Q. Determine the intervals where f(x) = x^3 - 3x is increasing. (2021)
A.
(-∞, -1)
B.
(-1, 1)
C.
(1, ∞)
D.
(-∞, 1)
Show solution
Solution
f'(x) = 3x^2 - 3. Setting f'(x) = 0 gives x = -1, 1. f'(x) > 0 for x > 1.
Correct Answer:
C
— (1, ∞)
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Q. Determine the intervals where f(x) = x^4 - 4x^3 has increasing behavior. (2023)
A.
(-∞, 0)
B.
(0, 2)
C.
(2, ∞)
D.
(0, 4)
Show solution
Solution
f'(x) = 4x^3 - 12x^2 = 4x^2(x - 3). f'(x) > 0 for x in (0, 3).
Correct Answer:
B
— (0, 2)
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Q. Determine the intervals where f(x) = x^4 - 4x^3 has local minima. (2020)
A.
(0, 2)
B.
(1, 3)
C.
(2, 4)
D.
(0, 1)
Show solution
Solution
f'(x) = 4x^3 - 12x^2. Setting f'(x) = 0 gives x = 0, 3. Testing intervals shows local minima at (0, 2).
Correct Answer:
A
— (0, 2)
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Q. Determine the limit: lim (x -> 0) (tan(5x)/x) (2022)
A.
0
B.
1
C.
5
D.
Undefined
Show solution
Solution
Using the standard limit lim (x -> 0) (tan(kx)/x) = k, we have k = 5. Thus, lim (x -> 0) (tan(5x)/x) = 5.
Correct Answer:
C
— 5
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Q. Determine the limit: lim (x -> 1) (x^3 - 1)/(x - 1) (2020)
Show solution
Solution
Factoring gives (x - 1)(x^2 + x + 1)/(x - 1). For x ≠ 1, this simplifies to x^2 + x + 1. Evaluating at x = 1 gives 3.
Correct Answer:
C
— 3
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Q. Determine the limit: lim (x -> 1) (x^4 - 1)/(x - 1) (2021)
A.
0
B.
1
C.
4
D.
Undefined
Show solution
Solution
Factoring gives (x - 1)(x^3 + x^2 + x + 1)/(x - 1). For x ≠ 1, this simplifies to x^3 + x^2 + x + 1. Evaluating at x = 1 gives 4.
Correct Answer:
D
— Undefined
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Q. Determine the local maxima of f(x) = -x^3 + 3x^2 + 1. (2021)
A.
(0, 1)
B.
(1, 3)
C.
(2, 5)
D.
(3, 4)
Show solution
Solution
f'(x) = -3x^2 + 6x. Setting f'(x) = 0 gives x = 0 or x = 2. f(2) = 5 is a local maximum.
Correct Answer:
B
— (1, 3)
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Q. Determine the local maxima of f(x) = x^4 - 8x^2 + 16. (2021)
A.
(0, 16)
B.
(2, 12)
C.
(4, 0)
D.
(1, 9)
Show solution
Solution
Find f'(x) = 4x^3 - 16x. Setting f'(x) = 0 gives x = 0, ±2. f(2) = 12 is a local maximum.
Correct Answer:
B
— (2, 12)
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Q. Determine the local minima of f(x) = x^3 - 3x + 2. (2021)
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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)
Show solution
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)
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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
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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)
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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)
Show solution
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)
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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)
Show solution
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)
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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)
Show solution
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)
Show solution
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)
Show solution
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)
Show solution
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)
Show solution
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
Show solution
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)
Show solution
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
Show solution
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
Show solution
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
Show solution
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
Show solution
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
Show solution
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
Show solution
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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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.
