Undergraduate MCQ & Objective Questions
The undergraduate level is a crucial phase in a student's academic journey, especially for those preparing for school and competitive exams. Mastering this stage can significantly enhance your understanding and retention of key concepts. Practicing MCQs and objective questions is essential, as it not only helps in reinforcing knowledge but also boosts your confidence in tackling important questions during exams.
What You Will Practise Here
Fundamental concepts in Mathematics and Science
Key definitions and theories across various subjects
Important formulas and their applications
Diagrams and graphical representations
Critical thinking and problem-solving techniques
Subject-specific MCQs designed for competitive exams
Revision of essential topics for better retention
Exam Relevance
Undergraduate topics are integral to various examinations such as CBSE, State Boards, NEET, and JEE. These subjects often feature a mix of conceptual and application-based questions. Common patterns include multiple-choice questions that assess both theoretical knowledge and practical application, making it vital for students to be well-versed in undergraduate concepts.
Common Mistakes Students Make
Overlooking the importance of understanding concepts rather than rote memorization
Misinterpreting questions due to lack of careful reading
Neglecting to practice numerical problems that require application of formulas
Failing to review mistakes made in previous practice tests
FAQs
Question: What are some effective strategies for solving undergraduate MCQ questions?Answer: Focus on understanding the concepts, practice regularly, and review your answers to learn from mistakes.
Question: How can I improve my speed in answering objective questions?Answer: Time yourself while practicing and gradually increase the number of questions you attempt in a set time.
Start your journey towards mastering undergraduate subjects today! Solve practice MCQs and test your understanding to ensure you are well-prepared for your exams. Your success is just a question away!
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)
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Solution
Centroid = ((0+6+0)/3, (0+0+8)/3) = (2, 2).
Correct Answer:
A
— (2, 2)
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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)
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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)
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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)
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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)
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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)
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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)
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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
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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
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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
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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
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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
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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
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Q. Find the determinant of F = [[4, 3], [2, 1]]. (2018)
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Solution
Det(F) = (4*1) - (3*2) = 4 - 6 = -2.
Correct Answer:
A
— -2
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Q. Find the determinant of F = [[4, 5], [6, 7]]. (2020)
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Solution
Det(F) = (4*7) - (5*6) = 28 - 30 = -2.
Correct Answer:
A
— -2
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Q. Find the determinant of G = [[1, 2], [2, 4]]. (2020)
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Solution
Determinant of G = (1*4) - (2*2) = 4 - 4 = 0.
Correct Answer:
A
— 0
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Q. Find the determinant of H = [[3, 1], [2, 5]]. (2021)
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Solution
Determinant of H = (3*5) - (1*2) = 15 - 2 = 13.
Correct Answer:
A
— 7
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Q. Find the determinant of J = [[5, 2], [1, 3]]. (2020)
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Solution
The determinant of J is calculated as (5*3) - (2*1) = 15 - 2 = 13.
Correct Answer:
A
— 10
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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
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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
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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
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Q. Find the determinant of the matrix \( J = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \). (2022)
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Solution
The determinant is \( 2*7 - 3*5 = 14 - 15 = -1 \).
Correct Answer:
A
— 1
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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
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Q. Find the determinant of \( G = \begin{pmatrix} 4 & 2 \\ 3 & 1 \end{pmatrix} \). (2020)
Show solution
Solution
The determinant is \( 4*1 - 2*3 = 4 - 6 = -2 \).
Correct Answer:
A
— -2
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Q. Find the dimensions of a box with a square base that maximizes volume given a surface area of 600 sq. units. (2020)
A.
10, 10
B.
15, 15
C.
12, 12
D.
20, 20
Show solution
Solution
Let x be the side of the base and h the height. The surface area constraint gives 2x^2 + 4xh = 600. Max volume occurs at x = 12.
Correct Answer:
C
— 12, 12
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Q. Find the dimensions of a rectangle with a fixed area of 50 m^2 that minimizes the perimeter. (2021)
A.
5, 10
B.
7, 7.14
C.
8, 6.25
D.
10, 5
Show solution
Solution
For a fixed area, the minimum perimeter occurs when the rectangle is a square. Thus, dimensions are approximately 7 m by 7.14 m.
Correct Answer:
B
— 7, 7.14
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Q. Find the dimensions of a rectangle with a fixed area of 50 square units that minimizes the perimeter. (2020)
A.
5, 10
B.
7, 7
C.
10, 5
D.
8, 6.25
Show solution
Solution
For a fixed area, the perimeter is minimized when the rectangle is a square. Thus, side = √50.
Correct Answer:
B
— 7, 7
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Q. Find the dimensions of a rectangle with a fixed area of 50 square units that minimizes the perimeter. (2022) 2022
A.
5, 10
B.
7, 7.14
C.
10, 5
D.
8, 6.25
Show solution
Solution
For minimum perimeter, the rectangle should be a square. Thus, side = sqrt(50) ≈ 7.07.
Correct Answer:
B
— 7, 7.14
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Q. Find the distance between the parallel planes 2x + 3y + 4z = 5 and 2x + 3y + 4z = 10. (2023)
A.
5/√29
B.
10/√29
C.
15/√29
D.
20/√29
Show solution
Solution
Distance = |d1 - d2| / √(a² + b² + c²) = |5 - 10| / √(2² + 3² + 4²) = 5 / √29.
Correct Answer:
B
— 10/√29
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Q. Find the distance between the parallel planes 2x + 3y + z = 5 and 2x + 3y + z = 10. (2022)
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Solution
Distance = |d1 - d2| / √(A² + B² + C²) = |5 - 10| / √(2² + 3² + 1²) = 5 / √14.
Correct Answer:
A
— 5
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