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. Find the integral of e^x dx. (2022)
A.
e^x + C
B.
e^x
C.
x e^x + C
D.
ln(e^x) + C
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Solution
The integral of e^x is e^x + C.
Correct Answer:
A
— e^x + C
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Q. Find the integral of sin(x) with respect to x. (2020)
A.
-cos(x) + C
B.
cos(x) + C
C.
sin(x) + C
D.
-sin(x) + C
Show solution
Solution
The integral of sin(x) is -cos(x) + C.
Correct Answer:
A
— -cos(x) + C
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Q. Find the integral of sin(x). (2020)
A.
-cos(x) + C
B.
cos(x) + C
C.
sin(x) + C
D.
-sin(x) + C
Show solution
Solution
The integral of sin(x) is -cos(x) + C.
Correct Answer:
A
— -cos(x) + C
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Q. Find the integral of sin(x)dx. (2020)
A.
-cos(x) + C
B.
cos(x) + C
C.
sin(x) + C
D.
-sin(x) + C
Show solution
Solution
The integral of sin(x) is -cos(x) + C.
Correct Answer:
A
— -cos(x) + C
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Q. Find the integral of x^5 dx. (2020)
A.
(1/6)x^6 + C
B.
(1/5)x^6 + C
C.
(1/4)x^6 + C
D.
(1/7)x^6 + C
Show solution
Solution
The integral is (1/6)x^6 + C.
Correct Answer:
B
— (1/5)x^6 + C
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Q. Find the length of the diagonal of a cuboid with dimensions 3, 4, and 12 units. (2020)
A.
√169
B.
√145
C.
√153
D.
√157
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Solution
Diagonal = √(3² + 4² + 12²) = √(9 + 16 + 144) = √169 = 13.
Correct Answer:
C
— √153
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Q. Find the length of the diagonal of a rectangular box with dimensions 2, 3, and 6 units. (2022)
A.
√49
B.
√45
C.
√36
D.
√50
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Solution
Diagonal = √(2² + 3² + 6²) = √(4 + 9 + 36) = √49 = 7 units.
Correct Answer:
A
— √49
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Q. Find the length of the diagonal of a rectangular box with dimensions 2, 3, and 6. (2023)
A.
√49
B.
√36
C.
√45
D.
√50
Show solution
Solution
Diagonal = √(2² + 3² + 6²) = √(4 + 9 + 36) = √49 = 7.
Correct Answer:
A
— √49
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Q. Find the limit: lim (x -> 0) (x^2)/(sin(x)) (2023)
A.
0
B.
1
C.
2
D.
Undefined
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Solution
As x approaches 0, sin(x) approaches x, thus lim (x -> 0) (x^2/sin(x)) = lim (x -> 0) (x^2/x) = lim (x -> 0) x = 0.
Correct Answer:
A
— 0
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Q. Find the limit: lim (x -> 1) (x^4 - 1)/(x - 1) (2023)
A.
0
B.
1
C.
4
D.
Undefined
Show solution
Solution
Factoring gives ((x - 1)(x^3 + x^2 + x + 1))/(x - 1). For x ≠ 1, this simplifies to x^3 + x^2 + x + 1. Thus, lim (x -> 1) = 4.
Correct Answer:
A
— 0
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Q. Find the limit: lim (x -> 2) (x^2 + 3x - 10)/(x - 2) (2021)
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Solution
Factoring gives (x - 2)(x + 5)/(x - 2). For x ≠ 2, this simplifies to x + 5. Evaluating at x = 2 gives 7.
Correct Answer:
D
— 7
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Q. Find the limit: lim (x -> 2) (x^2 - 3x + 2)/(x - 2) (2021)
A.
1
B.
2
C.
0
D.
Undefined
Show solution
Solution
The expression is undefined at x=2. The limit does not exist as the function approaches infinity.
Correct Answer:
D
— Undefined
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Q. Find the limit: lim (x -> 3) (x^2 - 9)/(x - 3) (2023)
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Solution
The expression can be factored as ((x - 3)(x + 3))/(x - 3). For x ≠ 3, this simplifies to x + 3. Thus, lim (x -> 3) (x + 3) = 6.
Correct Answer:
A
— 0
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Q. Find the local maxima of f(x) = -x^2 + 4x + 1. (2020)
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Solution
The maximum occurs at x = -b/(2a) = -4/(2*-1) = 2. f(2) = -2^2 + 4(2) + 1 = 5.
Correct Answer:
B
— 5
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Q. Find the local maxima of f(x) = -x^3 + 3x^2 + 1. (2020)
A.
(0, 1)
B.
(1, 3)
C.
(2, 5)
D.
(3, 1)
Show solution
Solution
f'(x) = -3x^2 + 6x. Setting f'(x) = 0 gives x(3x - 6) = 0, so x = 0 or x = 2. f(2) = 5.
Correct Answer:
B
— (1, 3)
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Q. Find the local maximum of f(x) = -x^3 + 3x^2 + 4. (2020)
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Solution
Set f'(x) = 0 to find critical points. The local maximum occurs at x = 2. f(2) = 5.
Correct Answer:
B
— 5
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Q. Find the magnitude of the vector A = 3i - 4j. (2020)
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Solution
|A| = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5.
Correct Answer:
A
— 5
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Q. Find the maximum area of a triangle with a base of 10 m and height varying. (2020)
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Solution
Area = 1/2 * base * height. Max area occurs when height is maximized, thus Area = 1/2 * 10 * 10 = 50.
Correct Answer:
B
— 50
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Q. Find the maximum area of a triangle with a base of 10 units and height as a function of the base. (2021)
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Solution
Area = 1/2 * base * height. Max area occurs when height is maximized at 10 units, giving Area = 50.
Correct Answer:
B
— 50
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Q. Find the maximum area of a triangle with a base of 10 units and height as a function of x. (2022)
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Solution
Area = 1/2 * base * height. Max area occurs when height is maximized, which is 10 units, giving Area = 50.
Correct Answer:
B
— 50
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Q. Find the maximum area of a triangle with a fixed perimeter of 30 cm. (2022)
A.
75 cm²
B.
100 cm²
C.
50 cm²
D.
60 cm²
Show solution
Solution
For maximum area, the triangle should be equilateral. Area = (sqrt(3)/4) * (10)^2 = 75 cm².
Correct Answer:
A
— 75 cm²
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Q. Find the maximum height of the projectile modeled by h(t) = -16t^2 + 32t + 48. (2020)
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Solution
The maximum occurs at t = -b/(2a) = -32/(2*-16) = 1. h(1) = 64.
Correct Answer:
A
— 48
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Q. Find the maximum height of the projectile modeled by h(t) = -16t^2 + 64t + 48. (2020)
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Solution
The maximum occurs at t = -b/(2a) = 64/(2*16) = 2. h(2) = -16(2^2) + 64(2) + 48 = 80.
Correct Answer:
B
— 64
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Q. Find the maximum value of the function f(x) = -2x^2 + 8x - 3. (2021) 2021
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Solution
The function is a downward-opening parabola. The maximum occurs at x = -b/(2a) = -8/(2*-2) = 2. f(2) = -2(2^2) + 8(2) - 3 = 8.
Correct Answer:
B
— 8
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Q. Find the midpoint of the line segment joining the points (2, 3) and (4, 7). (2022) 2022
A.
(3, 5)
B.
(2, 5)
C.
(4, 5)
D.
(3, 4)
Show solution
Solution
Midpoint = ((2+4)/2, (3+7)/2) = (3, 5).
Correct Answer:
A
— (3, 5)
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Q. Find the minimum value of f(x) = 4x^2 - 16x + 20. (2022)
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Solution
The vertex gives the minimum at x = 2. f(2) = 4(2^2) - 16(2) + 20 = 4.
Correct Answer:
A
— 4
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Q. Find the minimum value of f(x) = x^2 - 4x + 6. (2021)
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Solution
The vertex form gives the minimum at x = 2. f(2) = 2.
Correct Answer:
A
— 2
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Q. Find the minimum value of f(x) = x^2 - 4x + 7. (2021)
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Solution
The vertex form gives the minimum at x = 2. f(2) = 2^2 - 4*2 + 7 = 3.
Correct Answer:
A
— 3
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Q. Find the minimum value of f(x) = x^2 - 4x + 7. (2021) 2021
Show solution
Solution
The vertex form gives the minimum at x = 2. f(2) = 2^2 - 4*2 + 7 = 3.
Correct Answer:
A
— 3
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Q. Find the minimum value of the function f(x) = 2x^2 - 8x + 10. (2022)
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Solution
The minimum occurs at x = 2. f(2) = 2(2^2) - 8(2) + 10 = 6.
Correct Answer:
B
— 4
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