
D.
They are collinear
Show solution
Solution
If A · B = 0, then the vectors are orthogonal.
Correct Answer:
B
— They are orthogonal
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Q. If the scalar product of vectors A = (x, y, z) and B = (2, -1, 3) is 10, what is the equation?
A.
2x - y + 3z = 10
B.
2x + y + 3z = 10
C.
2x - y - 3z = 10
D.
2x + y - 3z = 10
Show solution
Solution
A · B = 2x - y + 3z = 10.
Correct Answer:
A
— 2x - y + 3z = 10
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Q. If the scores of 10 students are: 50, 60, 70, 80, 90, 100, 50, 60, 70, 80, what is the mode?
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Solution
Mode is the value that appears most frequently. Here, 50, 60, 70, and 80 all appear twice, but 50 is the smallest.
Correct Answer:
A
— 50
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Q. If the scores of 5 students are 10, 20, 30, 40, and x, and the mean is 30, what is the value of x?
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Solution
Mean = (10 + 20 + 30 + 40 + x) / 5 = 30. Solving gives x = 50.
Correct Answer:
C
— 50
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Q. If the scores of 7 students are 50, 60, 70, 80, 90, 100, and 110, what is the median score?
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Solution
Arranging the scores: 50, 60, 70, 80, 90, 100, 110. Median = 80 (4th value).
Correct Answer:
B
— 80
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Q. If the scores of a student are 50, 60, 70, 80, and 90, what is the mode?
A.
50
B.
60
C.
70
D.
No mode
Show solution
Solution
All scores occur only once, so there is no mode.
Correct Answer:
D
— No mode
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Q. If the scores of a student in five subjects are 60, 70, 80, 90, and 100, what is the median score?
Show solution
Solution
Arranging the scores: 60, 70, 80, 90, 100. Median = 80 (middle value).
Correct Answer:
B
— 80
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