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 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)
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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 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
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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
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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
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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
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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
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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
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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
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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.
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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
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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
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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.
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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
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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
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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
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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
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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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Q. Find the coefficient of x^5 in the expansion of (x + 1)^7.
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Solution
The coefficient of x^5 is C(7,5) = 21.
Correct Answer:
C
— 35
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Q. Find 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
— 56
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Q. Find the coefficient of x^6 in the expansion of (x + 1)^10. (2023)
A.
10
B.
45
C.
120
D.
210
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Solution
The coefficient of x^6 is given by 10C6 = 210.
Correct Answer:
D
— 210
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Q. Find the constant term in the expansion of (3x - 4/x)^5.
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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
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Q. Find the constant term in the expansion of (x - 2/x)^6. (2022)
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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
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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)
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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 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)
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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)
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