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MHT-CET

Chemistry (MHT-CET) Mathematics (MHT-CET) Physics (MHT-CET)

Q. Find the determinant of \( G = \begin{pmatrix} 4 & 2 \\ 3 & 1 \end{pmatrix} \). (2020)

A. -2
B. 2
C. 0
D. 1

Solution

The determinant is \( 4*1 - 2*3 = 4 - 6 = -2 \).

Correct Answer: A — -2

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Q. Find the dimensions of a box with a square base that maximizes volume given a surface area of 600 sq. units. (2020)

A. 10, 10
B. 15, 15
C. 12, 12
D. 20, 20

Solution

Let x be the side of the base and h the height. The surface area constraint gives 2x^2 + 4xh = 600. Max volume occurs at x = 12.

Correct Answer: C — 12, 12

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Q. Find the dimensions of a rectangle with a fixed area of 50 m^2 that minimizes the perimeter. (2021)

A. 5, 10
B. 7, 7.14
C. 8, 6.25
D. 10, 5

Solution

For a fixed area, the minimum perimeter occurs when the rectangle is a square. Thus, dimensions are approximately 7 m by 7.14 m.

Correct Answer: B — 7, 7.14

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Q. Find the dimensions of a rectangle with a fixed area of 50 square units that minimizes the perimeter. (2022) 2022

A. 5, 10
B. 7, 7.14
C. 10, 5
D. 8, 6.25

Solution

For minimum perimeter, the rectangle should be a square. Thus, side = sqrt(50) ≈ 7.07.

Correct Answer: B — 7, 7.14

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Q. Find the dimensions of a rectangle with a fixed area of 50 square units that minimizes the perimeter. (2020)

A. 5, 10
B. 7, 7
C. 10, 5
D. 8, 6.25

Solution

For a fixed area, the perimeter is minimized when the rectangle is a square. Thus, side = √50.

Correct Answer: B — 7, 7

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Q. Find the distance between the parallel planes 2x + 3y + 4z = 5 and 2x + 3y + 4z = 10. (2023)

A. 5/√29
B. 10/√29
C. 15/√29
D. 20/√29

Solution

Distance = |d1 - d2| / √(a² + b² + c²) = |5 - 10| / √(2² + 3² + 4²) = 5 / √29.

Correct Answer: B — 10/√29

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Q. Find the distance between the parallel planes 2x + 3y + z = 5 and 2x + 3y + z = 10. (2022)

A. 5
B. 10
C. √14
D. √10

Solution

Distance = |d1 - d2| / √(A² + B² + C²) = |5 - 10| / √(2² + 3² + 1²) = 5 / √14.

Correct Answer: A — 5

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Q. Find the distance between the parallel planes x + 2y + 3z = 4 and x + 2y + 3z = 10. (2023)

A. 2
B. 3
C. 4
D. 5

Solution

Distance = |d1 - d2| / √(a² + b² + c²) = |4 - 10| / √(1² + 2² + 3²) = 6 / √14.

Correct Answer: A — 2

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Q. Find the equation of the line parallel to y = 3x + 2 and passing through (4, 5).

A. y = 3x - 7
B. y = 3x + 5
C. y = 3x + 2
D. y = 3x - 2

Solution

Since the line is parallel, it has the same slope. Using point-slope form: y - 5 = 3(x - 4) gives y = 3x - 7.

Correct Answer: A — y = 3x - 7

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Q. Find the equation of the line parallel to y = 3x + 2 that passes through the point (4, 1).

A. y = 3x - 11
B. y = 3x + 1
C. y = 3x + 2
D. y = 3x - 2

Solution

Since the line is parallel, it has the same slope (3). Using point-slope form: y - 1 = 3(x - 4) gives y = 3x - 11.

Correct Answer: A — y = 3x - 11

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Q. Find the equation of the line parallel to y = 5x - 2 that passes through the point (2, 3).

A. y = 5x - 7
B. y = 5x + 2
C. y = 5x - 5
D. y = 5x + 1

Solution

Since the slope is the same (5), using point-slope form: y - 3 = 5(x - 2) gives y = 5x - 7.

Correct Answer: A — y = 5x - 7

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Q. Find the equation of the line parallel to y = 5x - 3 that passes through the point (2, 1).

A. y = 5x - 9
B. y = 5x + 1
C. y = 5x - 7
D. y = 5x + 3

Solution

Since the slope is the same (5), using point-slope form: y - 1 = 5(x - 2) gives y = 5x - 9.

Correct Answer: A — y = 5x - 9

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Q. Find the equation of the line that passes through (0, 0) and has a slope of 5.

A. y = 5x
B. y = x/5
C. y = 5/x
D. y = 1/5x

Solution

Using the slope-intercept form y = mx + b, with m = 5 and b = 0, we get y = 5x.

Correct Answer: A — y = 5x

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Q. Find the equation of the line that passes through (2, 3) and is perpendicular to the line y = 4x - 1.

A. y = -1/4x + 4
B. y = 4x - 5
C. y = -4x + 11
D. y = 1/4x + 2

Solution

The slope of the given line is 4, so the perpendicular slope is -1/4. Using point-slope form, we get y - 3 = -1/4(x - 2) which simplifies to y = -1/4x + 11/4.

Correct Answer: C — y = -4x + 11

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Q. Find the equation of the line that passes through (2, 3) and is perpendicular to the line y = 1/3x + 2.

A. y = -3x + 9
B. y = 3x - 3
C. y = -1/3x + 4
D. y = 1/3x + 1

Solution

The slope of the given line is 1/3, so the perpendicular slope is -3. Using point-slope form, y - 3 = -3(x - 2) gives y = -3x + 9.

Correct Answer: A — y = -3x + 9

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Q. Find the equation of the line that passes through the origin and has a slope of -3.

A. y = -3x
B. y = 3x
C. y = -x/3
D. y = 1/3x

Solution

Using the slope-intercept form, the equation is y = -3x.

Correct Answer: A — y = -3x

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Q. Find the equation of the line that passes through the point (2, -3) and has a slope of 4.

A. y = 4x - 11
B. y = 4x + 5
C. y = 4x - 3
D. y = 4x + 3

Solution

Using point-slope form, y + 3 = 4(x - 2) simplifies to y = 4x - 11.

Correct Answer: A — y = 4x - 11

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Q. Find the equation of the line that passes through the point (4, -1) and is perpendicular to the line y = 3x + 2.

A. y = -1/3x + 5/3
B. y = 3x - 13
C. y = -3x + 11
D. y = 1/3x - 5/3

Solution

The slope of the given line is 3, so the slope of the perpendicular line is -1/3. Using point-slope form, we get y + 1 = -1/3(x - 4), which simplifies to y = -1/3x + 11/3.

Correct Answer: C — y = -3x + 11

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Q. Find the equation of the line that passes through the point (4, 5) and is perpendicular to the line y = 1/3x + 2.

A. y = -3x + 17
B. y = 3x - 7
C. y = -3x + 5
D. y = 1/3x + 5

Solution

The slope of the given line is 1/3, so the slope of the perpendicular line is -3. Using point-slope form, we get y - 5 = -3(x - 4), which simplifies to y = -3x + 17.

Correct Answer: A — y = -3x + 17

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Q. Find the equation of the line that passes through the points (2, 3) and (4, 7).

A. y = 2x - 1
B. y = 2x + 1
C. y = 3x - 3
D. y = x + 1

Solution

The slope m = (7 - 3) / (4 - 2) = 2. Using point-slope form: y - 3 = 2(x - 2) gives y = 2x + 1.

Correct Answer: B — y = 2x + 1

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Q. Find the general solution of dy/dx = 3x^2. (2020)

A. y = x^3 + C
B. y = 3x^3 + C
C. y = x^2 + C
D. y = 3x + C

Solution

Integrating 3x^2 gives y = x^3 + C.

Correct Answer: A — y = x^3 + C

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Q. Find the general solution of the equation y' = 3x^2y.

A. y = Ce^(x^3)
B. y = Ce^(3x^3)
C. y = C/x^3
D. y = Cx^3

Solution

This is a separable equation. Integrating gives y = Ce^(x^3).

Correct Answer: A — y = Ce^(x^3)

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Q. Find the general solution of the equation y' = 5y + 3.

A. y = Ce^(5x) - 3/5
B. y = Ce^(5x) + 3/5
C. y = 3/5 + Ce^(-5x)
D. y = 5x + C

Solution

The integrating factor method gives the general solution y = Ce^(5x) - 3/5.

Correct Answer: A — y = Ce^(5x) - 3/5

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Q. Find the general solution of the equation y'' - 3y' + 2y = 0.

A. y = C1 e^(2x) + C2 e^(x)
B. y = C1 e^(x) + C2 e^(2x)
C. y = C1 e^(3x) + C2 e^(0)
D. y = C1 e^(0) + C2 e^(3x)

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^(x) + C2 e^(2x).

Correct Answer: B — y = C1 e^(x) + C2 e^(2x)

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Q. Find the integral of (2x + 1)^3 dx. (2019)

A. (1/4)(2x + 1)^4 + C
B. (1/3)(2x + 1)^4 + C
C. (1/5)(2x + 1)^4 + C
D. (1/2)(2x + 1)^4 + C

Solution

Using substitution, the integral is (1/4)(2x + 1)^4 + C.

Correct Answer: A — (1/4)(2x + 1)^4 + C

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Q. Find the integral of (2x + 3)dx. (2022)

A. x^2 + 3x + C
B. x^2 + 3x + 1
C. x^2 + 3 + C
D. 2x^2 + 3x + C

Solution

Integrating term by term: ∫2xdx = x^2 and ∫3dx = 3x. Thus, ∫(2x + 3)dx = x^2 + 3x + C.

Correct Answer: A — x^2 + 3x + C

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Q. Find the integral of cos(2x)dx. (2023)

A. (1/2)sin(2x) + C
B. sin(2x) + C
C. (1/2)cos(2x) + C
D. 2sin(2x) + C

Solution

The integral of cos(kx) is (1/k)sin(kx) + C. Here, k=2, so the integral is (1/2)sin(2x) + C.

Correct Answer: A — (1/2)sin(2x) + C

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Q. Find the integral of cos(x) with respect to x. (2023)

A. sin(x) + C
B. -sin(x) + C
C. cos(x) + C
D. -cos(x) + C

Solution

The integral of cos(x) is sin(x) + C.

Correct Answer: A — sin(x) + C

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Q. Find the integral of cos(x). (2023)

A. sin(x) + C
B. -sin(x) + C
C. cos(x) + C
D. -cos(x) + C

Solution

The integral of cos(x) is sin(x) + C.

Correct Answer: A — sin(x) + C

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Q. Find the integral of cos(x)dx. (2023)

A. sin(x) + C
B. -sin(x) + C
C. cos(x) + C
D. -cos(x) + C

Solution

The integral of cos(x) is sin(x) + C.

Correct Answer: A — sin(x) + C

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MHT-CET MCQ & Objective Questions

The MHT-CET exam is a crucial stepping stone for students aspiring to pursue engineering and pharmacy courses in Maharashtra. Mastering the MHT-CET MCQ format is essential, as it not only tests your knowledge but also enhances your exam preparation strategy. Practicing objective questions helps in identifying important concepts and improves your chances of scoring better in this competitive exam.

What You Will Practise Here

Fundamental concepts in Physics, Chemistry, and Mathematics
Key formulas and their applications in problem-solving
Important definitions and terminologies relevant to MHT-CET
Diagrams and illustrations for better conceptual understanding
Practice questions that mirror the exam pattern
Analysis of previous years' MHT-CET questions
Techniques for tackling tricky MCQs effectively

Exam Relevance

The MHT-CET exam is aligned with the syllabus of CBSE, State Boards, and is also relevant for students preparing for NEET and JEE. Many concepts from the MHT-CET syllabus appear in these competitive exams, often in the form of application-based questions or conceptual MCQs. Understanding the common question patterns can significantly enhance your preparation and performance.

Common Mistakes Students Make

Misinterpreting questions due to lack of clarity in reading
Neglecting to review fundamental concepts before attempting MCQs
Overlooking units and dimensions in Physics and Chemistry problems
Rushing through practice questions without thorough understanding
Failing to manage time effectively during the exam

FAQs

Question: What are the best resources for MHT-CET MCQ questions?
Answer: Utilizing online platforms like SoulShift, which offer a variety of practice questions and mock tests, can be very beneficial.

Question: How can I improve my speed in solving MHT-CET objective questions?
Answer: Regular practice and timed mock tests can help enhance your speed and accuracy in solving MCQs.

Start your journey towards success by solving MHT-CET practice MCQs today! Test your understanding and build your confidence for the exam ahead.

MHT-CET

MHT-CET MCQ & Objective Questions

What You Will Practise Here

Exam Relevance

Common Mistakes Students Make

FAQs

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