Q. What is the distance from the point (1, 2) to the line x + y = 5? (2020)
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Solution
Distance = |1 + 2 - 5| / √(1² + 1²) = | -2 | / √2 = 2/√2 = √2.
Correct Answer:
A
— 3
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Q. What is the distance from the point (2, 3) to the line x + y - 5 = 0? (2022)
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Solution
Distance = |(1*2 + 1*3 - 5)| / √(1² + 1²) = |5 - 5| / √2 = 0
Correct Answer:
A
— 1
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Q. What is the distance from the point (2, 3) to the line x + y = 5? (2020)
Show solution
Solution
Distance = |(1*2 + 1*3 - 5)| / √(1² + 1²) = |5 - 5| / √2 = 0/√2 = 0
Correct Answer:
B
— 2
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Q. What is the distance from the point (3, 4) to the line x + y = 5? (2022)
Show solution
Solution
Distance = |3 + 4 - 5| / √(1² + 1²) = |2| / √2 = 2/√2 = √2.
Correct Answer:
B
— 2
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Q. What is the dot product of vectors A = 2i + 3j and B = 4i - j? (2022)
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Solution
A · B = (2)(4) + (3)(-1) = 8 - 3 = 5.
Correct Answer:
B
— 10
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Q. What is the equation of a plane passing through the point (1, 2, 3) with normal vector (2, -1, 3)? (2021)
A.
2x - y + 3z = 12
B.
2x + y - 3z = 0
C.
2x - y + 3z = 0
D.
2x + y + 3z = 12
Show solution
Solution
Equation of the plane: 2(x-1) - 1(y-2) + 3(z-3) = 0 simplifies to 2x - y + 3z = 12.
Correct Answer:
C
— 2x - y + 3z = 0
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Q. What is the equation of a plane passing through the point (1, 2, 3) with normal vector (1, 1, 1)? (2022)
A.
x + y + z = 6
B.
x + y + z = 3
C.
x + y + z = 1
D.
x + y + z = 0
Show solution
Solution
Equation of the plane: 1(x-1) + 1(y-2) + 1(z-3) = 0 => x + y + z = 6.
Correct Answer:
A
— x + y + z = 6
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Q. What is the equation of the line parallel to y = 3x + 4 that passes through the point (2, 5)? (2022)
A.
y = 3x - 1
B.
y = 3x + 1
C.
y = 3x + 2
D.
y = 3x + 3
Show solution
Solution
Since parallel lines have the same slope, the equation is y - 5 = 3(x - 2) which simplifies to y = 3x + 1.
Correct Answer:
B
— y = 3x + 1
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Q. What is the equation of the line parallel to y = 3x - 5 and passing through (2, 1)?
A.
y = 3x - 8
B.
y = 3x + 5
C.
y = 3x - 1
D.
y = 3x + 1
Show solution
Solution
Parallel lines have the same slope. The slope is 3. Using point-slope form: y - 1 = 3(x - 2) gives y = 3x - 8.
Correct Answer:
A
— y = 3x - 8
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Q. What is the equation of the line parallel to y = 3x - 5 that passes through the point (2, 1)?
A.
y = 3x - 8
B.
y = 3x + 5
C.
y = 3x - 1
D.
y = 3x + 1
Show solution
Solution
Since the lines are parallel, they have the same slope. Using point-slope form: y - 1 = 3(x - 2) gives y = 3x - 8.
Correct Answer:
A
— y = 3x - 8
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Q. What is the equation of the line passing through (0, 0) and (2, 4)? (2019)
A.
y = 2x
B.
y = x
C.
y = 4x
D.
y = 3x
Show solution
Solution
Slope = (4-0)/(2-0) = 2, so the equation is y = 2x.
Correct Answer:
A
— y = 2x
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Q. What is the equation of the line passing through (0, 0) with a slope of 3? (2021)
A.
y = 3x
B.
y = x/3
C.
y = 3/x
D.
y = 1/3x
Show solution
Solution
Equation of line: y = mx + c; here m = 3, c = 0 => y = 3x
Correct Answer:
A
— y = 3x
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Q. What is the equation of the line passing through (2, 3) with a slope of 2? (2021)
A.
y = 2x - 1
B.
y = 2x + 1
C.
y = 2x + 3
D.
y = 2x - 3
Show solution
Solution
Using point-slope form: y - 3 = 2(x - 2) => y = 2x - 4 + 3 => y = 2x - 1.
Correct Answer:
B
— y = 2x + 1
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Q. What is the equation of the line passing through the points (1, 2) and (3, 4)?
A.
y = x + 1
B.
y = 2x
C.
y = x + 2
D.
y = 2x - 2
Show solution
Solution
The slope m = (4 - 2) / (3 - 1) = 1. Using point-slope form, y - 2 = 1(x - 1) gives y = x + 1.
Correct Answer:
A
— y = x + 1
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Q. What is the equation of the line passing through the points (1, 2) and (3, 6)?
A.
y = 2x
B.
y = 3x - 1
C.
y = x + 1
D.
y = 4x - 2
Show solution
Solution
The slope m = (6 - 2) / (3 - 1) = 2. Using point-slope form, y - 2 = 2(x - 1) gives y = 2x.
Correct Answer:
A
— y = 2x
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Q. What is the equation of the line perpendicular to y = 3x + 1 that passes through (2, 3)?
A.
y = -1/3x + 4
B.
y = 3x - 3
C.
y = -3x + 9
D.
y = 1/3x + 2
Show solution
Solution
The slope of the perpendicular line is -1/3. Using point-slope form, we find y - 3 = -1/3(x - 2) which simplifies to y = -1/3x + 4.
Correct Answer:
A
— y = -1/3x + 4
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Q. What is the equation of the line that passes through the origin and has a slope of -1?
A.
y = -x
B.
y = x
C.
y = -2x
D.
y = 2x
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Solution
The equation of a line through the origin with slope m is y = mx. Thus, y = -1x or y = -x.
Correct Answer:
A
— y = -x
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Q. What is the equation of the line that passes through the origin and has a slope of -5?
A.
y = -5x
B.
y = 5x
C.
y = -x/5
D.
y = 5/x
Show solution
Solution
The equation of a line through the origin with slope m is y = mx. Thus, y = -5x.
Correct Answer:
A
— y = -5x
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Q. What is the equation of the plane passing through the point (1, 2, 3) with normal vector (1, -1, 1)? (2023)
A.
x - y + z = 0
B.
x + y + z = 6
C.
x - y + z = 1
D.
x + y - z = 0
Show solution
Solution
Equation of the plane: 1(x-1) - 1(y-2) + 1(z-3) = 0 => x - y + z = 1.
Correct Answer:
C
— x - y + z = 1
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Q. What is the equation of the plane passing through the points (1, 2, 3), (4, 5, 6), and (7, 8, 9)? (2021)
A.
0 = 0
B.
x + y + z = 12
C.
x + y + z = 10
D.
x + y + z = 9
Show solution
Solution
The points are collinear, hence the equation of the plane is 0 = 0.
Correct Answer:
A
— 0 = 0
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Q. What is the general solution of the equation y' + 4y = 0?
A.
y = Ce^(-4x)
B.
y = Ce^(4x)
C.
y = 4x + C
D.
y = Cx^4
Show solution
Solution
This is a separable equation, and integrating gives y = Ce^(-4x).
Correct Answer:
A
— y = Ce^(-4x)
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Q. What is the general solution of the equation y' = 4y + 3?
A.
y = Ce^(4x) - 3/4
B.
y = Ce^(4x) + 3/4
C.
y = 3e^(4x)
D.
y = Ce^(3x) + 4
Show solution
Solution
The integrating factor is e^(-4x). The solution is y = Ce^(4x) + 3/4.
Correct Answer:
B
— y = Ce^(4x) + 3/4
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Q. What is the general solution of the equation y'' - 3y' + 2y = 0?
A.
y = C1 e^(x) + C2 e^(2x)
B.
y = C1 e^(2x) + C2 e^(x)
C.
y = C1 e^(3x) + C2 e^(0)
D.
y = C1 e^(0) + C2 e^(3x)
Show solution
Solution
The characteristic equation is r^2 - 3r + 2 = 0, which factors to (r - 1)(r - 2) = 0. Thus, the general solution is y = C1 e^(2x) + C2 e^(x).
Correct Answer:
B
— y = C1 e^(2x) + C2 e^(x)
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Q. What is the general solution of the equation y'' - 4y' + 4y = 0?
A.
y = (C1 + C2x)e^(2x)
B.
y = C1 e^(2x) + C2 e^(-2x)
C.
y = C1 e^(4x) + C2 e^(-4x)
D.
y = C1 cos(2x) + C2 sin(2x)
Show solution
Solution
The characteristic equation has a repeated root r = 2. The general solution is y = (C1 + C2x)e^(2x).
Correct Answer:
A
— y = (C1 + C2x)e^(2x)
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Q. What is the integral of 1/x with respect to x? (2022)
A.
ln
B.
x
C.
+ C
D.
1/x + C
.
x + C
.
e^x + C
Show solution
Solution
The integral of 1/x is ln|x| + C.
Correct Answer:
A
— ln
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Q. What is the integral of 1/x? (2022)
A.
ln
B.
x
C.
+ C
D.
1/x + C
.
x + C
.
x^2 + C
Show solution
Solution
The integral of 1/x is ln|x| + C.
Correct Answer:
A
— ln
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Q. What is the integral of cos(2x) dx? (2021)
A.
(1/2)sin(2x) + C
B.
sin(2x) + C
C.
(1/2)cos(2x) + C
D.
2sin(2x) + C
Show solution
Solution
The integral of cos(2x) is (1/2)sin(2x) + C.
Correct Answer:
A
— (1/2)sin(2x) + C
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Q. What is the integral of e^x with respect to x? (2023)
A.
e^x + C
B.
xe^x + C
C.
e^x/x + C
D.
x^2e^x + C
Show solution
Solution
The integral of e^x is e^x + C.
Correct Answer:
A
— e^x + C
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Q. What is the integral of e^x? (2023)
A.
e^x + C
B.
xe^x + C
C.
e^x/x + C
D.
x^2e^x + C
Show solution
Solution
The integral of e^x is e^x + C.
Correct Answer:
A
— e^x + C
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Q. What is the integral of sin(x) dx? (2021)
A.
-cos(x) + C
B.
cos(x) + C
C.
sin(x) + C
D.
-sin(x) + C
Show solution
Solution
The integral of sin(x) is -cos(x) + C.
Correct Answer:
A
— -cos(x) + C
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Showing 751 to 780 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!
