Mathematics (MHT-CET)

3D Geometry Applications of Derivatives Binomial Theorem Circles Complex Numbers Conic Sections Coordinate Geometry Differential Equations Differentiation Integration Limits & Continuity Matrices & Determinants Permutations & Combinations Probability Quadratic Equations Sequences & Series Sets & Relations Straight Lines Trigonometry Vector Algebra

Q. Determine the local minima of f(x) = x^3 - 3x + 2. (2021)

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

Solution

f'(x) = 3x^2 - 3. Setting f'(x) = 0 gives x = 1. f(1) = 0.

Correct Answer: B — 0

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Q. Determine the local minima of f(x) = x^4 - 4x^2. (2021)

A. -2
B. 0
C. 2
D. 4

Solution

f'(x) = 4x^3 - 8x. Setting f'(x) = 0 gives x = 0, ±2. f(0) = 0.

Correct Answer: B — 0

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Q. Determine the maximum area of a triangle with a base of 10 units and height as a function of x. (2020)

A. 25
B. 50
C. 30
D. 40

Solution

Area = 1/2 * base * height = 5h. Max area occurs when h is maximized, thus Area = 50 when h = 10.

Correct Answer: B — 50

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Q. Determine the maximum height of the function f(x) = -x^2 + 6x + 5. (2020) 2020

A. 8
B. 10
C. 12
D. 6

Solution

The vertex occurs at x = 3. f(3) = -3^2 + 6*3 + 5 = 8.

Correct Answer: A — 8

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Q. Determine the maximum height of the projectile given by h(t) = -16t^2 + 64t + 80. (2023)

A. 80
B. 64
C. 48
D. 96

Solution

The maximum height occurs at t = -b/(2a) = -64/(2*-16) = 2. h(2) = -16(2^2) + 64(2) + 80 = 80.

Correct Answer: A — 80

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Q. Determine the maximum height of the projectile modeled by h(t) = -16t^2 + 64t + 80. (2020)

A. 80
B. 64
C. 48
D. 96

Solution

The maximum height occurs at t = -b/(2a) = 64/(2*16) = 2. h(2) = -16(2^2) + 64(2) + 80 = 80.

Correct Answer: A — 80

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Q. Determine the maximum value of f(x) = -x^2 + 6x - 8. (2022)

A. 2
B. 4
C. 6
D. 8

Solution

The maximum occurs at x = 3. f(3) = -3^2 + 6(3) - 8 = 6.

Correct Answer: C — 6

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Q. Determine the minimum value of f(x) = x^2 - 4x + 5. (2021)

A. 1
B. 2
C. 3
D. 4

Solution

The vertex form gives the minimum at x = 2. f(2) = 2^2 - 4(2) + 5 = 1.

Correct Answer: A — 1

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Q. Determine the minimum value of f(x) = x^2 - 4x + 7. (2021)

A. 3
B. 5
C. 4
D. 6

Solution

The vertex form gives the minimum at x = 2. f(2) = 2^2 - 4(2) + 7 = 3.

Correct Answer: A — 3

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Q. Determine the point of inflection for f(x) = x^4 - 4x^3 + 6. (2023)

A. (1, 3)
B. (2, 2)
C. (0, 6)
D. (3, 0)

Solution

f''(x) = 12x^2 - 24x. Setting f''(x) = 0 gives x(12x - 24) = 0, so x = 0 or x = 2. Check f(1) = 3.

Correct Answer: A — (1, 3)

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Q. Determine the point where the function f(x) = 2x^3 - 9x^2 + 12x has a local minimum. (2023)

A. (1, 5)
B. (2, 0)
C. (3, 3)
D. (4, 4)

Solution

Set f'(x) = 0. f'(x) = 6x^2 - 18x + 12 = 0 gives x = 2. f(2) = 0.

Correct Answer: C — (3, 3)

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Q. Determine the point where the function f(x) = 4x - x^2 has a maximum. (2022)

A. (0, 0)
B. (2, 4)
C. (1, 3)
D. (3, 3)

Solution

The maximum occurs at x = 2, found by setting f'(x) = 4 - 2x = 0. f(2) = 4(2) - (2^2) = 4.

Correct Answer: B — (2, 4)

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Q. Determine the product of the roots of the equation x² + 6x + 8 = 0. (2023)

A. 8
B. 6
C. 4
D. 2

Solution

The product of the roots is given by c/a = 8/1 = 8.

Correct Answer: A — 8

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Q. Determine the product of the roots of the equation x² + 6x + 9 = 0. (2021)

A. 9
B. 6
C. 3
D. 0

Solution

The product of the roots is c/a = 9/1 = 9.

Correct Answer: A — 9

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Q. Determine the roots of the equation x² + 2x - 8 = 0. (2023)

A. -4 and 2
B. 4 and -2
C. 2 and -4
D. 0 and 8

Solution

Factoring gives (x + 4)(x - 2) = 0, hence the roots are -4 and 2.

Correct Answer: A — -4 and 2

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Q. Determine the roots of the equation x² + 6x + 9 = 0. (2023)

A. -3
B. 3
C. 0
D. -6

Solution

This is a perfect square: (x + 3)² = 0, hence the root is x = -3.

Correct Answer: A — -3

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Q. Evaluate the integral ∫ (3x^2 + 2x) dx. (2020)

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

Solution

The integral is (3/3)x^3 + (2/2)x^2 + C = x^3 + x^2 + C.

Correct Answer: A — x^3 + x^2 + C

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Q. Evaluate the integral ∫(3x^2 + 2)dx. (2022)

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

Solution

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

Correct Answer: A — x^3 + 2x + C

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Q. Evaluate the limit: lim (x -> 0) (tan(x)/x) (2023)

A. 0
B. 1
C. ∞
D. Undefined

Solution

Using the limit property lim (x -> 0) (tan(x)/x) = 1, we find that the limit is 1.

Correct Answer: B — 1

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Q. Evaluate the limit: lim (x -> 0) (x - sin(x))/x^3 (2022)

A. 0
B. 1/6
C. 1/3
D. 1/2

Solution

Using the Taylor series expansion for sin(x), we find that lim (x -> 0) (x - sin(x))/x^3 = 1/6.

Correct Answer: B — 1/6

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Q. Evaluate the limit: lim (x -> 0) (x^3)/(sin(x)) (2022)

A. 0
B. 1
C. Infinity
D. Undefined

Solution

As x approaches 0, x^3 approaches 0 and sin(x) approaches 0, thus the limit is 0.

Correct Answer: A — 0

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Q. Evaluate the limit: lim (x -> 3) (x^2 - 9)/(x - 3) (2020)

A. 3
B. 6
C. 9
D. Undefined

Solution

Factoring gives (x - 3)(x + 3)/(x - 3). Canceling (x - 3) gives lim (x -> 3) (x + 3) = 6.

Correct Answer: B — 6

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Q. Evaluate ∫ (2x + 3) dx. (2022)

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

Solution

The integral is (2/2)x^2 + 3x + C = x^2 + 3x + C.

Correct Answer: A — x^2 + 3x + C

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Q. Evaluate ∫ (4x^3 - 2x) dx. (2019)

A. x^4 - x^2 + C
B. x^4 - x^2 + 2C
C. x^4 - x + C
D. 4x^4 - 2x^2 + C

Solution

The integral is (4/4)x^4 - (2/2)x^2 + C = x^4 - x^2 + C.

Correct Answer: A — x^4 - x^2 + C

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Q. Evaluate ∫ (5 - 3x) dx. (2022)

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

Solution

The integral is 5x - (3/2)x^2 + C.

Correct Answer: A — 5x - (3/2)x^2 + C

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Q. Evaluate ∫(2x^2 + 3x + 1)dx. (2021)

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

Solution

Integrating term by term: ∫2x^2dx = (2/3)x^3, ∫3xdx = (3/2)x^2, and ∫1dx = x. Thus, ∫(2x^2 + 3x + 1)dx = (2/3)x^3 + (3/2)x^2 + x + C.

Correct Answer: A — (2/3)x^3 + (3/2)x^2 + x + C

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Q. Evaluate ∫(5x^4)dx. (2020)

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

Solution

The integral of 5x^4 is (5/5)x^5 + C = x^5 + C.

Correct Answer: A — (5/5)x^5 + C

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Q. Evaluate ∫(6x^2 + 3)dx. (2022)

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

Solution

Integrating term by term: ∫6x^2dx = 2x^3 and ∫3dx = 3x. Thus, ∫(6x^2 + 3)dx = 2x^3 + 3x + C.

Correct Answer: A — 2x^3 + 3x + C

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Q. Find the area of a triangle with vertices at A(0, 0, 0), B(1, 0, 0), and C(0, 1, 0). (2023)

A. 0.5
B. 1
C. 2
D. 0

Solution

Area = 0.5 * base * height = 0.5 * 1 * 1 = 0.5 square units.

Correct Answer: A — 0.5

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Q. Find the area of the triangle formed by the points (0, 0), (4, 0), and (0, 3). (2022) 2022

A. 6
B. 12
C. 8
D. 10

Solution

Area = 1/2 * base * height = 1/2 * 4 * 3 = 6.

Correct Answer: A — 6

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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!

Mathematics (MHT-CET)

Mathematics (MHT-CET) MCQ & Objective Questions

What You Will Practise Here

Exam Relevance

Common Mistakes Students Make

FAQs

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