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. A jar contains 6 green and 4 yellow marbles. What is the probability of picking a yellow marble?

A. 2/5
B. 1/2
C. 4/10
D. 3/5

Solution

Total marbles = 6 + 4 = 10. Probability of yellow marble = 4/10 = 2/5.

Correct Answer: A — 2/5

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Q. A jar contains 7 red, 5 blue, and 8 green marbles. What is the probability of selecting a blue marble?

A. 5/20
B. 1/4
C. 1/5
D. 1/3

Solution

Total marbles = 7 + 5 + 8 = 20. Probability of blue marble = 5/20 = 1/4.

Correct Answer: A — 5/20

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Q. A jar contains 8 red and 4 blue marbles. What is the probability of selecting a blue marble?

A. 1/3
B. 1/2
C. 1/4
D. 1/5

Solution

Total marbles = 8 + 4 = 12. Probability of blue marble = 4/12 = 1/3.

Correct Answer: A — 1/3

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Q. A jar contains 8 red, 6 blue, and 4 green marbles. What is the probability of selecting a blue marble?

A. 1/3
B. 1/4
C. 2/5
D. 3/10

Solution

Total marbles = 8 + 6 + 4 = 18. Probability of blue marble = 6/18 = 1/3.

Correct Answer: D — 3/10

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Q. A rectangle has a perimeter of 40 cm. What dimensions maximize the area? (2022)

A. 10 cm by 10 cm
B. 8 cm by 12 cm
C. 5 cm by 15 cm
D. 6 cm by 14 cm

Solution

For maximum area, the rectangle should be a square. Thus, each side = 40/4 = 10 cm.

Correct Answer: A — 10 cm by 10 cm

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Q. A rectangle has a perimeter of 40 cm. What dimensions will maximize the area? (2022)

A. 10 cm by 10 cm
B. 15 cm by 5 cm
C. 20 cm by 0 cm
D. 12 cm by 8 cm

Solution

For maximum area, the rectangle should be a square. Thus, each side = 40/4 = 10 cm.

Correct Answer: A — 10 cm by 10 cm

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Q. A rectangle has a perimeter of 40 units. What dimensions maximize the area? (2022)

A. 10, 10
B. 8, 12
C. 6, 14
D. 5, 15

Solution

For a fixed perimeter, the area is maximized when the rectangle is a square. Thus, side = 10 units.

Correct Answer: A — 10, 10

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Q. A rectangle has a perimeter of 40 units. What dimensions maximize the area? (2022) 2022

A. 10, 10
B. 5, 15
C. 8, 12
D. 6, 14

Solution

For maximum area, the rectangle should be a square. Thus, each side = 40/4 = 10.

Correct Answer: A — 10, 10

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Q. A student has a 70% chance of passing an exam. What is the probability of failing the exam?

A. 0.3
B. 0.7
C. 0.5
D. 0.2

Solution

Probability of failing = 1 - Probability of passing = 1 - 0.7 = 0.3.

Correct Answer: A — 0.3

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Q. At what point does the function f(x) = x^3 - 3x^2 + 4 have a local minimum? (2020)

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

Solution

To find local minima, we find f'(x) = 3x^2 - 6x. Setting f'(x) = 0 gives x = 0 and x = 2. Checking the second derivative, f''(2) = 6 > 0, so (2, 1) is a local minimum.

Correct Answer: A — (1, 2)

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Q. At which point does the function f(x) = -x^3 + 3x^2 + 4 have a local maximum? (2023)

A. (0, 4)
B. (1, 6)
C. (2, 5)
D. (3, 4)

Solution

Setting f'(x) = -3x^2 + 6x = 0 gives x = 0 and x = 2. f''(2) < 0 indicates a local maximum at (2, 5).

Correct Answer: B — (1, 6)

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Q. Calculate the coefficient of x^2 in the expansion of (2x + 3)^4.

A. 36
B. 48
C. 54
D. 64

Solution

The coefficient of x^2 is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.

Correct Answer: B — 48

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Q. Calculate the coefficient of x^2 in the expansion of (x + 1/2)^6.

A. 15/4
B. 45/8
C. 15/8
D. 5/4

Solution

The coefficient of x^2 is C(6,2) * (1/2)^2 = 15 * 1/4 = 15/4.

Correct Answer: B — 45/8

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Q. Calculate the coefficient of x^2 in the expansion of (x + 1/2)^8. (2021)

A. 28
B. 56
C. 70
D. 84

Solution

The coefficient of x^2 is C(8,2) * (1/2)^6 = 28 * 1/64 = 28/64 = 7/16.

Correct Answer: C — 70

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Q. Calculate the coefficient of x^2 in the expansion of (x + 1/x)^6. (2019)

A. 15
B. 30
C. 20
D. 10

Solution

The coefficient of x^2 is given by 6C2 * (1)^4 = 15.

Correct Answer: A — 15

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Q. Calculate the coefficient of x^2 in the expansion of (x + 4)^6.

A. 96
B. 144
C. 192
D. 256

Solution

The coefficient of x^2 is given by C(6,2) * 4^4 = 15 * 256 = 3840.

Correct Answer: A — 96

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Q. Calculate the coefficient of x^3 in the expansion of (x + 1/2)^6.

A. 20
B. 30
C. 40
D. 50

Solution

The coefficient of x^3 is given by C(6,3) * (1/2)^3 = 20 * 1/8 = 2.5.

Correct Answer: A — 20

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Q. Calculate the coefficient of x^3 in the expansion of (x - 1)^5.

A. -5
B. 10
C. -10
D. 5

Solution

The coefficient of x^3 is C(5,3) * (-1)^2 = 10.

Correct Answer: B — 10

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Q. Calculate the coefficient of x^4 in the expansion of (3x - 2)^6.

A. 540
B. 720
C. 810
D. 960

Solution

The coefficient of x^4 is C(6,4) * (3)^4 * (-2)^2 = 15 * 81 * 4 = 4860.

Correct Answer: A — 540

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Q. Calculate the coefficient of x^4 in the expansion of (x + 1/2)^6. (2021)

A. 15/8
B. 45/8
C. 5/8
D. 1/8

Solution

The coefficient of x^4 is C(6,4)(1/2)^2 = 15 * 1/4 = 15/4.

Correct Answer: B — 45/8

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Q. Calculate the coefficient of x^4 in the expansion of (x + 2)^6.

A. 15
B. 60
C. 90
D. 120

Solution

The coefficient of x^4 is C(6,4) * 2^2 = 15 * 4 = 60.

Correct Answer: C — 90

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Q. Calculate the coefficient of x^4 in the expansion of (x + 3)^6. (2021)

A. 54
B. 81
C. 108
D. 729

Solution

The coefficient of x^4 is C(6,4)(3)^2 = 15 * 9 = 135.

Correct Answer: C — 108

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Q. Calculate the coefficient of x^4 in the expansion of (x + 5)^6.

A. 150
B. 600
C. 750
D. 1000

Solution

The coefficient of x^4 is C(6,4) * 5^2 = 15 * 25 = 375.

Correct Answer: C — 750

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Q. Calculate the coefficient of x^5 in the expansion of (x + 2)^7.

A. 21
B. 42
C. 63
D. 84

Solution

The coefficient of x^5 is C(7,5) * (2)^2 = 21 * 4 = 84.

Correct Answer: C — 63

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Q. Calculate the coefficient of x^5 in the expansion of (x - 3)^7. (2021)

A. -189
B. -243
C. -126
D. -21

Solution

The coefficient of x^5 is C(7,5) * (-3)^2 = 21 * 9 = -189.

Correct Answer: A — -189

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Q. Calculate the derivative of f(x) = 5x^5. (2016)

A. 25x^4
B. 5x^4
C. 20x^4
D. 10x^4

Solution

The derivative f'(x) = d/dx(5x^5) = 25x^4.

Correct Answer: A — 25x^4

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Q. Calculate the derivative of f(x) = ln(x^2 + 1).

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

Solution

Using the chain rule, f'(x) = d/dx(ln(x^2 + 1)) = (2x)/(x^2 + 1).

Correct Answer: A — 2x/(x^2 + 1)

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Q. Calculate the derivative of f(x) = x^2 * e^x. (2023) 2023

A. e^x(2x + 1)
B. e^x(2x - 1)
C. 2xe^x
D. x^2e^x

Solution

Using the product rule, f'(x) = d/dx(x^2 * e^x) = e^x(2x + 1).

Correct Answer: A — e^x(2x + 1)

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Q. Calculate the determinant of D = [[2, 3, 1], [1, 0, 2], [4, 1, 0]]. (2020)

A. -10
B. 10
C. 0
D. 5

Solution

Det(D) = 2(0*0 - 2*1) - 3(1*0 - 2*4) + 1(1*1 - 0*4) = 2(0 - 2) - 3(0 - 8) + 1(1) = -4 + 24 + 1 = 21.

Correct Answer: A — -10

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Q. Calculate the determinant of D = [[3, 2, 1], [1, 0, 2], [0, 1, 3]]. (2023)

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

Solution

Det(D) = 3(0*3 - 2*1) - 2(1*3 - 0*2) + 1(1*1 - 0*0) = 3(0 - 2) - 2(3) + 1(1) = -6 - 6 + 1 = -11.

Correct Answer: A — 1

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Showing 31 to 60 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

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