Mathematics (MHT-CET) MCQ & Objective Questions
Mathematics plays a crucial role in the MHT-CET exams, serving as a foundation for various scientific and engineering disciplines. Practicing MCQs and objective questions not only enhances your problem-solving skills but also boosts your confidence in tackling important questions during exams. Engaging with practice questions is essential for effective exam preparation, helping you identify your strengths and areas that need improvement.
What You Will Practise Here
Algebra: Understanding equations, inequalities, and functions.
Geometry: Key concepts of shapes, theorems, and properties.
Trigonometry: Ratios, identities, and applications in problems.
Calculus: Basics of differentiation and integration.
Statistics: Data interpretation, mean, median, and mode.
Probability: Fundamental principles and problem-solving techniques.
Coordinate Geometry: Graphing lines, circles, and conic sections.
Exam Relevance
Mathematics is a significant component of various examinations including CBSE, State Boards, NEET, and JEE. In these exams, you can expect a mix of direct application questions and conceptual problems. Common question patterns include multiple-choice questions that test your understanding of formulas, definitions, and theorems, making it imperative to be well-versed in the subject matter.
Common Mistakes Students Make
Misinterpreting the question, leading to incorrect answers.
Overlooking the importance of units in calculations.
Rushing through problems without checking for calculation errors.
Neglecting to review fundamental concepts before advanced topics.
FAQs
Question: What types of questions can I expect in Mathematics (MHT-CET)?Answer: You can expect a variety of MCQs that cover theoretical concepts, problem-solving, and application-based questions.
Question: How can I improve my performance in Mathematics (MHT-CET)?Answer: Regular practice of Mathematics (MHT-CET) MCQ questions and understanding the underlying concepts will significantly enhance your performance.
Start solving practice MCQs today to test your understanding and sharpen your skills. Remember, consistent practice is the key to success in Mathematics (MHT-CET) and achieving your academic goals!
Q. A box contains 4 white and 6 black balls. What is the probability of drawing a black ball? (2023)
A.
2/5
B.
3/5
C.
4/5
D.
1/5
Show solution
Solution
Total balls = 4 + 6 = 10. Probability of black ball = 6/10 = 3/5.
Correct Answer:
B
— 3/5
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Q. A box contains 4 white and 6 black balls. What is the probability of picking a black ball?
A.
2/5
B.
3/5
C.
4/5
D.
1/5
Show solution
Solution
Total balls = 4 + 6 = 10. Probability of black ball = 6/10 = 3/5.
Correct Answer:
B
— 3/5
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Q. A box contains 5 white and 3 black balls. What is the probability of drawing a black ball?
A.
3/8
B.
5/8
C.
1/2
D.
1/3
Show solution
Solution
Total balls = 5 + 3 = 8. Probability of black ball = 3/8.
Correct Answer:
A
— 3/8
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Q. A box contains 5 white and 3 black balls. What is the probability of picking a black ball? (2021)
A.
3/8
B.
5/8
C.
1/2
D.
1/3
Show solution
Solution
Total balls = 5 + 3 = 8. Probability of black ball = 3/8.
Correct Answer:
A
— 3/8
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Q. A card is drawn from a standard deck of 52 cards. What is the probability of drawing a heart?
A.
1/4
B.
1/13
C.
1/2
D.
1/52
Show solution
Solution
Number of hearts = 13. Probability = 13/52 = 1/4.
Correct Answer:
A
— 1/4
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Q. A chord of a circle is 10 cm long and is 6 cm away from the center. What is the radius of the circle? (2023)
A.
8 cm
B.
10 cm
C.
12 cm
D.
14 cm
Show solution
Solution
Using Pythagoras theorem: r² = (10/2)² + 6²; r² = 25 + 36 = 61; r = √61 ≈ 10 cm.
Correct Answer:
B
— 10 cm
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Q. A chord of a circle is 12 cm long and is 5 cm away from the center. What is the radius of the circle? (2020)
A.
10 cm
B.
13 cm
C.
15 cm
D.
12 cm
Show solution
Solution
Using Pythagoras theorem: r² = (5)² + (6)² = 25 + 36 = 61; r = √61 ≈ 7.81 cm.
Correct Answer:
B
— 13 cm
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Q. A circle has a diameter of 10 cm. What is its circumference? (2022)
A.
31.4 cm
B.
20 cm
C.
15.7 cm
D.
25 cm
Show solution
Solution
Circumference = πd = π * 10 = 31.4 cm.
Correct Answer:
A
— 31.4 cm
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Q. A circle has a diameter of 20 cm. What is its circumference? (2022)
A.
62.8 cm
B.
40 cm
C.
31.4 cm
D.
20 cm
Show solution
Solution
Circumference = πd = π * 20 = 62.8 cm.
Correct Answer:
A
— 62.8 cm
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Q. A circle has a radius of 10 cm. What is the diameter? (2020)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Diameter = 2 * radius = 2 * 10 cm = 20 cm.
Correct Answer:
D
— 20 cm
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Q. A circle has a radius of 12 cm. What is the diameter? (2020)
A.
6 cm
B.
12 cm
C.
24 cm
D.
18 cm
Show solution
Solution
Diameter = 2 * radius = 2 * 12 = 24 cm.
Correct Answer:
C
— 24 cm
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Q. A circle has a radius of 3 cm. What is the diameter in millimeters? (2023)
A.
30 mm
B.
60 mm
C.
90 mm
D.
120 mm
Show solution
Solution
Diameter = 2 * radius = 2 * 3 cm = 6 cm = 60 mm.
Correct Answer:
A
— 30 mm
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Q. A circle has a radius of 3 m. What is the diameter? (2022)
A.
3 m
B.
6 m
C.
9 m
D.
12 m
Show solution
Solution
Diameter = 2 * radius = 2 * 3 m = 6 m.
Correct Answer:
B
— 6 m
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Q. A circle has a radius of 5 cm. What is the length of an arc that subtends a central angle of 60 degrees? (2021)
A.
5.24 cm
B.
10.47 cm
C.
3.14 cm
D.
6.28 cm
Show solution
Solution
Arc length = (θ/360) * 2πr; = (60/360) * 2π * 5 = 10.47 cm.
Correct Answer:
B
— 10.47 cm
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Q. A circle has a radius of 5 cm. What is the length of an arc that subtends an angle of 60 degrees? (2023)
A.
5.24 cm
B.
3.14 cm
C.
5.00 cm
D.
10.47 cm
Show solution
Solution
Arc length = (θ/360) × 2πr; = (60/360) × 2π × 5 ≈ 5.24 cm.
Correct Answer:
A
— 5.24 cm
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Q. A circle has a radius of 5 cm. What is the length of an arc that subtends an angle of 60 degrees at the center? (2020)
A.
5.24 cm
B.
3.14 cm
C.
5.00 cm
D.
10.47 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * π * 5 = 5.24 cm.
Correct Answer:
A
— 5.24 cm
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Q. A circle has an area of 154 cm². What is the radius? (2019)
A.
7 cm
B.
14 cm
C.
21 cm
D.
28 cm
Show solution
Solution
Area = πr². Therefore, r = √(Area/π) = √(154/3.14) ≈ 7 cm.
Correct Answer:
B
— 14 cm
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Q. A circle has an area of 154 cm². What is the radius? (2019) 2019
A.
7 cm
B.
14 cm
C.
21 cm
D.
28 cm
Show solution
Solution
Area = πr². Therefore, r = √(Area/π) = √(154/3.14) ≈ 7 cm.
Correct Answer:
B
— 14 cm
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Q. A circle has an area of 78.5 cm². What is its radius? (Use π = 3.14) (2019)
A.
5 cm
B.
7 cm
C.
10 cm
D.
12 cm
Show solution
Solution
Area = πr². Therefore, r² = Area / π = 78.5 cm² / 3.14 = 25. r = √25 = 5 cm.
Correct Answer:
B
— 7 cm
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Q. A circle has an area of 78.5 cm². What is the radius? (Use π = 3.14) (2022)
A.
5 cm
B.
7 cm
C.
10 cm
D.
12 cm
Show solution
Solution
Area = πr². Therefore, r² = Area / π = 78.5 cm² / 3.14 = 25. r = √25 = 5 cm.
Correct Answer:
B
— 7 cm
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Q. A circle is inscribed in a square of side 10 cm. What is the area of the circle? (2019)
A.
78.5 cm²
B.
100 cm²
C.
50 cm²
D.
25 cm²
Show solution
Solution
Radius = 10/2 = 5 cm; Area = πr² = π * 5² = 78.5 cm².
Correct Answer:
A
— 78.5 cm²
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Q. A circle is inscribed in a square of side 10 cm. What is the area of the circle? (Use π = 3.14) (2020)
A.
78.5 cm²
B.
50 cm²
C.
100 cm²
D.
25 cm²
Show solution
Solution
Radius of the circle = side/2 = 10 cm / 2 = 5 cm. Area = πr² = 3.14 * 5² = 78.5 cm².
Correct Answer:
A
— 78.5 cm²
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Q. A circle is inscribed in a square of side 8 cm. What is the area of the circle? (2022)
A.
50.24 cm²
B.
64 cm²
C.
25.12 cm²
D.
32 cm²
Show solution
Solution
Radius = 8/2 = 4 cm; Area = πr² = π * 4² = 50.24 cm².
Correct Answer:
A
— 50.24 cm²
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Q. A cylindrical can is to be made with a fixed volume of 1000 cm³. What dimensions minimize the surface area? (2022)
A.
10 cm height, 10 cm radius
B.
5 cm height, 15.87 cm radius
C.
8 cm height, 12.5 cm radius
D.
12 cm height, 8.33 cm radius
Show solution
Solution
Using the formula for surface area and volume, the optimal dimensions are found to be 5 cm height and approximately 15.87 cm radius.
Correct Answer:
B
— 5 cm height, 15.87 cm radius
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Q. A cylindrical can is to be made with a fixed volume of 1000 cm³. What dimensions minimize the surface area? (2022) 2022
A.
10, 10
B.
5, 20
C.
8, 15
D.
6, 18
Show solution
Solution
Using the formula for surface area and volume, the optimal dimensions are found to be radius = 5 and height = 20.
Correct Answer:
C
— 8, 15
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Q. A cylindrical can is to be made with a volume of 1000 cm³. What dimensions minimize the surface area? (2021)
A.
10, 10
B.
5, 20
C.
8, 15
D.
6, 18
Show solution
Solution
Using the formula for volume and surface area, the optimal dimensions are found to be radius = 5 cm and height = 20 cm.
Correct Answer:
B
— 5, 20
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Q. A farmer wants to fence a rectangular area of 200 m^2. What dimensions will minimize the fencing required? (2021)
A.
10, 20
B.
14, 14.28
C.
15, 13.33
D.
20, 10
Show solution
Solution
For a fixed area, the minimum perimeter occurs when the rectangle is a square. Thus, dimensions are approximately 14 m by 14.28 m.
Correct Answer:
B
— 14, 14.28
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Q. A farmer wants to fence a rectangular field with 100 m of fencing. What dimensions will maximize the area? (2022)
A.
25 m by 25 m
B.
30 m by 20 m
C.
40 m by 10 m
D.
50 m by 0 m
Show solution
Solution
For maximum area, the rectangle should be a square. Each side = 100/4 = 25 m.
Correct Answer:
A
— 25 m by 25 m
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Q. A jar contains 10 candies, 4 of which are chocolate. What is the probability of selecting a chocolate candy?
A.
2/5
B.
1/2
C.
4/10
D.
3/10
Show solution
Solution
Probability of chocolate candy = 4/10 = 2/5.
Correct Answer:
B
— 1/2
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Q. A jar contains 4 green, 5 yellow, and 1 red marble. What is the probability of picking a yellow marble? (2019)
A.
1/10
B.
1/5
C.
1/2
D.
5/10
Show solution
Solution
Total marbles = 4 + 5 + 1 = 10. Probability of yellow = 5/10 = 1/2.
Correct Answer:
D
— 5/10
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