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. Evaluate ∫ (2x + 3) dx. (2022)
A.
x^2 + 3x + C
B.
x^2 + 3 + C
C.
x^2 + 3x + 1
D.
2x^2 + 3 + C
Show solution
Solution
The integral is (2/2)x^2 + 3x + C = x^2 + 3x + C.
Correct Answer:
A
— x^2 + 3x + C
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Q. Evaluate ∫ (4x^3 - 2x) dx. (2019)
A.
x^4 - x^2 + C
B.
x^4 - x^2 + 2C
C.
x^4 - x + C
D.
4x^4 - 2x^2 + C
Show solution
Solution
The integral is (4/4)x^4 - (2/2)x^2 + C = x^4 - x^2 + C.
Correct Answer:
A
— x^4 - x^2 + C
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Q. Evaluate ∫ (5 - 3x) dx. (2022)
A.
5x - (3/2)x^2 + C
B.
5x - (3/3)x^2 + C
C.
5x - (3/4)x^2 + C
D.
5x - (3/5)x^2 + C
Show solution
Solution
The integral is 5x - (3/2)x^2 + C.
Correct Answer:
A
— 5x - (3/2)x^2 + C
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Q. Evaluate ∫(2x^2 + 3x + 1)dx. (2021)
A.
(2/3)x^3 + (3/2)x^2 + x + C
B.
(2/3)x^3 + (3/2)x + C
C.
(2/3)x^3 + (3/2)x^2 + C
D.
(2/3)x^3 + 3x + C
Show solution
Solution
Integrating term by term: ∫2x^2dx = (2/3)x^3, ∫3xdx = (3/2)x^2, and ∫1dx = x. Thus, ∫(2x^2 + 3x + 1)dx = (2/3)x^3 + (3/2)x^2 + x + C.
Correct Answer:
A
— (2/3)x^3 + (3/2)x^2 + x + C
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Q. Evaluate ∫(5x^4)dx. (2020)
A.
(5/5)x^5 + C
B.
(1/5)x^5 + C
C.
(5/4)x^4 + C
D.
(1/4)x^4 + C
Show solution
Solution
The integral of 5x^4 is (5/5)x^5 + C = x^5 + C.
Correct Answer:
A
— (5/5)x^5 + C
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Q. Evaluate ∫(6x^2 + 3)dx. (2022)
A.
2x^3 + 3x + C
B.
2x^3 + 3 + C
C.
2x^3 + 3x^2 + C
D.
2x^3 + 3x^3 + C
Show solution
Solution
Integrating term by term: ∫6x^2dx = 2x^3 and ∫3dx = 3x. Thus, ∫(6x^2 + 3)dx = 2x^3 + 3x + C.
Correct Answer:
A
— 2x^3 + 3x + C
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Q. Find the area of a triangle with vertices at A(0, 0, 0), B(1, 0, 0), and C(0, 1, 0). (2023)
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Solution
Area = 0.5 * base * height = 0.5 * 1 * 1 = 0.5 square units.
Correct Answer:
A
— 0.5
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Q. Find the area of the triangle formed by the points (0, 0), (4, 0), and (0, 3). (2022) 2022
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Solution
Area = 1/2 * base * height = 1/2 * 4 * 3 = 6.
Correct Answer:
A
— 6
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Q. Find the area of the triangle formed by the points A(0, 0, 0), B(1, 0, 0), and C(0, 1, 0). (2023)
Show solution
Solution
Area = 0.5 * base * height = 0.5 * 1 * 1 = 0.5 square units.
Correct Answer:
A
— 0.5
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Q. Find the area of the triangle formed by the points A(1, 2, 3), B(4, 5, 6), and C(7, 8, 9). (2022)
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Solution
The points are collinear, hence the area = 0.
Correct Answer:
A
— 0
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Q. Find the coefficient of x^0 in the expansion of (2x - 3)^3.
A.
-27
B.
-24
C.
-18
D.
-12
Show solution
Solution
The coefficient of x^0 is (-3)^3 = -27.
Correct Answer:
A
— -27
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Q. Find the coefficient of x^1 in the expansion of (x + 4)^3.
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Solution
The coefficient of x^1 is C(3,1) * (4)^2 = 3 * 16 = 48.
Correct Answer:
A
— 12
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Q. Find the coefficient of x^2 in the expansion of (2x + 3)^6.
A.
540
B.
720
C.
810
D.
960
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Solution
The coefficient of x^2 is given by 6C2 * (2)^2 * (3)^4 = 15 * 4 * 81 = 4860.
Correct Answer:
A
— 540
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Q. Find the coefficient of x^2 in the expansion of (x + 4)^5. (2023)
A.
80
B.
100
C.
120
D.
160
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Solution
The coefficient of x^2 is C(5,2)(4)^3 = 10 * 64 = 640.
Correct Answer:
A
— 80
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Q. Find the coefficient of x^2 in the expansion of (x - 5)^5.
A.
100
B.
150
C.
200
D.
250
Show solution
Solution
The coefficient of x^2 is C(5,2) * (-5)^3 = 10 * (-125) = -1250.
Correct Answer:
A
— 100
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Q. Find the coefficient of x^3 in the expansion of (2x - 3)^4. (2022)
A.
-54
B.
-108
C.
108
D.
54
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Solution
The coefficient of x^3 is C(4,3) * (2)^3 * (-3)^1 = 4 * 8 * (-3) = -96.
Correct Answer:
B
— -108
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Q. Find the coefficient of x^3 in the expansion of (x - 1)^7.
A.
-35
B.
-21
C.
-7
D.
-49
Show solution
Solution
The coefficient of x^3 is given by 7C3 * (-1)^4 = 35.
Correct Answer:
A
— -35
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Q. Find the coefficient of x^3 in the expansion of (x - 2)^5.
A.
-40
B.
-80
C.
-60
D.
-100
Show solution
Solution
The coefficient of x^3 is C(5,3) * (-2)^2 = 10 * 4 = 40.
Correct Answer:
A
— -40
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Q. Find the coefficient of x^4 in the expansion of (2x - 3)^5.
A.
-240
B.
-360
C.
-480
D.
-600
Show solution
Solution
The coefficient of x^4 is C(5,4) * (2)^4 * (-3)^1 = 5 * 16 * (-3) = -240.
Correct Answer:
A
— -240
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Q. Find the coefficient of x^4 in the expansion of (2x - 3)^6.
A.
540
B.
720
C.
810
D.
900
Show solution
Solution
The coefficient of x^4 is C(6,4) * (2)^4 * (-3)^2 = 15 * 16 * 9 = 2160.
Correct Answer:
A
— 540
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Q. Find the coefficient of x^4 in the expansion of (3x + 2)^5. (2022)
A.
240
B.
360
C.
480
D.
600
Show solution
Solution
The coefficient of x^4 is C(5,4)(3)^4(2)^1 = 5 * 81 * 2 = 810.
Correct Answer:
B
— 360
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Q. Find the coefficient of x^4 in the expansion of (x + 1)^6.
Show solution
Solution
The coefficient of x^4 is C(6,4) * 1^2 = 15.
Correct Answer:
B
— 20
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Q. Find the coefficient of x^4 in the expansion of (x + 2)^6.
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Solution
The coefficient of x^4 is C(6,4) * (2)^2 = 15 * 4 = 60.
Correct Answer:
B
— 30
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Q. Find the coefficient of x^4 in the expansion of (x + 3)^6.
A.
81
B.
162
C.
243
D.
729
Show solution
Solution
The coefficient of x^4 is C(6,4) * (3)^2 = 15 * 9 = 135.
Correct Answer:
C
— 243
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Q. Find the coefficient of x^4 in the expansion of (x + 5)^7.
A.
210
B.
1260
C.
1750
D.
2450
Show solution
Solution
The coefficient of x^4 is given by C(7,4) * 5^3 = 35 * 125 = 4375.
Correct Answer:
B
— 1260
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Q. Find the coefficient of x^4 in the expansion of (x - 1)^5.
Show solution
Solution
The coefficient of x^4 is C(5,4) * (-1)^1 = 5 * (-1) = -5.
Correct Answer:
C
— -10
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Q. Find the coefficient of x^4 in the expansion of (x - 5)^6.
A.
150
B.
200
C.
250
D.
300
Show solution
Solution
The coefficient of x^4 is given by C(6,4) * (-5)^2 = 15 * 25 = 375.
Correct Answer:
B
— 200
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Q. Find the coefficient of x^5 in the expansion of (2x - 3)^6. (2022)
A.
-540
B.
540
C.
-720
D.
720
Show solution
Solution
The coefficient of x^5 is C(6,5) * (2)^5 * (-3)^1 = 6 * 32 * (-3) = -576.
Correct Answer:
A
— -540
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Q. Find the coefficient of x^5 in the expansion of (2x - 3)^7. (2023)
A.
168
B.
252
C.
336
D.
504
Show solution
Solution
The coefficient of x^5 is C(7,5) * (2)^5 * (-3)^2 = 21 * 32 * 9 = 6048.
Correct Answer:
B
— 252
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Q. Find the coefficient of x^5 in the expansion of (2x - 3)^8.
A.
-6720
B.
6720
C.
-3360
D.
3360
Show solution
Solution
The coefficient of x^5 is C(8,5) * (2)^5 * (-3)^3 = 56 * 32 * (-27) = -6720.
Correct Answer:
A
— -6720
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