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 pair of lines represented by ax^2 + 2hxy + by^2 = 0 are perpendicular, then:
A.
a + b = 0
B.
a - b = 0
C.
h = 0
D.
a = b
Show solution
Solution
For the lines to be perpendicular, the condition a + b = 0 must hold.
Correct Answer:
A
— a + b = 0
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Q. If the pair of lines represented by the equation ax^2 + 2hxy + by^2 = 0 are perpendicular, then:
A.
a + b = 0
B.
a - b = 0
C.
h = 0
D.
a = b
Show solution
Solution
For the lines to be perpendicular, the condition a*b + h^2 = 0 must hold.
Correct Answer:
A
— a + b = 0
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Q. If the parabola y = ax^2 + bx + c has its vertex at (1, -2), what is the value of a if it passes through the point (0, 0)?
Show solution
Solution
Using the vertex form y = a(x - 1)^2 - 2 and substituting (0, 0), we get 0 = a(0 - 1)^2 - 2 => 2 = a => a = 2.
Correct Answer:
B
— 2
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Q. If the parabola y^2 = 16x opens to the right, what is the value of p?
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Solution
In the equation y^2 = 4px, we have 4p = 16, thus p = 4.
Correct Answer:
B
— 4
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Q. If the parabola y^2 = 20x opens to the right, what is the value of p?
Show solution
Solution
In the equation y^2 = 4px, we have 4p = 20, thus p = 20/4 = 5.
Correct Answer:
A
— 5
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Q. If the peak current in an AC circuit is 5 A, what is the average current over one complete cycle?
A.
5 A
B.
2.5 A
C.
0 A
D.
7.07 A
Show solution
Solution
The average current over one complete cycle is I_avg = I_peak/√2 = 5/√2 = 2.5 A.
Correct Answer:
B
— 2.5 A
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Q. If the peak voltage of an AC source is 200 V, what is the RMS voltage?
A.
100 V
B.
141.42 V
C.
200 V
D.
282.84 V
Show solution
Solution
The RMS voltage (V_rms) is given by V_rms = V_peak / √2. Therefore, V_rms = 200 V / √2 = 141.42 V.
Correct Answer:
B
— 141.42 V
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Q. If the peak voltage of an AC source is 220 V, what is the RMS voltage?
A.
110 V
B.
154 V
C.
220 V
D.
311 V
Show solution
Solution
The RMS voltage (V_rms) is given by V_rms = V_peak / √2. Therefore, V_rms = 220 V / √2 = 110 V.
Correct Answer:
A
— 110 V
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Q. If the period of a satellite in a circular orbit is T, what is the relationship between T and the radius r of the orbit?
A.
T ∝ r
B.
T ∝ r²
C.
T ∝ √r
D.
T ∝ 1/√r
Show solution
Solution
T = 2π√(r³/GM), thus T ∝ √r.
Correct Answer:
C
— T ∝ √r
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Q. If the photoelectric effect is observed, what can be inferred about the incident light?
A.
It has a frequency below the threshold
B.
It has a frequency equal to the threshold
C.
It has a frequency above the threshold
D.
It has any frequency
Show solution
Solution
The photoelectric effect occurs only when the frequency of the incident light is above the threshold frequency.
Correct Answer:
C
— It has a frequency above the threshold
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Q. If the points (1, 2), (3, 4), and (5, 6) are collinear, what is the slope of the line?
A.
1
B.
2
C.
0
D.
undefined
Show solution
Solution
Slope = (4-2)/(3-1) = 1, and it remains the same for other points.
Correct Answer:
A
— 1
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Q. If the points A(1, 2), B(3, 4), and C(5, 6) are collinear, what is the area of triangle ABC?
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Solution
Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | = 0.
Correct Answer:
A
— 0
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Q. If the polynomial P(x) = x^3 - 6x^2 + 11x - 6 has a root at x = 1, what is P(2)?
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Solution
P(2) = 2^3 - 6(2^2) + 11(2) - 6 = 8 - 24 + 22 - 6 = 0.
Correct Answer:
D
— 3
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Q. If the position vector of a point is (5, 12), what is its distance from the origin?
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Solution
Distance = √(5^2 + 12^2) = √(25 + 144) = √169 = 13
Correct Answer:
A
— 13
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Q. If the position vector of a point is given by r = (2t, 3t, 4t), what is the velocity vector?
A.
(2, 3, 4)
B.
(4, 6, 8)
C.
(2t, 3t, 4t)
D.
(0, 0, 0)
Show solution
Solution
Velocity vector = dr/dt = (2, 3, 4)
Correct Answer:
A
— (2, 3, 4)
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Q. If the position vector of a point P is (2, 3, 4), what is the distance from the origin to point P?
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Solution
Distance = √(2^2 + 3^2 + 4^2) = √(4 + 9 + 16) = √29 ≈ 5.385.
Correct Answer:
B
— 6
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Q. If the position vector of a point P is (x, y, z) and the vector a = (1, 2, 3), what is the projection of P onto a?
A.
(1, 2, 3)
B.
(2, 4, 6)
C.
(0, 0, 0)
D.
(x, y, z)
Show solution
Solution
Projection of P onto a = ((P · a) / |a|^2) * a.
Correct Answer:
D
— (x, y, z)
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Q. If the position vector of a point P is given by r = (2t, 3t, 4t), find the coordinates of P when t = 1.
A.
(2, 3, 4)
B.
(1, 1, 1)
C.
(0, 0, 0)
D.
(2, 4, 6)
Show solution
Solution
Substituting t = 1, r = (2*1, 3*1, 4*1) = (2, 3, 4).
Correct Answer:
A
— (2, 3, 4)
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Q. If the position vector of point P is (3, -2) and Q is (1, 4), what is the vector PQ?
A.
(-2, 6)
B.
(2, -6)
C.
(4, -6)
D.
(6, 2)
Show solution
Solution
Vector PQ = Q - P = (1 - 3, 4 - (-2)) = (-2, 6).
Correct Answer:
A
— (-2, 6)
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Q. If the position vector of point P is (3, 4) and Q is (1, 2), what is the vector PQ?
A.
(2, 2)
B.
(4, 6)
C.
(2, 4)
D.
(1, 1)
Show solution
Solution
Vector PQ = Q - P = (1 - 3, 2 - 4) = (-2, -2).
Correct Answer:
A
— (2, 2)
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Q. If the principal quantum number n = 4 and the azimuthal quantum number l = 2, what is the maximum number of electrons in this subshell?
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Solution
The maximum number of electrons in a subshell is given by 2(2l + 1). For l = 2, it is 2(2*2 + 1) = 10.
Correct Answer:
C
— 14
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Q. If the principal quantum number n = 4, what are the possible values of l?
A.
0, 1, 2, 3
B.
1, 2, 3, 4
C.
0, 1, 2, 3, 4
D.
0, 1, 2
Show solution
Solution
For n=4, l can take values 0, 1, 2, or 3.
Correct Answer:
A
— 0, 1, 2, 3
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Q. If the principal quantum number n = 4, what are the possible values of the azimuthal quantum number l?
A.
0, 1, 2, 3
B.
1, 2, 3, 4
C.
0, 1, 2, 3, 4
D.
0, 1, 2
Show solution
Solution
For n=4, l can take values from 0 to n-1, which are 0, 1, 2, and 3.
Correct Answer:
A
— 0, 1, 2, 3
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Q. If the probability of an event A is 0.3, what is the probability of the event not occurring?
A.
0.7
B.
0.3
C.
0.5
D.
0.2
Show solution
Solution
Probability of not A = 1 - P(A) = 1 - 0.3 = 0.7.
Correct Answer:
A
— 0.7
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Q. If the probability of an event A is 0.7, what is the probability of the event not occurring?
A.
0.3
B.
0.7
C.
0.5
D.
0.1
Show solution
Solution
Probability of not A = 1 - P(A) = 1 - 0.7 = 0.3.
Correct Answer:
A
— 0.3
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Q. If the probability of an event is 0.7, what is the probability of its complement?
A.
0.3
B.
0.7
C.
1
D.
0.5
Show solution
Solution
Probability of complement = 1 - P(event) = 1 - 0.7 = 0.3.
Correct Answer:
A
— 0.3
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Q. If the probability of an event is 0.7, what is the probability of the event not occurring?
A.
0.3
B.
0.7
C.
0.5
D.
0.1
Show solution
Solution
Probability of not occurring = 1 - P(event) = 1 - 0.7 = 0.3.
Correct Answer:
A
— 0.3
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Q. If the probability of event A is 0.4 and event B is 0.5, what is the probability of both events occurring if they are independent?
A.
0.2
B.
0.4
C.
0.5
D.
0.6
Show solution
Solution
P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.
Correct Answer:
A
— 0.2
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Q. If the quadratic equation ax^2 + bx + c = 0 has roots 3 and -2, what is the value of a?
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Solution
Using the fact that the product of the roots is c/a and the sum is -b/a, we can set a = 1, b = -1, c = -6.
Correct Answer:
A
— 1
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Q. If the quadratic equation x^2 + 2px + p^2 - 4 = 0 has real roots, what is the condition on p?
A.
p > 2
B.
p < 2
C.
p = 2
D.
p >= 2
Show solution
Solution
The discriminant must be non-negative: (2p)^2 - 4(1)(p^2 - 4) >= 0 => 4p^2 - 4p^2 + 16 >= 0, which is always true. Thus, p can be any real number.
Correct Answer:
D
— p >= 2
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