Q. What is the product of the roots of the equation 3x² - 6x + 2 = 0? (2023)
A.
1/3
B.
2/3
C.
1/2
D.
1
Show solution
Solution
The product of the roots is given by c/a = 2/3.
Correct Answer:
B
— 2/3
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Q. What is the product of the roots of the equation x² + 5x + 6 = 0? (2022)
Show solution
Solution
The product of the roots is given by c/a = 6/1 = 6.
Correct Answer:
A
— 6
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Q. What is the product of the roots of the equation x² - 10x + 24 = 0? (2021)
Show solution
Solution
The product of the roots is given by c/a = 24/1 = 24.
Correct Answer:
A
— 24
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Q. What is the product of the roots of the equation x² - 8x + 15 = 0? (2022)
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Solution
The product of the roots is given by c/a = 15/1 = 15.
Correct Answer:
A
— 15
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Q. What is the projection of vector A = 3i + 4j onto vector B = i + j? (2020)
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Solution
proj_B(A) = (A · B / |B|^2)B = ((3*1 + 4*1) / (1^2 + 1^2))(i + j) = (7/2)(i + j) = 3.5.
Correct Answer:
C
— 5
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Q. What is the radius of a circle if its circumference is 62.8 cm? (2022)
A.
10 cm
B.
15 cm
C.
20 cm
D.
5 cm
Show solution
Solution
Circumference = 2πr; 62.8 = 2πr; r = 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the radius of a circle if the area is 154 square units? (2023)
A.
7 units
B.
14 units
C.
11 units
D.
10 units
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Solution
Area = πr²; 154 = 22/7 * r²; r² = 154 * 7/22 = 49; r = 7 units.
Correct Answer:
A
— 7 units
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Q. What is the radius of a circle if the circumference is 31.4 m? (2020)
A.
5 m
B.
10 m
C.
15 m
D.
20 m
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Solution
Circumference = 2πr; 31.4 = 2πr; r = 31.4/(2π) ≈ 5 m.
Correct Answer:
A
— 5 m
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Q. What is the radius of a circle if the circumference is 62.8 cm? (2016)
A.
10 cm
B.
15 cm
C.
20 cm
D.
25 cm
Show solution
Solution
Circumference = 2πr; 62.8 = 2πr; r = 62.8/(2π) ≈ 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the radius of a circle if the diameter is 14 cm? (2021)
A.
7 cm
B.
14 cm
C.
21 cm
D.
28 cm
Show solution
Solution
Radius is half of the diameter. Therefore, radius = 14 cm / 2 = 7 cm.
Correct Answer:
A
— 7 cm
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Q. What is the real part of the complex number 4 + 5i? (2023)
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Solution
The real part of the complex number 4 + 5i is 4.
Correct Answer:
A
— 4
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Q. What is the real part of the complex number 7 - 4i? (2023)
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Solution
The real part of the complex number 7 - 4i is 7.
Correct Answer:
A
— 7
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Q. What is the slope of the line passing through the points (1, 2) and (3, 6)? (2020) 2020
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Solution
Slope = (6-2)/(3-1) = 4/2 = 2.
Correct Answer:
A
— 2
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Q. What is the slope of the line perpendicular to the line 3x + 4y = 12?
A.
-3/4
B.
4/3
C.
3/4
D.
-4/3
Show solution
Solution
The slope of the line 3x + 4y = 12 is -3/4. The slope of the perpendicular line is the negative reciprocal, which is 4/3.
Correct Answer:
B
— 4/3
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Q. What is the slope of the line perpendicular to the line 4x + 2y = 8?
A.
-1/2
B.
1/2
C.
2
D.
-2
Show solution
Solution
The slope of the line is -2 (from y = -2x + 4). The slope of the perpendicular line is the negative reciprocal, which is 1/2.
Correct Answer:
A
— -1/2
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Q. What is the slope of the line perpendicular to the line 4x + 3y = 12?
A.
-3/4
B.
4/3
C.
3/4
D.
-4/3
Show solution
Solution
The slope of the line 4x + 3y = 12 is -4/3. The slope of the perpendicular line is the negative reciprocal, which is 3/4.
Correct Answer:
D
— -4/3
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Q. What is the slope of the line perpendicular to the line 5x + 2y = 10?
A.
-2/5
B.
5/2
C.
2/5
D.
-5/2
Show solution
Solution
The slope of the line is -5/2. The slope of the perpendicular line is the negative reciprocal, which is 2/5.
Correct Answer:
A
— -2/5
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Q. What is the slope of the line perpendicular to the line 7x - 2y + 3 = 0?
A.
1/2
B.
-1/2
C.
2
D.
-2
Show solution
Solution
The slope of the line is 7/2. The slope of the perpendicular line is the negative reciprocal, which is -2/7.
Correct Answer:
B
— -1/2
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Q. What is the slope of the line perpendicular to the line 7x - 2y = 14?
A.
1/7
B.
-1/7
C.
2/7
D.
-2/7
Show solution
Solution
The slope of the line is 7/2. The slope of the perpendicular line is the negative reciprocal, which is -2/7.
Correct Answer:
B
— -1/7
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Q. What is the slope of the line perpendicular to the line with slope 3?
A.
-1/3
B.
1/3
C.
3
D.
-3
Show solution
Solution
Slope of perpendicular line = -1/m = -1/3.
Correct Answer:
A
— -1/3
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Q. What is the slope of the line perpendicular to the line y = 3x + 1? (2023)
A.
-1/3
B.
1/3
C.
3
D.
-3
Show solution
Solution
Slope of perpendicular line = -1/(slope of original line) = -1/3.
Correct Answer:
A
— -1/3
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Q. What is the slope of the line that passes through the points (4, 5) and (6, 9)?
Show solution
Solution
The slope m = (9 - 5) / (6 - 4) = 4/2 = 2.
Correct Answer:
A
— 2
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Q. What is the slope of the tangent line to f(x) = x^2 + 2x at x = 1? (2023)
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Solution
f'(x) = 2x + 2. At x = 1, f'(1) = 2(1) + 2 = 4.
Correct Answer:
B
— 3
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Q. What is the slope of the tangent line to the curve y = x^2 - 4x + 5 at x = 3? (2023)
Show solution
Solution
The slope is given by f'(x) = 2x - 4. At x = 3, f'(3) = 2(3) - 4 = 2.
Correct Answer:
C
— 2
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Q. What is the slope of the tangent to the curve y = x^2 + 2x at x = 1? (2023)
Show solution
Solution
f'(x) = 2x + 2. At x = 1, f'(1) = 2(1) + 2 = 4.
Correct Answer:
B
— 3
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Q. What is the solution of the differential equation dy/dx = y^2?
A.
y = 1/(C - x)
B.
y = C/(x + 1)
C.
y = Cx
D.
y = e^(x + C)
Show solution
Solution
Separating variables and integrating gives 1/y = x + C, leading to y = 1/(C - x).
Correct Answer:
A
— y = 1/(C - x)
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Q. What is the solution of the differential equation y' = 2y + 3?
A.
y = Ce^(2x) - 3/2
B.
y = Ce^(2x) + 3/2
C.
y = 3e^(2x)
D.
y = 2e^(x) + C
Show solution
Solution
The integrating factor is e^(-2x). Solving gives y = Ce^(2x) + 3/2.
Correct Answer:
B
— y = Ce^(2x) + 3/2
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Q. What is the solution of the differential equation y' = 5y + 3?
A.
y = (3/5) + Ce^(5x)
B.
y = Ce^(5x) - (3/5)
C.
y = (3/5)e^(5x)
D.
y = Ce^(3x) + 5
Show solution
Solution
Using the integrating factor method, we find the general solution to be y = Ce^(5x) - (3/5).
Correct Answer:
B
— y = Ce^(5x) - (3/5)
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Q. What is the solution of the equation dy/dx = 3x^2?
A.
y = x^3 + C
B.
y = 3x^3 + C
C.
y = x^2 + C
D.
y = 3x^2 + C
Show solution
Solution
Integrating both sides gives y = ∫3x^2 dx = x^3 + C.
Correct Answer:
A
— y = x^3 + C
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Q. What is the solution of the equation dy/dx = 4y + 2? (2021)
A.
y = Ce^(4x) - 1/2
B.
y = Ce^(-4x) + 1/2
C.
y = 2e^(4x) + C
D.
y = 4e^(4x) + C
Show solution
Solution
Using an integrating factor, the solution is y = Ce^(4x) - 1/2.
Correct Answer:
A
— y = Ce^(4x) - 1/2
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Showing 841 to 870 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!
