Q. Find the integral of e^x dx. (2022)
A.
e^x + C
B.
e^x
C.
x e^x + C
D.
ln(e^x) + C
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Solution
The integral of e^x is e^x + C.
Correct Answer:
A
— e^x + C
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Q. Find the integral of sin(x) with respect to x. (2020)
A.
-cos(x) + C
B.
cos(x) + C
C.
sin(x) + C
D.
-sin(x) + C
Show solution
Solution
The integral of sin(x) is -cos(x) + C.
Correct Answer:
A
— -cos(x) + C
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Q. Find the integral of sin(x). (2020)
A.
-cos(x) + C
B.
cos(x) + C
C.
sin(x) + C
D.
-sin(x) + C
Show solution
Solution
The integral of sin(x) is -cos(x) + C.
Correct Answer:
A
— -cos(x) + C
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Q. Find the integral of sin(x)dx. (2020)
A.
-cos(x) + C
B.
cos(x) + C
C.
sin(x) + C
D.
-sin(x) + C
Show solution
Solution
The integral of sin(x) is -cos(x) + C.
Correct Answer:
A
— -cos(x) + C
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Q. Find the integral of x^5 dx. (2020)
A.
(1/6)x^6 + C
B.
(1/5)x^6 + C
C.
(1/4)x^6 + C
D.
(1/7)x^6 + C
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Solution
The integral is (1/6)x^6 + C.
Correct Answer:
B
— (1/5)x^6 + C
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Q. Find the length of the diagonal of a cuboid with dimensions 3, 4, and 12 units. (2020)
A.
√169
B.
√145
C.
√153
D.
√157
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Solution
Diagonal = √(3² + 4² + 12²) = √(9 + 16 + 144) = √169 = 13.
Correct Answer:
C
— √153
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Q. Find the length of the diagonal of a rectangular box with dimensions 2, 3, and 6 units. (2022)
A.
√49
B.
√45
C.
√36
D.
√50
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Solution
Diagonal = √(2² + 3² + 6²) = √(4 + 9 + 36) = √49 = 7 units.
Correct Answer:
A
— √49
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Q. Find the length of the diagonal of a rectangular box with dimensions 2, 3, and 6. (2023)
A.
√49
B.
√36
C.
√45
D.
√50
Show solution
Solution
Diagonal = √(2² + 3² + 6²) = √(4 + 9 + 36) = √49 = 7.
Correct Answer:
A
— √49
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Q. Find the limit: lim (x -> 0) (x^2)/(sin(x)) (2023)
A.
0
B.
1
C.
2
D.
Undefined
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Solution
As x approaches 0, sin(x) approaches x, thus lim (x -> 0) (x^2/sin(x)) = lim (x -> 0) (x^2/x) = lim (x -> 0) x = 0.
Correct Answer:
A
— 0
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Q. Find the limit: lim (x -> 1) (x^4 - 1)/(x - 1) (2023)
A.
0
B.
1
C.
4
D.
Undefined
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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. Thus, lim (x -> 1) = 4.
Correct Answer:
A
— 0
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Q. Find the limit: lim (x -> 2) (x^2 + 3x - 10)/(x - 2) (2021)
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Solution
Factoring gives (x - 2)(x + 5)/(x - 2). For x ≠ 2, this simplifies to x + 5. Evaluating at x = 2 gives 7.
Correct Answer:
D
— 7
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Q. Find the limit: lim (x -> 2) (x^2 - 3x + 2)/(x - 2) (2021)
A.
1
B.
2
C.
0
D.
Undefined
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Solution
The expression is undefined at x=2. The limit does not exist as the function approaches infinity.
Correct Answer:
D
— Undefined
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Q. Find the limit: lim (x -> 3) (x^2 - 9)/(x - 3) (2023)
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Solution
The expression can be factored as ((x - 3)(x + 3))/(x - 3). For x ≠ 3, this simplifies to x + 3. Thus, lim (x -> 3) (x + 3) = 6.
Correct Answer:
A
— 0
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Q. Find the local maxima of f(x) = -x^2 + 4x + 1. (2020)
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Solution
The maximum occurs at x = -b/(2a) = -4/(2*-1) = 2. f(2) = -2^2 + 4(2) + 1 = 5.
Correct Answer:
B
— 5
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Q. Find the local maxima of f(x) = -x^3 + 3x^2 + 1. (2020)
A.
(0, 1)
B.
(1, 3)
C.
(2, 5)
D.
(3, 1)
Show solution
Solution
f'(x) = -3x^2 + 6x. Setting f'(x) = 0 gives x(3x - 6) = 0, so x = 0 or x = 2. f(2) = 5.
Correct Answer:
B
— (1, 3)
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Q. Find the local maximum of f(x) = -x^3 + 3x^2 + 4. (2020)
Show solution
Solution
Set f'(x) = 0 to find critical points. The local maximum occurs at x = 2. f(2) = 5.
Correct Answer:
B
— 5
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Q. Find the magnitude of the vector A = 3i - 4j. (2020)
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Solution
|A| = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5.
Correct Answer:
A
— 5
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Q. Find the maximum area of a triangle with a base of 10 m and height varying. (2020)
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Solution
Area = 1/2 * base * height. Max area occurs when height is maximized, thus Area = 1/2 * 10 * 10 = 50.
Correct Answer:
B
— 50
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Q. Find the maximum area of a triangle with a base of 10 units and height as a function of the base. (2021)
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Solution
Area = 1/2 * base * height. Max area occurs when height is maximized at 10 units, giving Area = 50.
Correct Answer:
B
— 50
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Q. Find the maximum area of a triangle with a base of 10 units and height as a function of x. (2022)
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Solution
Area = 1/2 * base * height. Max area occurs when height is maximized, which is 10 units, giving Area = 50.
Correct Answer:
B
— 50
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Q. Find the maximum area of a triangle with a fixed perimeter of 30 cm. (2022)
A.
75 cm²
B.
100 cm²
C.
50 cm²
D.
60 cm²
Show solution
Solution
For maximum area, the triangle should be equilateral. Area = (sqrt(3)/4) * (10)^2 = 75 cm².
Correct Answer:
A
— 75 cm²
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Q. Find the maximum height of the projectile modeled by h(t) = -16t^2 + 32t + 48. (2020)
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Solution
The maximum occurs at t = -b/(2a) = -32/(2*-16) = 1. h(1) = 64.
Correct Answer:
A
— 48
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Q. Find the maximum height of the projectile modeled by h(t) = -16t^2 + 64t + 48. (2020)
Show solution
Solution
The maximum occurs at t = -b/(2a) = 64/(2*16) = 2. h(2) = -16(2^2) + 64(2) + 48 = 80.
Correct Answer:
B
— 64
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Q. Find the maximum value of the function f(x) = -2x^2 + 8x - 3. (2021) 2021
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Solution
The function is a downward-opening parabola. The maximum occurs at x = -b/(2a) = -8/(2*-2) = 2. f(2) = -2(2^2) + 8(2) - 3 = 8.
Correct Answer:
B
— 8
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Q. Find the midpoint of the line segment joining the points (2, 3) and (4, 7). (2022) 2022
A.
(3, 5)
B.
(2, 5)
C.
(4, 5)
D.
(3, 4)
Show solution
Solution
Midpoint = ((2+4)/2, (3+7)/2) = (3, 5).
Correct Answer:
A
— (3, 5)
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Q. Find the minimum value of f(x) = 4x^2 - 16x + 20. (2022)
Show solution
Solution
The vertex gives the minimum at x = 2. f(2) = 4(2^2) - 16(2) + 20 = 4.
Correct Answer:
A
— 4
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Q. Find the minimum value of f(x) = x^2 - 4x + 6. (2021)
Show solution
Solution
The vertex form gives the minimum at x = 2. f(2) = 2.
Correct Answer:
A
— 2
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Q. Find the minimum value of f(x) = x^2 - 4x + 7. (2021)
Show solution
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. Find the minimum value of f(x) = x^2 - 4x + 7. (2021) 2021
Show solution
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. Find the minimum value of the function f(x) = 2x^2 - 8x + 10. (2022)
Show solution
Solution
The minimum occurs at x = 2. f(2) = 2(2^2) - 8(2) + 10 = 6.
Correct Answer:
B
— 4
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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.
