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
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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
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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
Show solution
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
Show solution
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
Show solution
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
Show solution
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)
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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
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Solution
Area = 1/2 * base * height = 1/2 * 4 * 3 = 6.
Correct Answer:
A
— 6
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Q. Find the area of the triangle formed by the points A(0, 0, 0), B(1, 0, 0), and C(0, 1, 0). (2023)
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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 A(1, 2, 3), B(4, 5, 6), and C(7, 8, 9). (2022)
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Solution
The points are collinear, hence the area = 0.
Correct Answer:
A
— 0
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Q. Find the coefficient of x^0 in the expansion of (2x - 3)^3.
A.
-27
B.
-24
C.
-18
D.
-12
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Solution
The coefficient of x^0 is (-3)^3 = -27.
Correct Answer:
A
— -27
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Q. Find the coefficient of x^1 in the expansion of (x + 4)^3.
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Solution
The coefficient of x^1 is C(3,1) * (4)^2 = 3 * 16 = 48.
Correct Answer:
A
— 12
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Q. Find the coefficient of x^2 in the expansion of (2x + 3)^6.
A.
540
B.
720
C.
810
D.
960
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Solution
The coefficient of x^2 is given by 6C2 * (2)^2 * (3)^4 = 15 * 4 * 81 = 4860.
Correct Answer:
A
— 540
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Q. Find the coefficient of x^2 in the expansion of (x + 4)^5. (2023)
A.
80
B.
100
C.
120
D.
160
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Solution
The coefficient of x^2 is C(5,2)(4)^3 = 10 * 64 = 640.
Correct Answer:
A
— 80
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Q. Find the coefficient of x^2 in the expansion of (x - 5)^5.
A.
100
B.
150
C.
200
D.
250
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Solution
The coefficient of x^2 is C(5,2) * (-5)^3 = 10 * (-125) = -1250.
Correct Answer:
A
— 100
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Q. Find the coefficient of x^3 in the expansion of (2x - 3)^4. (2022)
A.
-54
B.
-108
C.
108
D.
54
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Solution
The coefficient of x^3 is C(4,3) * (2)^3 * (-3)^1 = 4 * 8 * (-3) = -96.
Correct Answer:
B
— -108
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Q. Find the coefficient of x^3 in the expansion of (x - 1)^7.
A.
-35
B.
-21
C.
-7
D.
-49
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Solution
The coefficient of x^3 is given by 7C3 * (-1)^4 = 35.
Correct Answer:
A
— -35
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Q. Find the coefficient of x^3 in the expansion of (x - 2)^5.
A.
-40
B.
-80
C.
-60
D.
-100
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Solution
The coefficient of x^3 is C(5,3) * (-2)^2 = 10 * 4 = 40.
Correct Answer:
A
— -40
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Q. Find the coefficient of x^4 in the expansion of (2x - 3)^5.
A.
-240
B.
-360
C.
-480
D.
-600
Show solution
Solution
The coefficient of x^4 is C(5,4) * (2)^4 * (-3)^1 = 5 * 16 * (-3) = -240.
Correct Answer:
A
— -240
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Q. Find the coefficient of x^4 in the expansion of (2x - 3)^6.
A.
540
B.
720
C.
810
D.
900
Show solution
Solution
The coefficient of x^4 is C(6,4) * (2)^4 * (-3)^2 = 15 * 16 * 9 = 2160.
Correct Answer:
A
— 540
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Q. Find the coefficient of x^4 in the expansion of (3x + 2)^5. (2022)
A.
240
B.
360
C.
480
D.
600
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Solution
The coefficient of x^4 is C(5,4)(3)^4(2)^1 = 5 * 81 * 2 = 810.
Correct Answer:
B
— 360
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Q. Find the coefficient of x^4 in the expansion of (x + 1)^6.
Show solution
Solution
The coefficient of x^4 is C(6,4) * 1^2 = 15.
Correct Answer:
B
— 20
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Q. Find the coefficient of x^4 in the expansion of (x + 2)^6.
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Solution
The coefficient of x^4 is C(6,4) * (2)^2 = 15 * 4 = 60.
Correct Answer:
B
— 30
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Q. Find the coefficient of x^4 in the expansion of (x + 3)^6.
A.
81
B.
162
C.
243
D.
729
Show solution
Solution
The coefficient of x^4 is C(6,4) * (3)^2 = 15 * 9 = 135.
Correct Answer:
C
— 243
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Q. Find the coefficient of x^4 in the expansion of (x + 5)^7.
A.
210
B.
1260
C.
1750
D.
2450
Show solution
Solution
The coefficient of x^4 is given by C(7,4) * 5^3 = 35 * 125 = 4375.
Correct Answer:
B
— 1260
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Q. Find the coefficient of x^4 in the expansion of (x - 1)^5.
Show solution
Solution
The coefficient of x^4 is C(5,4) * (-1)^1 = 5 * (-1) = -5.
Correct Answer:
C
— -10
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Q. Find the coefficient of x^4 in the expansion of (x - 5)^6.
A.
150
B.
200
C.
250
D.
300
Show solution
Solution
The coefficient of x^4 is given by C(6,4) * (-5)^2 = 15 * 25 = 375.
Correct Answer:
B
— 200
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Q. Find the coefficient of x^5 in the expansion of (2x - 3)^6. (2022)
A.
-540
B.
540
C.
-720
D.
720
Show solution
Solution
The coefficient of x^5 is C(6,5) * (2)^5 * (-3)^1 = 6 * 32 * (-3) = -576.
Correct Answer:
A
— -540
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Q. Find the coefficient of x^5 in the expansion of (2x - 3)^7. (2023)
A.
168
B.
252
C.
336
D.
504
Show solution
Solution
The coefficient of x^5 is C(7,5) * (2)^5 * (-3)^2 = 21 * 32 * 9 = 6048.
Correct Answer:
B
— 252
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Q. Find the coefficient of x^5 in the expansion of (2x - 3)^8.
A.
-6720
B.
6720
C.
-3360
D.
3360
Show solution
Solution
The coefficient of x^5 is C(8,5) * (2)^5 * (-3)^3 = 56 * 32 * (-27) = -6720.
Correct Answer:
A
— -6720
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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.