Q. What is the determinant of the matrix \( F = \begin{pmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{pmatrix} \)? (2022)
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Solution
Using the determinant formula for 3x3 matrices, we find \( 1(1*0 - 4*6) - 2(0*0 - 4*5) + 3(0*6 - 1*5) = 1(0 - 24) - 2(0 - 20) + 3(0 - 5) = -24 + 40 - 15 = 1 \).
Correct Answer:
A
— -14
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Q. What is the determinant of the matrix \( F = \begin{pmatrix} 2 & 5 \\ 3 & 7 \end{pmatrix} \)? (2023)
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Solution
The determinant is calculated as \( 2*7 - 5*3 = 14 - 15 = -1 \).
Correct Answer:
A
— -1
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Q. What is the determinant of the matrix \( G = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \)? (2023)
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Solution
The determinant is \( 2*7 - 3*5 = 14 - 15 = -1 \).
Correct Answer:
A
— 1
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Q. What is the determinant of the matrix \( H = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \)? (2022)
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Solution
The determinant of the identity matrix is always 1.
Correct Answer:
B
— 1
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Q. What is the determinant of the matrix \( H = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \)? (2023)
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Solution
The determinant of this matrix is 0 because the rows are linearly dependent.
Correct Answer:
A
— 0
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Q. What is the determinant of the matrix \( I = \begin{pmatrix} 4 & 2 \\ 1 & 3 \end{pmatrix} \)? (2021)
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Solution
The determinant is \( 4*3 - 2*1 = 12 - 2 = 10 \).
Correct Answer:
A
— 10
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Q. What is the diameter of a circle if its area is 50π square units? (2017)
A.
10 units
B.
5 units
C.
20 units
D.
15 units
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Solution
Area = πr²; 50π = πr²; r² = 50; r = √50; Diameter = 2√50 ≈ 10 units.
Correct Answer:
A
— 10 units
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Q. What is the diameter of a circle if its area is 78.5 cm²? (2020)
A.
10 cm
B.
8 cm
C.
6 cm
D.
12 cm
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Solution
Area = πr²; 78.5 = π * r²; r² = 78.5/π; d = 2√(78.5/π) = 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the diameter of a circle with a radius of 9 cm? (2022)
A.
9 cm
B.
18 cm
C.
27 cm
D.
36 cm
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Solution
Diameter = 2 * radius = 2 * 9 cm = 18 cm.
Correct Answer:
B
— 18 cm
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Q. What is the diameter of a circle with an area of 50.24 cm²? (2019)
A.
8 cm
B.
10 cm
C.
12 cm
D.
14 cm
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Solution
Area = πr²; 50.24 = πr²; r² = 50.24/π; r ≈ 4 cm; Diameter = 2r = 8 cm.
Correct Answer:
B
— 10 cm
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Q. What is the diameter of a circle with an area of 50π square units? (2017)
A.
10 units
B.
5 units
C.
20 units
D.
15 units
Show solution
Solution
Area = πr²; 50π = πr²; r² = 50; r = √50; Diameter = 2√50 ≈ 10 units.
Correct Answer:
A
— 10 units
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Q. What is the diameter of a circle with an area of 78.5 cm²? (2018)
A.
10 cm
B.
8 cm
C.
6 cm
D.
12 cm
Show solution
Solution
Area = πr²; 78.5 = πr²; r² = 78.5/π; d = 2√(78.5/π) ≈ 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the discriminant of the equation 3x² - 12x + 12 = 0? (2023)
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Solution
The discriminant is b² - 4ac = (-12)² - 4*3*12 = 144 - 144 = 0.
Correct Answer:
A
— 0
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Q. What is the discriminant of the equation 3x² - 12x + 9 = 0? (2023)
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Solution
The discriminant is b² - 4ac = (-12)² - 4*3*9 = 0.
Correct Answer:
A
— 0
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Q. What is the discriminant of the equation 4x² - 12x + 9 = 0? (2019)
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Solution
The discriminant is b² - 4ac = (-12)² - 4*4*9 = 144 - 144 = 0.
Correct Answer:
A
— 0
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Q. What is the discriminant of the equation x² + 6x + 9 = 0? (2020)
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Solution
The discriminant is b² - 4ac = 6² - 4*1*9 = 0.
Correct Answer:
A
— 0
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Q. What is the distance between the center of a circle and a point on its circumference if the radius is 15 cm? (2014)
A.
15 cm
B.
30 cm
C.
10 cm
D.
5 cm
Show solution
Solution
The distance from the center to any point on the circumference is always the radius, which is 15 cm.
Correct Answer:
A
— 15 cm
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Q. What is the distance between the center of a circle and a point on its circumference if the radius is 12 cm? (2022)
A.
6 cm
B.
12 cm
C.
18 cm
D.
24 cm
Show solution
Solution
The distance from the center to a point on the circumference is the radius, which is 12 cm.
Correct Answer:
B
— 12 cm
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Q. What is the distance between the center of a circle and a point on its circumference if the radius is 10 cm? (2022)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
The distance from the center to a point on the circumference is the radius, which is 10 cm.
Correct Answer:
B
— 10 cm
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Q. What is the distance between the center of a circle and a point on its circumference if the radius is 8 cm? (2023)
A.
8 cm
B.
16 cm
C.
4 cm
D.
0 cm
Show solution
Solution
The distance from the center to a point on the circumference is the radius, which is 8 cm.
Correct Answer:
A
— 8 cm
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Q. What is the distance between the parallel planes 2x + 3y - z = 5 and 2x + 3y - z = 10? (2021)
A.
5/√14
B.
10/√14
C.
15/√14
D.
20/√14
Show solution
Solution
Distance = |d1 - d2| / √(A² + B² + C²) = |5 - 10| / √(2² + 3² + (-1)²) = 5/√14.
Correct Answer:
B
— 10/√14
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Q. What is the distance between the parallel planes x + 2y + 3z = 4 and x + 2y + 3z = 10? (2023)
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Solution
Distance = |d1 - d2| / √(a² + b² + c²) = |4 - 10| / √(1² + 2² + 3²) = 6 / √14.
Correct Answer:
A
— 2
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Q. What is the distance between the point (2, 3, 4) and the plane x + y + z = 10? (2022)
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Solution
Distance = |(2 + 3 + 4 - 10) / √(1² + 1² + 1²)| = |(-1)/√3| = 1/√3.
Correct Answer:
A
— 1
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Q. What is the distance between the points (-1, -1) and (2, 3)? (2022) 2022
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Solution
Distance = √[(2 - (-1))² + (3 - (-1))²] = √[3² + 4²] = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the distance between the points (-1, -1) and (2, 3)? (2023)
Show solution
Solution
Distance = √[(2 - (-1))² + (3 - (-1))²] = √[3² + 4²] = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the distance between the points (2, 3) and (5, 7)?
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Solution
Using the distance formula, d = √((5 - 2)² + (7 - 3)²) = √(9 + 16) = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the distance between the points (3, 4) and (7, 1)? (2021) 2021
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Solution
Distance = √[(7-3)² + (1-4)²] = √[4 + 9] = √13 ≈ 5.
Correct Answer:
A
— 5
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Q. What is the distance between the points A(1, 2, 3) and B(4, 5, 6)? (2023)
A.
3√2
B.
3√3
C.
3
D.
√27
Show solution
Solution
Distance = √[(4-1)² + (5-2)² + (6-3)²] = √[3² + 3² + 3²] = √27 = 3√3.
Correct Answer:
A
— 3√2
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Q. What is the distance from the point (1, 1) to the line x + y = 2? (2023)
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Solution
Distance = |1 + 1 - 2| / √(1² + 1²) = 0 / √2 = 0.
Correct Answer:
A
— 1
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Q. What is the distance from the point (1, 2) to the line x + y - 3 = 0? (2023)
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Solution
Distance = |1 + 2 - 3| / √(1² + 1²) = |0| / √2 = 0, closest option is 1.
Correct Answer:
B
— 2
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Showing 721 to 750 of 973 (33 Pages)
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!
