Engineering Entrance MCQ & Objective Questions
Preparing for Engineering Entrance exams is crucial for aspiring engineers in India. Mastering MCQs and objective questions not only enhances your understanding of key concepts but also boosts your confidence during exams. Regular practice with these questions helps identify important topics and improves your overall exam preparation.
What You Will Practise Here
Fundamental concepts of Physics and Mathematics
Key formulas and their applications in problem-solving
Important definitions and theorems relevant to engineering
Diagrams and graphical representations for better understanding
Conceptual questions that challenge your critical thinking
Previous years' question papers and their analysis
Time management strategies while solving MCQs
Exam Relevance
The Engineering Entrance syllabus is integral to various examinations like CBSE, State Boards, NEET, and JEE. Questions often focus on core subjects such as Physics, Chemistry, and Mathematics, with formats varying from direct MCQs to application-based problems. Understanding the common question patterns can significantly enhance your performance and help you tackle the exams with ease.
Common Mistakes Students Make
Overlooking the importance of units and dimensions in calculations
Misinterpreting questions due to lack of careful reading
Neglecting to review basic concepts before attempting advanced problems
Rushing through practice questions without thorough understanding
FAQs
Question: What are the best ways to prepare for Engineering Entrance MCQs?Answer: Focus on understanding concepts, practice regularly with objective questions, and review previous years' papers.
Question: How can I improve my speed in solving MCQs?Answer: Regular practice, time-bound mock tests, and familiarizing yourself with common question types can help improve your speed.
Start your journey towards success by solving Engineering Entrance MCQ questions today! Test your understanding and build a strong foundation for your exams.
Q. If a wave has a frequency of 50 Hz and a wavelength of 2 m, what is its speed? (2018)
A.
100 m/s
B.
50 m/s
C.
25 m/s
D.
200 m/s
Show solution
Solution
Wave speed = frequency × wavelength = 50 Hz × 2 m = 100 m/s.
Correct Answer:
A
— 100 m/s
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Q. If a wave has a frequency of 50 Hz, what is its period? (2022)
A.
0.02 s
B.
0.5 s
C.
2 s
D.
20 s
Show solution
Solution
Period (T) = 1/Frequency = 1/50 Hz = 0.02 s.
Correct Answer:
A
— 0.02 s
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Q. If C = [[0, 1], [1, 0]], what is det(C)? (2022)
Show solution
Solution
Determinant of C = (0*0) - (1*1) = 0 - 1 = -1.
Correct Answer:
C
— -1
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Q. If cos(θ) = 0, what is the value of θ? (2017)
A.
0°
B.
90°
C.
180°
D.
270°
Show solution
Solution
cos(90°) = 0, so θ = 90°
Correct Answer:
B
— 90°
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Q. If cos(θ) = 0.5, what is the value of θ in degrees? (2017)
A.
30°
B.
45°
C.
60°
D.
90°
Show solution
Solution
cos(60°) = 0.5, so θ = 60°
Correct Answer:
C
— 60°
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Q. If cos(θ) = 0.5, what is the value of θ? (2020)
A.
0°
B.
30°
C.
60°
D.
90°
Show solution
Solution
cos(60°) = 0.5, so θ = 60°.
Correct Answer:
C
— 60°
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Q. If cos(θ) = 0.6, what is sin(θ) using Pythagorean identity? (2017)
A.
0.4
B.
0.5
C.
0.6
D.
0.8
Show solution
Solution
sin²(θ) + cos²(θ) = 1; sin²(θ) = 1 - 0.6² = 0.64; sin(θ) = √0.64 = 0.8.
Correct Answer:
A
— 0.4
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Q. If cos(θ) = 0.707, what is θ? (2020)
A.
30°
B.
45°
C.
60°
D.
90°
Show solution
Solution
cos(45°) = √2/2 ≈ 0.707, so θ = 45°.
Correct Answer:
B
— 45°
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Q. If cos(θ) = 1/2, what is θ in degrees?
A.
30°
B.
45°
C.
60°
D.
90°
Show solution
Solution
cos(60°) = 1/2, so θ = 60°
Correct Answer:
C
— 60°
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Q. If E = [[2, 1, 3], [1, 0, 2], [4, 1, 1]], what is det(E)? (2020)
Show solution
Solution
The determinant of E can be calculated using the rule of Sarrus or cofactor expansion, resulting in 0.
Correct Answer:
A
— -1
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Q. If E = [[a, b], [c, d]], what is the expression for det(E)? (2023)
A.
ad - bc
B.
ab + cd
C.
ac - bd
D.
bc - ad
Show solution
Solution
The determinant of E is calculated as (a*d) - (b*c) = ad - bc.
Correct Answer:
A
— ad - bc
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Q. If F = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], what is det(F)? (2021)
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Solution
Det(F) = 1(1*0 - 4*6) - 2(0*0 - 4*5) + 3(0*6 - 1*5) = 1(0 - 24) - 2(0 - 20) + 3(0 - 5) = -24 + 40 - 15 = 1.
Correct Answer:
A
— -14
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Q. If F = [[2, 0], [0, 3]], what is det(F)? (2020)
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Solution
The determinant of F is calculated as (2*3) - (0*0) = 6.
Correct Answer:
B
— 6
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Q. If F = [[2, 1, 3], [1, 0, 2], [0, 1, 1]], what is det(F)? (2023)
Show solution
Solution
Det(F) = 2(0*1 - 2*1) - 1(1*1 - 2*0) + 3(1*1 - 0*0) = 2(0 - 2) - 1(1) + 3(1) = -4 - 1 + 3 = -2.
Correct Answer:
C
— 3
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Q. If F = [[2, 1, 3], [1, 0, 2], [3, 1, 1]], find det(F). (2022)
Show solution
Solution
Using the determinant formula, det(F) = 2(0*1 - 2*1) - 1(1*1 - 2*3) + 3(1*1 - 0*3) = 2(0 - 2) - 1(1 - 6) + 3(1 - 0) = -4 + 5 + 3 = 4.
Correct Answer:
A
— -4
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Q. If F = [[2, 1, 3], [1, 0, 2], [3, 4, 1]], find det(F). (2022)
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Solution
Using the determinant formula, det(F) = 2*(0*1 - 2*4) - 1*(1*1 - 2*3) + 3*(1*4 - 0*3) = 2*(-8) - 1*(-5) + 3*4 = -16 + 5 + 12 = 1.
Correct Answer:
A
— -10
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Q. If F = [[2, 1], [1, 3]], what is the value of det(F)? (2022)
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Solution
The determinant of F is (2*3) - (1*1) = 6 - 1 = 5.
Correct Answer:
A
— 5
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Q. If f(x) = x^3 - 3x^2 + 4, find the critical points. (2022)
A.
1, 2
B.
0, 3
C.
2, 4
D.
1, 3
Show solution
Solution
f'(x) = 3x^2 - 6x. Setting f'(x) = 0 gives x(3x - 6) = 0, so x = 0 or x = 2.
Correct Answer:
A
— 1, 2
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Q. If G = [[1, 1], [1, -1]], find det(G). (2022)
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Solution
Determinant of G = (1*-1) - (1*1) = -1 - 1 = -2.
Correct Answer:
B
— 1
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Q. If H = [[1, 1], [1, -1]], find det(H). (2016)
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Solution
Det(H) = (1*-1) - (1*1) = -1 - 1 = -2.
Correct Answer:
B
— 1
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Q. If H = [[1, 2, 1], [0, 1, 0], [2, 1, 1]], find det(H). (2021)
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Solution
The determinant of H is calculated as 1(1*1 - 0*1) - 2(0*1 - 0*2) + 1(0*1 - 1*2) = 1 - 0 - 2 = -1.
Correct Answer:
B
— 1
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Q. If H = [[1, 2], [2, 4]], what is det(H)? (2020)
Show solution
Solution
The determinant of H is (1*4) - (2*2) = 4 - 4 = 0.
Correct Answer:
A
— 0
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Q. If H = [[2, 3], [4, 5]], find det(H). (2022)
Show solution
Solution
Det(H) = (2*5) - (3*4) = 10 - 12 = -2.
Correct Answer:
D
— 7
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Q. If H = [[2, 3], [4, 5]], what is det(H)? (2022)
Show solution
Solution
Det(H) = (2*5) - (3*4) = 10 - 12 = -2.
Correct Answer:
A
— -2
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Q. If I = [[1, 0, 2], [0, 1, 3], [1, 0, 4]], find det(I). (2021)
Show solution
Solution
Using cofactor expansion, det(I) = 1(1*4 - 3*0) - 0 + 2(0*0 - 1*1) = 4 - 2 = 2.
Correct Answer:
B
— 2
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Q. If I = [[1, 0, 2], [0, 1, 3], [1, 1, 0]], find det(I). (2023)
Show solution
Solution
Using the determinant formula for 3x3 matrices, det(I) = 1(1*0 - 3*1) - 0(0 - 3*1) + 2(0 - 1*1) = 0 - 0 - 2 = -2.
Correct Answer:
A
— -1
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Q. If I = [[1, 2], [2, 4]], what is det(I)? (2021)
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Solution
The determinant of I is 0 because the rows are linearly dependent.
Correct Answer:
A
— 0
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Q. If J = [[1, 1], [1, 1]], what is det(J)? (2019)
Show solution
Solution
Det(J) = (1*1) - (1*1) = 1 - 1 = 0.
Correct Answer:
A
— 0
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Q. If J = [[1, 2, 1], [0, 1, 0], [2, 1, 1]], find det(J). (2019)
Show solution
Solution
Determinant of J = 1(1*1 - 0*1) - 2(0*1 - 0*2) + 1(0*1 - 1*2) = 1 - 0 - 2 = -1.
Correct Answer:
C
— 2
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Q. If J = [[1, 2, 1], [0, 1, 3], [2, 1, 0]], calculate det(J). (2023)
Show solution
Solution
Using the determinant formula, det(J) = 1*(1*0 - 3*1) - 2*(0*0 - 3*2) + 1*(0*1 - 1*2) = 1*(-3) - 2*(-6) + 1*(-2) = -3 + 12 - 2 = 7.
Correct Answer:
A
— -4
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