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. What is the maximum profit if the profit function is P(x) = -x^2 + 10x - 16? (2021)

A. 4
B. 6
C. 8
D. 10

Solution

The maximum profit occurs at x = -b/(2a) = 10/2 = 5. P(5) = -5^2 + 10*5 - 16 = 9.

Correct Answer: C — 8

Learn More →

Q. What is the maximum value of f(x) = -x^2 + 4x + 1? (2023)

A. 5
B. 6
C. 7
D. 8

Solution

The vertex occurs at x = 2. f(2) = -2^2 + 4(2) + 1 = 5.

Correct Answer: A — 5

Learn More →

Q. What is the maximum value of f(x) = -x^2 + 6x - 8? (2023)

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

Solution

The vertex occurs at x = 3. f(3) = -9 + 18 - 8 = 1.

Correct Answer: C — 6

Learn More →

Q. What is the minimum distance from the point (3, 4) to the line 2x + 3y - 6 = 0? (2023)

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

Solution

Using the distance formula from a point to a line, the minimum distance is calculated to be 2 units.

Correct Answer: A — 2

Learn More →

Q. What is the minimum value of f(x) = 3x^2 - 12x + 12? (2021)

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

Solution

The vertex occurs at x = 2. f(2) = 3(2^2) - 12(2) + 12 = 0.

Correct Answer: B — 3

Learn More →

Q. What is the minimum value of f(x) = 3x^2 - 12x + 7? (2022)

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

Solution

The vertex occurs at x = 2. f(2) = -5.

Correct Answer: A — -5

Learn More →

Q. What is the minimum value of f(x) = 3x^2 - 12x + 9? (2022)

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

Solution

The vertex occurs at x = 2. f(2) = 3(2^2) - 12(2) + 9 = 0.

Correct Answer: B — 1

Learn More →

Q. What is the minimum value of f(x) = x^2 - 4x + 5? (2020)

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

Solution

The vertex form gives the minimum at x = 2. f(2) = 2.

Correct Answer: A — 1

Learn More →

Q. What is the minimum value of f(x) = x^2 - 4x + 6? (2022)

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

Solution

The vertex occurs at x = 2. f(2) = 2.

Correct Answer: B — 3

Learn More →

Q. What is the minimum value of f(x) = x^2 - 4x + 7? (2023)

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

Solution

The vertex form gives the minimum at x = 2. f(2) = 2, thus minimum value is 3.

Correct Answer: A — 3

Learn More →

Q. What is the minimum value of f(x) = x^2 - 6x + 10? (2020)

A. 4
B. 6
C. 10
D. 8

Solution

The vertex form gives the minimum at x = 3. f(3) = 3^2 - 6(3) + 10 = 1.

Correct Answer: A — 4

Learn More →

Q. What is the minimum value of the function f(x) = 4x^2 - 16x + 20? (2021)

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

Solution

The vertex gives the minimum at x = 2. f(2) = 4(2^2) - 16(2) + 20 = 4.

Correct Answer: B — 5

Learn More →

Q. What is the minimum value of the function f(x) = 4x^2 - 16x + 20? (2021) 2021

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

Solution

The vertex occurs at x = 2. f(2) = 4(2^2) - 16(2) + 20 = 4.

Correct Answer: B — 5

Learn More →

Q. What is the modulus of the complex number 3 + 4i? (2023)

A. 5
B. 7
C. 1
D. 4

Solution

The modulus is calculated as √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

Learn More →

Q. What is the nature of the roots of the equation x² + 2x + 5 = 0? (2023)

A. Real and distinct
B. Real and equal
C. Complex
D. None of the above

Solution

The discriminant D = 2² - 4*1*5 = 4 - 20 = -16, which indicates complex roots.

Correct Answer: C — Complex

Learn More →

Q. What is the particular solution of dy/dx = 4y with the initial condition y(0) = 2?

A. y = 2e^(4x)
B. y = e^(4x)
C. y = 4e^(4x)
D. y = 2e^(x)

Solution

The general solution is y = Ce^(4x). Using the initial condition y(0) = 2, we find C = 2, thus y = 2e^(4x).

Correct Answer: A — y = 2e^(4x)

Learn More →

Q. What is the point of inflection for the function f(x) = x^3 - 6x^2 + 9x? (2023) 2023

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

Solution

To find inflection points, set f''(x) = 0. f''(x) = 6x - 12 = 0, x = 2. f(2) = 4.

Correct Answer: A — (1, 4)

Learn More →

Q. What is the point of intersection of the lines x + 2y = 5 and 2x - y = 1?

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

Solution

Solving the equations simultaneously, we find the intersection point is (1, 2).

Correct Answer: A — (1, 2)

Learn More →

Q. What is the point of intersection of the lines x + y = 5 and 2x - y = 1?

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

Solution

Solving the equations simultaneously, we find x = 2 and y = 3. Thus, the point of intersection is (2, 3).

Correct Answer: A — (2, 3)

Learn More →

Q. What is the point of intersection of the lines y = 2x + 1 and y = -x + 4?

A. (1, 3)
B. (2, 5)
C. (3, 7)
D. (0, 1)

Solution

Setting 2x + 1 = -x + 4 gives 3x = 3, thus x = 1. Substituting back, y = 2(1) + 1 = 3. The intersection is (1, 3).

Correct Answer: A — (1, 3)

Learn More →

Q. What is the point of intersection of the lines y = 3x + 1 and y = -x + 5?

A. (1, 4)
B. (2, 7)
C. (3, 10)
D. (4, 13)

Solution

Setting 3x + 1 = -x + 5 gives 4x = 4, thus x = 1. Substituting x back gives y = 4. The intersection point is (1, 4).

Correct Answer: A — (1, 4)

Learn More →

Q. What is the probability of drawing a king from a standard deck of cards? (2023)

A. 1/13
B. 1/52
C. 1/4
D. 1/12

Solution

Number of kings = 4. Probability = 4/52 = 1/13.

Correct Answer: A — 1/13

Learn More →

Q. What is the probability of drawing a queen from a standard deck of cards?

A. 1/13
B. 1/26
C. 1/52
D. 1/4

Solution

Number of queens = 4. Probability = 4/52 = 1/13.

Correct Answer: A — 1/13

Learn More →

Q. What is the probability of flipping a coin and getting heads? (2023)

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

Solution

There are 2 outcomes: heads or tails. Probability of heads = 1/2.

Correct Answer: A — 1/2

Learn More →

Q. What is the probability of rolling a sum of 7 with two dice?

A. 1/6
B. 1/12
C. 1/36
D. 5/36

Solution

Possible combinations for sum of 7 = (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6. Total outcomes = 36. Probability = 6/36 = 1/6.

Correct Answer: D — 5/36

Learn More →

Q. What is the product of 9 and 6? (2016)

A. 54
B. 60
C. 48
D. 72

Solution

9 × 6 = 54.

Correct Answer: A — 54

Learn More →

Q. What is the product of the complex numbers (1 + i) and (1 - i)? (2023) 2023

A. 2
B. 0
C. 1
D. 1 + 0i

Solution

(1 + i)(1 - i) = 1^2 - i^2 = 1 - (-1) = 2.

Correct Answer: A — 2

Learn More →

Q. What is the product of the complex numbers 2 + 3i and 4 - i? (2021)

A. 11 + 10i
B. 14 + 5i
C. 5 + 10i
D. 10 + 5i

Solution

(2 + 3i)(4 - i) = 8 - 2i + 12i - 3i^2 = 8 + 10i + 3 = 11 + 10i.

Correct Answer: A — 11 + 10i

Learn More →

Q. What is the product of the roots of the equation 2x² - 8x + 6 = 0? (2022)

A. 3
B. 2
C. 1.5
D. 4

Solution

The product of the roots is given by c/a = 6/2 = 3.

Correct Answer: A — 3

Learn More →

Q. What is the product of the roots of the equation 3x² - 12x + 9 = 0? (2022)

A. 1
B. 3
C. 4
D. 9

Solution

The product of the roots is given by c/a = 9/3 = 3.

Correct Answer: B — 3

Learn More →

Showing 811 to 840 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!

Mathematics (MHT-CET)

Mathematics (MHT-CET) MCQ & Objective Questions

What You Will Practise Here

Exam Relevance

Common Mistakes Students Make

FAQs

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?