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. If the radius of a circle is 4 cm, what is the length of a chord that is 3 cm from the center? (2014)
A.
5 cm
B.
6 cm
C.
7 cm
D.
8 cm
Show solution
Solution
Using Pythagoras theorem: chord length = 2√(r² - d²) = 2√(4² - 3²) = 2√(16 - 9) = 2√7 ≈ 5.29 cm.
Correct Answer:
A
— 5 cm
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Q. If the radius of a circle is 7 cm, what is its circumference? (Use π = 22/7) (2014)
A.
44 cm
B.
22 cm
C.
14 cm
D.
28 cm
Show solution
Solution
Circumference = 2πr = 2 × (22/7) × 7 = 44 cm.
Correct Answer:
A
— 44 cm
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Q. If the radius of a circle is decreased by 2 cm, how does the area change? (Original radius is 10 cm) (2021)
A.
Decreases by 12.56 cm²
B.
Decreases by 25.12 cm²
C.
Decreases by 31.4 cm²
D.
Decreases by 50.24 cm²
Show solution
Solution
Original area = π(10)² = 314 cm²; New area = π(8)² = 201.06 cm². Change = 314 - 201.06 = 112.94 cm².
Correct Answer:
B
— Decreases by 25.12 cm²
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Q. If the radius of a circle is decreased by 2 cm, how does the area change? (Use π = 3.14) (2020)
A.
Decreases by 12.56 cm²
B.
Decreases by 25.12 cm²
C.
Increases by 12.56 cm²
D.
Remains the same
Show solution
Solution
Area change = π[(r-2)² - r²] = π[-4r + 4] = 3.14 * (-4r + 4).
Correct Answer:
B
— Decreases by 25.12 cm²
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Q. If the radius of a circle is doubled, how does the area change? (2021)
A.
It doubles
B.
It triples
C.
It quadruples
D.
It remains the same
Show solution
Solution
Area = πr²; if r is doubled, area = π(2r)² = 4πr², so it quadruples.
Correct Answer:
C
— It quadruples
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Q. If the radius of a circle is halved, by what factor does the circumference decrease? (2020)
A.
1/2
B.
1/4
C.
1/3
D.
1/6
Show solution
Solution
Circumference = 2πr; If r is halved, new circumference = πr; Factor = 1/2.
Correct Answer:
A
— 1/2
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Q. If the radius of a circle is halved, how does the circumference change? (2021)
A.
Halved
B.
Remains the same
C.
Doubled
D.
Tripled
Show solution
Solution
Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.
Correct Answer:
A
— Halved
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Q. If the radius of a circle is halved, how does the circumference change? (2022) 2022
A.
Halved
B.
Remains the same
C.
Doubled
D.
Quadrupled
Show solution
Solution
Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.
Correct Answer:
A
— Halved
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Q. If the radius of a circle is tripled, by what factor does the area increase? (2021)
Show solution
Solution
Area increases by a factor of (3r)²/r² = 9.
Correct Answer:
C
— 9
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Q. If the radius of a circle is tripled, how does the area change? (2019)
A.
Increases by 3 times
B.
Increases by 6 times
C.
Increases by 9 times
D.
Remains the same
Show solution
Solution
Area = πr². If radius is tripled, new area = π(3r)² = 9πr², which is 9 times the original area.
Correct Answer:
C
— Increases by 9 times
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Q. If the radius of a rotating object is halved while keeping the angular velocity constant, what happens to its linear velocity? (2022)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
Linear velocity v = rω, so if r is halved and ω remains constant, v also halves.
Correct Answer:
B
— It halves
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Q. If the radius of curvature of a concave mirror is 20 cm, what is its focal length? (2022)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
The focal length (f) of a concave mirror is given by f = R/2, where R is the radius of curvature. Thus, f = 20 cm / 2 = 10 cm.
Correct Answer:
B
— 10 cm
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Q. If the radius of curvature of a convex lens is 20 cm, what is its focal length? (2022)
A.
10 cm
B.
20 cm
C.
30 cm
D.
40 cm
Show solution
Solution
The focal length f of a lens is given by f = R/2. Therefore, f = 20 cm / 2 = 10 cm.
Correct Answer:
B
— 20 cm
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Q. If the radius of curvature of a convex mirror is 20 cm, what is its focal length? (2022)
A.
10 cm
B.
20 cm
C.
30 cm
D.
40 cm
Show solution
Solution
The focal length (f) of a mirror is given by f = R/2. For a convex mirror, R is positive, so f = 20 cm / 2 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. If the radius of the Earth is doubled, what will happen to the gravitational force experienced by an object on its surface?
A.
It will double
B.
It will remain the same
C.
It will be halved
D.
It will be quartered
Show solution
Solution
Gravitational force is inversely proportional to the square of the radius. If radius is doubled, F becomes F/4.
Correct Answer:
D
— It will be quartered
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Q. If the radius of the Earth were to increase by 50%, what would happen to the weight of an object on its surface?
A.
It increases by 50%
B.
It increases by 25%
C.
It decreases by 25%
D.
It remains the same
Show solution
Solution
Weight is inversely proportional to the square of the radius. If radius increases by 50%, weight decreases by 25%.
Correct Answer:
C
— It decreases by 25%
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Q. If the radius of the Earth were to increase while keeping its mass constant, what would happen to the gravitational acceleration at the surface? (2023)
A.
It increases
B.
It decreases
C.
It remains the same
D.
It becomes zero
Show solution
Solution
Gravitational acceleration is inversely proportional to the square of the radius. If radius increases, g decreases.
Correct Answer:
B
— It decreases
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Q. If the radius of the Earth were to increase while keeping its mass constant, what would happen to the gravitational acceleration at its surface?
A.
It increases
B.
It decreases
C.
It remains the same
D.
It becomes zero
Show solution
Solution
Gravitational acceleration g = GM/R². If R increases, g decreases.
Correct Answer:
B
— It decreases
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Q. If the radius of the Earth were to increase while keeping its mass constant, what would happen to the value of g? (2023)
A.
g increases
B.
g decreases
C.
g remains the same
D.
g becomes zero
Show solution
Solution
If the radius increases while mass remains constant, g decreases because g = G * M / r^2.
Correct Answer:
B
— g decreases
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Q. If the rate of a reaction doubles when the temperature increases by 10°C, what is the approximate activation energy? (2020)
A.
20 kJ/mol
B.
40 kJ/mol
C.
60 kJ/mol
D.
80 kJ/mol
Show solution
Solution
Using the Arrhenius equation, if the rate doubles for a 10°C increase, Ea is approximately 40 kJ/mol.
Correct Answer:
B
— 40 kJ/mol
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Q. If the rate of a reaction is directly proportional to the concentration of one reactant raised to the power of 3, what is the order of the reaction? (2023)
A.
Zero
B.
First
C.
Second
D.
Third
Show solution
Solution
The order of the reaction is third because the rate is proportional to the concentration raised to the power of 3.
Correct Answer:
D
— Third
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Q. If the rate of a reaction is given by rate = k[A]², what is the order of the reaction? (2021)
A.
Zero
B.
First
C.
Second
D.
Third
Show solution
Solution
The reaction is second-order because the rate depends on the square of the concentration of A.
Correct Answer:
C
— Second
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Q. If the resistance of a circuit is 10 ohms and the induced EMF is 5 V, what is the induced current? (2022)
A.
0.5 A
B.
1 A
C.
2 A
D.
5 A
Show solution
Solution
Using Ohm's law, I = V/R = 5 V / 10 ohms = 0.5 A.
Correct Answer:
A
— 0.5 A
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Q. If the resistance of a conductor is doubled while the voltage remains constant, what happens to the current? (2020)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
According to Ohm's Law, if the resistance (R) is doubled and the voltage (V) remains constant, the current (I) will be halved (I = V/R).
Correct Answer:
B
— It halves
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Q. If the resistance of a conductor is doubled, what happens to the current flowing through it when the voltage remains constant? (2022)
A.
Doubles
B.
Halves
C.
Remains the same
D.
Increases by 1.5 times
Show solution
Solution
According to Ohm's law, I = V/R. If R is doubled, I will be halved.
Correct Answer:
B
— Halves
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Q. If the revenue function is R(x) = 100x - 2x^2, find the number of units that maximizes revenue. (2021)
Show solution
Solution
Max revenue occurs at x = -b/(2a) = 100/(2*2) = 25.
Correct Answer:
B
— 50
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Q. If the revenue function is R(x) = 20x - 0.5x^2, find the quantity that maximizes revenue. (2021)
Show solution
Solution
R'(x) = 20 - x = 0 gives x = 20. This maximizes revenue.
Correct Answer:
B
— 20
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Q. If the revenue function is R(x) = 50x - 0.5x^2, find the number of units that maximizes revenue. (2023)
Show solution
Solution
Max revenue occurs at x = -b/(2a) = -50/(2*-0.5) = 50.
Correct Answer:
A
— 25
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Q. If the roots of the equation x² + 2x + k = 0 are 1 and -3, what is the value of k? (2020)
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Solution
Using the sum and product of roots: 1 + (-3) = -2 and 1 * (-3) = -3, thus k = 3.
Correct Answer:
C
— 3
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Q. If the roots of the equation x² + 2x + k = 0 are real and distinct, what is the condition for k? (2020)
A.
k > 1
B.
k < 1
C.
k > 4
D.
k < 4
Show solution
Solution
The discriminant must be greater than zero: 2² - 4*1*k > 0, which simplifies to k < 1.
Correct Answer:
C
— k > 4
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