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. Calculate the coefficient of x^2 in the expansion of (x + 4)^6.
A.
96
B.
144
C.
192
D.
256
Show solution
Solution
The coefficient of x^2 is given by C(6,2) * 4^4 = 15 * 256 = 3840.
Correct Answer:
A
— 96
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Q. Calculate the coefficient of x^3 in the expansion of (x + 1/2)^6.
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Solution
The coefficient of x^3 is given by C(6,3) * (1/2)^3 = 20 * 1/8 = 2.5.
Correct Answer:
A
— 20
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Q. Calculate the coefficient of x^3 in the expansion of (x - 1)^5.
Show solution
Solution
The coefficient of x^3 is C(5,3) * (-1)^2 = 10.
Correct Answer:
B
— 10
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Q. Calculate the coefficient of x^4 in the expansion of (3x - 2)^6.
A.
540
B.
720
C.
810
D.
960
Show solution
Solution
The coefficient of x^4 is C(6,4) * (3)^4 * (-2)^2 = 15 * 81 * 4 = 4860.
Correct Answer:
A
— 540
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Q. Calculate the coefficient of x^4 in the expansion of (x + 1/2)^6. (2021)
A.
15/8
B.
45/8
C.
5/8
D.
1/8
Show solution
Solution
The coefficient of x^4 is C(6,4)(1/2)^2 = 15 * 1/4 = 15/4.
Correct Answer:
B
— 45/8
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Q. Calculate the coefficient of x^4 in the expansion of (x + 2)^6.
Show solution
Solution
The coefficient of x^4 is C(6,4) * 2^2 = 15 * 4 = 60.
Correct Answer:
C
— 90
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Q. Calculate the coefficient of x^4 in the expansion of (x + 3)^6. (2021)
A.
54
B.
81
C.
108
D.
729
Show solution
Solution
The coefficient of x^4 is C(6,4)(3)^2 = 15 * 9 = 135.
Correct Answer:
C
— 108
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Q. Calculate the coefficient of x^4 in the expansion of (x + 5)^6.
A.
150
B.
600
C.
750
D.
1000
Show solution
Solution
The coefficient of x^4 is C(6,4) * 5^2 = 15 * 25 = 375.
Correct Answer:
C
— 750
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Q. Calculate the coefficient of x^5 in the expansion of (x + 2)^7.
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Solution
The coefficient of x^5 is C(7,5) * (2)^2 = 21 * 4 = 84.
Correct Answer:
C
— 63
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Q. Calculate the coefficient of x^5 in the expansion of (x - 3)^7. (2021)
A.
-189
B.
-243
C.
-126
D.
-21
Show solution
Solution
The coefficient of x^5 is C(7,5) * (-3)^2 = 21 * 9 = -189.
Correct Answer:
A
— -189
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Q. Calculate the derivative of f(x) = 5x^5. (2016)
A.
25x^4
B.
5x^4
C.
20x^4
D.
10x^4
Show solution
Solution
The derivative f'(x) = d/dx(5x^5) = 25x^4.
Correct Answer:
A
— 25x^4
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Q. Calculate the derivative of f(x) = ln(x^2 + 1).
A.
2x/(x^2 + 1)
B.
1/(x^2 + 1)
C.
2/(x^2 + 1)
D.
x/(x^2 + 1)
Show solution
Solution
Using the chain rule, f'(x) = d/dx(ln(x^2 + 1)) = (2x)/(x^2 + 1).
Correct Answer:
A
— 2x/(x^2 + 1)
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Q. Calculate the derivative of f(x) = x^2 * e^x. (2023) 2023
A.
e^x(2x + 1)
B.
e^x(2x - 1)
C.
2xe^x
D.
x^2e^x
Show solution
Solution
Using the product rule, f'(x) = d/dx(x^2 * e^x) = e^x(2x + 1).
Correct Answer:
A
— e^x(2x + 1)
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Q. Calculate the determinant of D = [[2, 3, 1], [1, 0, 2], [4, 1, 0]]. (2020)
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Solution
Det(D) = 2(0*0 - 2*1) - 3(1*0 - 2*4) + 1(1*1 - 0*4) = 2(0 - 2) - 3(0 - 8) + 1(1) = -4 + 24 + 1 = 21.
Correct Answer:
A
— -10
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Q. Calculate the determinant of D = [[3, 2, 1], [1, 0, 2], [0, 1, 3]]. (2023)
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Solution
Det(D) = 3(0*3 - 2*1) - 2(1*3 - 0*2) + 1(1*1 - 0*0) = 3(0 - 2) - 2(3) + 1(1) = -6 - 6 + 1 = -11.
Correct Answer:
A
— 1
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Q. Calculate the determinant of D = [[3, 2, 1], [1, 0, 2], [2, 1, 3]]. (2020)
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Solution
Det(D) = 3(0*3 - 2*1) - 2(1*3 - 2*2) + 1(1*1 - 0*2) = 3(0 - 2) - 2(3 - 4) + 1(1) = -6 + 2 + 1 = -3.
Correct Answer:
A
— 1
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Q. Calculate the determinant of D = [[4, 2], [1, 3]]. (2020)
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Solution
Determinant of D = (4*3) - (2*1) = 12 - 2 = 10.
Correct Answer:
A
— 10
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Q. Calculate the determinant of D = [[4, 2], [3, 1]]. (2020)
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Solution
Determinant of D = (4*1) - (2*3) = 4 - 6 = -2.
Correct Answer:
A
— -2
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Q. Calculate the determinant of D = [[4, 5, 6], [7, 8, 9], [1, 2, 3]]. (2020)
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Solution
Determinant of D = 4(8*3 - 9*2) - 5(7*3 - 9*1) + 6(7*2 - 8*1) = 0.
Correct Answer:
A
— 0
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Q. Calculate the determinant of F = [[1, 2, 3], [0, 1, 4], [5, 6, 0]]. (2023)
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Solution
Using the determinant formula, det(F) = 1(1*0 - 4*6) - 2(0*0 - 4*5) + 3(0*6 - 1*5) = -24 + 40 - 15 = 1.
Correct Answer:
A
— -14
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Q. Calculate the determinant of G = [[1, 1, 1], [1, 2, 3], [1, 3, 6]]. (2022)
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Solution
The determinant of G is 0 because the rows are linearly dependent.
Correct Answer:
A
— 0
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Q. Calculate the determinant of G = [[1, 2, 1], [0, 1, 0], [2, 3, 1]]. (2023)
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Solution
Using cofactor expansion, det(G) = 1(1*1 - 0*3) - 2(0*1 - 0*2) + 1(0*3 - 1*2) = 1 - 0 - 2 = -1.
Correct Answer:
A
— -1
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Q. Calculate the determinant of G = [[1, 2, 1], [0, 1, 4], [1, 0, 0]]. (2021)
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Solution
Using the determinant formula for 3x3 matrices, det(G) = 1(1*0 - 4*0) - 2(0*0 - 4*1) + 1(0*0 - 1*1) = 0 + 8 - 1 = 7.
Correct Answer:
A
— -2
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Q. Calculate the determinant of H = [[1, 2, 1], [0, 1, 2], [1, 0, 1]]. (2020)
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Solution
Det(H) = 1(1*1 - 2*0) - 2(0*1 - 2*1) + 1(0*0 - 1*1) = 1(1) - 2(-2) + 1(-1) = 1 + 4 - 1 = 4.
Correct Answer:
A
— 0
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Q. Calculate the determinant of H = [[1, 2, 1], [0, 1, 3], [1, 0, 1]]. (2023)
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Solution
Det(H) = 1(1*1 - 3*0) - 2(0*1 - 3*1) + 1(0*0 - 1*1) = 1(1) - 2(-3) + 1(-1) = 1 + 6 - 1 = 6.
Correct Answer:
A
— -1
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Q. Calculate the determinant of H = [[1, 2, 1], [0, 1, 3], [2, 1, 0]]. (2020)
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Solution
Det(H) = 1(1*0 - 3*1) - 2(0*0 - 3*2) + 1(0*1 - 1*2) = 1(0 - 3) - 2(0 - 6) + 1(0 - 2) = -3 + 12 - 2 = 7.
Correct Answer:
A
— -5
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Q. Calculate the determinant of H = [[1, 2, 3], [0, 1, 4], [5, 6, 0]]. (2021)
Show solution
Solution
Det(H) = 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. Calculate the determinant of H = [[3, 2], [1, 4]]. (2021)
Show solution
Solution
Determinant of H = (3*4) - (2*1) = 12 - 2 = 10.
Correct Answer:
A
— 10
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Q. Calculate the determinant of H = [[5, 4], [2, 3]]. (2021)
Show solution
Solution
Det(H) = (5*3) - (4*2) = 15 - 8 = 7.
Correct Answer:
B
— 8
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Q. Calculate the determinant of I = [[1, 2, 1], [0, 1, 2], [1, 0, 1]]. (2021)
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Solution
Det(I) = 1(1*1 - 2*0) - 2(0*1 - 2*1) + 1(0*0 - 1*1) = 1(1) - 2(-2) + 1(-1) = 1 + 4 - 1 = 4.
Correct Answer:
B
— 1
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