Q. Solve the first-order linear differential equation dy/dx + 2y = 6.
A.
y = 3 - Ce^(-2x)
B.
y = 3 + Ce^(-2x)
C.
y = 6 - Ce^(-2x)
D.
y = 6 + Ce^(-2x)
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Solution
Using an integrating factor e^(2x), we solve to get y = 3 - Ce^(-2x).
Correct Answer:
A
— y = 3 - Ce^(-2x)
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Q. Solve the first-order linear differential equation dy/dx + y/x = 1.
A.
y = x + C/x
B.
y = Cx - x
C.
y = Cx + x
D.
y = C/x + x
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Solution
Using the integrating factor e^(∫(1/x)dx) = x, we solve to get y = x + C/x.
Correct Answer:
A
— y = x + C/x
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Q. Solve the first-order linear differential equation dy/dx = y/x.
A.
y = Cx
B.
y = Cx^2
C.
y = C/x
D.
y = C ln(x)
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Solution
This is separable: dy/y = dx/x. Integrating gives ln|y| = ln|x| + C, thus y = Cx.
Correct Answer:
A
— y = Cx
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Q. The quadratic equation x² + 4x + 4 = 0 has how many distinct roots? (2021)
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Solution
The discriminant is 4² - 4*1*4 = 0, indicating one distinct root.
Correct Answer:
B
— 1
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Q. The roots of the equation x² + 2x + k = 0 are real and distinct if k is: (2020)
A.
< 1
B.
≥ 1
C.
≤ 1
D.
> 1
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Solution
For real and distinct roots, the discriminant must be positive: 2² - 4*1*k > 0, which simplifies to k < 1.
Correct Answer:
A
— < 1
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Q. The roots of the equation x² + 4x + 4 = 0 are: (2020)
A.
-2 and -2
B.
2 and 2
C.
0 and 4
D.
1 and 3
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Solution
The equation can be factored as (x + 2)² = 0, giving the double root x = -2.
Correct Answer:
A
— -2 and -2
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Q. The roots of the equation x² + 4x + k = 0 are 2 and -6. What is the value of k? (2021)
A.
-12
B.
-8
C.
-10
D.
-14
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Solution
Using the product of roots: k = 2 * (-6) = -12. The sum is 2 + (-6) = -4, which matches.
Correct Answer:
B
— -8
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Q. The roots of the equation x² - 8x + k = 0 are 4 and 4. Find k. (2021)
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Solution
Using the product of roots: k = 4 * 4 = 16.
Correct Answer:
A
— 16
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Q. What are the roots of the equation 3x² - 12x + 12 = 0? (2019)
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Solution
Dividing the equation by 3 gives x² - 4x + 4 = 0, which factors to (x - 2)² = 0, hence the root is 2.
Correct Answer:
B
— 4
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Q. What are the roots of the equation x² - 2x - 8 = 0? (2022)
A.
-2 and 4
B.
2 and -4
C.
4 and -2
D.
0 and 8
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Solution
Factoring gives (x - 4)(x + 2) = 0, hence the roots are 4 and -2.
Correct Answer:
C
— 4 and -2
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Q. What are the roots of the equation x² - 5x + 6 = 0? (2021)
A.
1 and 6
B.
2 and 3
C.
3 and 2
D.
0 and 5
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Solution
The roots can be found using the factorization method: (x - 2)(x - 3) = 0, hence the roots are 2 and 3.
Correct Answer:
B
— 2 and 3
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Q. What is the 10th term of the arithmetic sequence where the first term is 5 and the common difference is 3?
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Solution
The nth term of an arithmetic sequence is given by a_n = a + (n-1)d. Here, a = 5, d = 3, n = 10. So, a_10 = 5 + (10-1) * 3 = 5 + 27 = 32.
Correct Answer:
B
— 35
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Q. What is the 12th term of the arithmetic sequence where the first term is 7 and the common difference is 5?
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Solution
Using the formula a_n = a + (n-1)d, we have a_12 = 7 + (12-1) * 5 = 7 + 55 = 62.
Correct Answer:
A
— 62
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Q. What is the 3rd term in the expansion of (2x + 3)^4?
A.
108x^2
B.
216x^2
C.
324x^2
D.
432x^2
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Solution
The 3rd term is given by C(4,2) * (2x)^2 * (3)^2 = 6 * 4x^2 * 9 = 216x^2.
Correct Answer:
B
— 216x^2
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Q. What is the 3rd term in the expansion of (2x + 5)^6? (2000)
A.
600x^4
B.
1500x^4
C.
1800x^4
D.
2000x^4
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Solution
The 3rd term is given by C(6,2) * (2x)^2 * (5)^4 = 15 * 4 * 625 = 37500.
Correct Answer:
B
— 1500x^4
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Q. What is the 3rd term in the expansion of (2x - 3)^5? (2022)
A.
-90x^3
B.
90x^3
C.
-60x^3
D.
60x^3
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Solution
The 3rd term is C(5,2) * (2x)^3 * (-3)^2 = 10 * 8x^3 * 9 = -720x^3.
Correct Answer:
A
— -90x^3
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Q. What is the 3rd term in the expansion of (x + 2)^5? (2021)
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Solution
The 3rd term is given by C(5,2) * (x)^3 * (2)^2 = 10 * x^3 * 4 = 40.
Correct Answer:
C
— 60
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Q. What is the 3rd term in the expansion of (x + 2)^8? (2022)
A.
112
B.
128
C.
256
D.
64
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Solution
The 3rd term is given by 8C2 * (2)^2 * (x)^6 = 28 * 4 * x^6 = 112x^6.
Correct Answer:
A
— 112
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Q. What is the 3rd term in the expansion of (x + 3)^4? (2023)
A.
36x^2
B.
54x^2
C.
72x^2
D.
108x^2
Show solution
Solution
The 3rd term is C(4,2) * (3)^2 * (x)^2 = 6 * 9 * x^2 = 54x^2.
Correct Answer:
B
— 54x^2
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Q. What is the 3rd term in the expansion of (x + 3)^5? (2023)
A.
45
B.
90
C.
135
D.
180
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Solution
The 3rd term is C(5,2) * (3)^2 * (x)^3 = 10 * 9 * x^3 = 90.
Correct Answer:
B
— 90
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Q. What is the 3rd term in the expansion of (x + 3)^7? (2023)
A.
189
B.
441
C.
729
D.
1024
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Solution
The 3rd term is C(7,2) * (3)^2 * (x)^5 = 21 * 9 * x^5 = 189.
Correct Answer:
B
— 441
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Q. What is the 3rd term in the expansion of (x + 4)^5? (2023)
A.
80x^3
B.
160x^3
C.
240x^3
D.
320x^3
Show solution
Solution
The 3rd term is given by C(5,2) * (4)^2 * (x)^3 = 10 * 16 * x^3 = 160x^3.
Correct Answer:
C
— 240x^3
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Q. What is the 3rd term in the expansion of (x + 4)^6? (2020)
A.
240x^4
B.
360x^4
C.
480x^4
D.
600x^4
Show solution
Solution
The 3rd term is C(6,2) * (4)^2 * (x)^4 = 15 * 16 * x^4 = 240x^4.
Correct Answer:
B
— 360x^4
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Q. What is the 4th term in the expansion of (2x - 3)^6? (2020)
A.
-540
B.
540
C.
-720
D.
720
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Solution
The 4th term is C(6,3) * (2x)^3 * (-3)^3 = 20 * 8x^3 * -27 = -540.
Correct Answer:
A
— -540
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Q. What is the 5th term in the expansion of (2 + 3x)^6? (2023)
A.
486
B.
540
C.
729
D.
810
Show solution
Solution
The 5th term is given by 6C4 * (2)^(6-4) * (3x)^4 = 15 * 4 * 81x^4 = 4860x^4.
Correct Answer:
B
— 540
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Q. What is the 5th term in the expansion of (3x - 2)^7? (2023)
A.
-1680x^3
B.
1680x^3
C.
-2520x^3
D.
2520x^3
Show solution
Solution
The 5th term is given by C(7,4) * (3x)^4 * (-2)^3 = 35 * 81 * (-8) = -1680x^3.
Correct Answer:
A
— -1680x^3
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Q. What is the 5th term in the expansion of (x - 1)^8? (2022)
A.
-56x^4
B.
56x^4
C.
-70x^4
D.
70x^4
Show solution
Solution
The 5th term corresponds to k=4. Using the binomial theorem, it is given by 8C4 * (x)^4 * (-1)^4 = 70x^4.
Correct Answer:
A
— -56x^4
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Q. What is the 5th term of the sequence defined by a_n = 2n^2 + 3n - 1?
Show solution
Solution
To find the 5th term, substitute n = 5 into the formula: a_5 = 2(5^2) + 3(5) - 1 = 2(25) + 15 - 1 = 50 + 15 - 1 = 64.
Correct Answer:
B
— 47
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Q. What is the 8th term of the sequence defined by a_n = 3n - 2?
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Solution
Substituting n = 8 into the formula: a_8 = 3(8) - 2 = 24 - 2 = 22.
Correct Answer:
A
— 22
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Q. What is the angle between the lines y = 2x + 1 and y = -1/2x + 3?
A.
90 degrees
B.
60 degrees
C.
45 degrees
D.
30 degrees
Show solution
Solution
The slopes are m1 = 2 and m2 = -1/2. The angle θ = tan^(-1) |(m1 - m2) / (1 + m1*m2)| = tan^(-1)(5/4) which is approximately 60 degrees.
Correct Answer:
B
— 60 degrees
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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!
