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 coefficient of x^5 in the expansion of (x + 1)^7.
Show solution
Solution
The coefficient of x^5 is C(7,5) = 21.
Correct Answer:
C
— 35
Learn More →
Q. Find the coefficient of x^5 in the expansion of (x + 2)^7.
Show solution
Solution
The coefficient of x^5 is C(7,5) * 2^2 = 21 * 4 = 84.
Correct Answer:
C
— 56
Learn More →
Q. Find the coefficient of x^6 in the expansion of (x + 1)^10. (2023)
A.
10
B.
45
C.
120
D.
210
Show solution
Solution
The coefficient of x^6 is given by 10C6 = 210.
Correct Answer:
D
— 210
Learn More →
Q. Find the constant term in the expansion of (3x - 4/x)^5.
Show solution
Solution
The constant term occurs when the power of x is zero. The term is given by 5C2 * (3x)^2 * (-4/x)^3 = 10 * 9 * (-64) = -5760.
Correct Answer:
A
— -64
Learn More →
Q. Find the constant term in the expansion of (x - 2/x)^6. (2022)
Show solution
Solution
The constant term occurs when the power of x is zero. Setting 6 - 2k = 0 gives k = 3. The term is C(6,3)(-2)^3 = -64.
Correct Answer:
A
— -64
Learn More →
Q. Find the coordinates of the centroid of the triangle with vertices (0, 0), (6, 0), and (0, 8). (2022)
A.
(2, 2)
B.
(2, 3)
C.
(3, 2)
D.
(4, 4)
Show solution
Solution
Centroid = ((0+6+0)/3, (0+0+8)/3) = (2, 2).
Correct Answer:
A
— (2, 2)
Learn More →
Q. Find the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(4, 0, 0), C(0, 3, 0). (2021)
A.
(4/3, 1, 0)
B.
(2, 1, 0)
C.
(1, 1, 0)
D.
(0, 0, 0)
Show solution
Solution
Centroid G = ((0+4+0)/3, (0+0+3)/3, (0+0+0)/3) = (4/3, 1, 0).
Correct Answer:
B
— (2, 1, 0)
Learn More →
Q. Find the coordinates of the centroid of the triangle with vertices at (0, 0), (6, 0), and (0, 8).
A.
(2, 2)
B.
(2, 3)
C.
(3, 2)
D.
(4, 4)
Show solution
Solution
Centroid = ((0+6+0)/3, (0+0+8)/3) = (2, 2).
Correct Answer:
A
— (2, 2)
Learn More →
Q. Find the coordinates of the midpoint of the line segment joining A(2, -1, 3) and B(4, 3, 5). (2022)
A.
(3, 1, 4)
B.
(2, 1, 4)
C.
(3, 2, 3)
D.
(4, 2, 4)
Show solution
Solution
Midpoint M = ((2+4)/2, (-1+3)/2, (3+5)/2) = (3, 1, 4).
Correct Answer:
A
— (3, 1, 4)
Learn More →
Q. Find the coordinates of the midpoint of the line segment joining A(2, 3, 4) and B(4, 5, 6). (2023)
A.
(3, 4, 5)
B.
(2, 3, 4)
C.
(4, 5, 6)
D.
(5, 6, 7)
Show solution
Solution
Midpoint M = ((2+4)/2, (3+5)/2, (4+6)/2) = (3, 4, 5).
Correct Answer:
A
— (3, 4, 5)
Learn More →
Q. Find the critical points of f(x) = x^4 - 8x^2 + 16. (2021)
A.
(0, 16)
B.
(2, 0)
C.
(4, 0)
D.
(1, 15)
Show solution
Solution
f'(x) = 4x^3 - 16x. Setting f'(x) = 0 gives x = 0, ±2. f(2) = 0 is a critical point.
Correct Answer:
B
— (2, 0)
Learn More →
Q. Find the critical points of the function f(x) = x^4 - 8x^2 + 16. (2019)
A.
(0, 16)
B.
(2, 0)
C.
(4, 0)
D.
(1, 9)
Show solution
Solution
Setting f'(x) = 4x^3 - 16x = 0 gives x = 0, ±2. Evaluating f(2) = 0 shows (2, 0) is a critical point.
Correct Answer:
B
— (2, 0)
Learn More →
Q. Find the derivative of f(x) = sin(x) + cos(x).
A.
cos(x) - sin(x)
B.
-sin(x) - cos(x)
C.
sin(x) + cos(x)
D.
-cos(x) + sin(x)
Show solution
Solution
The derivative f'(x) = d/dx(sin(x) + cos(x)) = cos(x) - sin(x).
Correct Answer:
A
— cos(x) - sin(x)
Learn More →
Q. Find the derivative of f(x) = tan(x). (2022) 2022
A.
sec^2(x)
B.
csc^2(x)
C.
sec(x)
D.
tan^2(x)
Show solution
Solution
The derivative f'(x) = d/dx(tan(x)) = sec^2(x).
Correct Answer:
A
— sec^2(x)
Learn More →
Q. Find the derivative of f(x) = x^5 + 3x^3 - 2x.
A.
5x^4 + 9x^2 - 2
B.
5x^4 + 6x^2 - 2
C.
3x^2 + 5x^4 - 2
D.
5x^4 + 3x^2 - 2
Show solution
Solution
The derivative f'(x) = d/dx(x^5 + 3x^3 - 2x) = 5x^4 + 9x^2 - 2.
Correct Answer:
A
— 5x^4 + 9x^2 - 2
Learn More →
Q. Find the derivative of f(x) = x^5 - 3x + 2.
A.
5x^4 - 3
B.
5x^4 + 3
C.
4x^3 - 3
D.
5x^4 - 2
Show solution
Solution
The derivative f'(x) = d/dx(x^5) - d/dx(3x) + d/dx(2) = 5x^4 - 3.
Correct Answer:
A
— 5x^4 - 3
Learn More →
Q. Find the derivative of f(x) = x^5 - 3x^3 + 2. (2022)
A.
5x^4 - 9x^2
B.
5x^4 + 9x^2
C.
3x^2 - 9x
D.
5x^4 - 3x^2
Show solution
Solution
The derivative f'(x) = d/dx(x^5 - 3x^3 + 2) = 5x^4 - 9x^2.
Correct Answer:
A
— 5x^4 - 9x^2
Learn More →
Q. Find the determinant of E = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]. (2019)
Show solution
Solution
Determinant of E = 0 (rows are linearly dependent).
Correct Answer:
A
— 0
Learn More →
Q. Find the determinant of E = [[3, 2], [1, 4]]. (2022)
Show solution
Solution
Det(E) = (3*4) - (2*1) = 12 - 2 = 10.
Correct Answer:
A
— 10
Learn More →
Q. Find the determinant of E = [[4, 2], [1, 3]]. (2023)
Show solution
Solution
Det(E) = (4*3) - (2*1) = 12 - 2 = 10.
Correct Answer:
A
— 10
Learn More →
Q. Find the determinant of F = [[4, 3], [2, 1]]. (2018)
Show solution
Solution
Det(F) = (4*1) - (3*2) = 4 - 6 = -2.
Correct Answer:
A
— -2
Learn More →
Q. Find the determinant of F = [[4, 5], [6, 7]]. (2020)
Show solution
Solution
Det(F) = (4*7) - (5*6) = 28 - 30 = -2.
Correct Answer:
A
— -2
Learn More →
Q. Find the determinant of G = [[1, 2], [2, 4]]. (2020)
Show solution
Solution
Determinant of G = (1*4) - (2*2) = 4 - 4 = 0.
Correct Answer:
A
— 0
Learn More →
Q. Find the determinant of H = [[3, 1], [2, 5]]. (2021)
Show solution
Solution
Determinant of H = (3*5) - (1*2) = 15 - 2 = 13.
Correct Answer:
A
— 7
Learn More →
Q. Find the determinant of J = [[5, 2], [1, 3]]. (2020)
Show solution
Solution
The determinant of J is calculated as (5*3) - (2*1) = 15 - 2 = 13.
Correct Answer:
A
— 10
Learn More →
Q. Find the determinant of the matrix D = [[3, 2, 1], [1, 0, 2], [2, 1, 3]]. (2020)
Show solution
Solution
The determinant of D can be calculated using the rule of Sarrus or cofactor expansion, which results in 0.
Correct Answer:
A
— 0
Learn More →
Q. Find the determinant of the matrix D = [[4, 2], [3, 1]]. (2023)
Show solution
Solution
The determinant of D is calculated as (4*1) - (2*3) = 4 - 6 = -2.
Correct Answer:
A
— -2
Learn More →
Q. Find the determinant of the matrix \( E = \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \). (2021)
Show solution
Solution
The determinant is \( 3*4 - 2*1 = 12 - 2 = 10 \).
Correct Answer:
A
— 10
Learn More →
Q. Find the determinant of the matrix \( J = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \). (2022)
Show solution
Solution
The determinant is \( 2*7 - 3*5 = 14 - 15 = -1 \).
Correct Answer:
A
— 1
Learn More →
Q. Find the determinant of \( G = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \). (2021)
Show solution
Solution
The determinant is calculated as \( 2*7 - 3*5 = 14 - 15 = -1 \).
Correct Answer:
A
— 1
Learn More →
Showing 511 to 540 of 2530 (85 Pages)
