Q. What is the solution of the equation dy/dx = 6 - 2y? (2021)
A.
y = 3 - Ce^(-2x)
B.
y = 3 + Ce^(-2x)
C.
y = 2 - Ce^(2x)
D.
y = 6 - Ce^(2x)
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Solution
Rearranging gives dy/(6 - 2y) = dx. Integrating both sides leads to y = 3 - Ce^(-2x).
Correct Answer:
A
— y = 3 - Ce^(-2x)
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Q. What is the solution of the equation y' + 4y = 0?
A.
y = Ce^(-4x)
B.
y = Ce^(4x)
C.
y = 4Ce^x
D.
y = Ce^(x/4)
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Solution
This is a separable equation. The solution is y = Ce^(-4x).
Correct Answer:
A
— y = Ce^(-4x)
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Q. What is the solution of the equation y' = -ky, where k is a constant?
A.
y = Ce^(kt)
B.
y = Ce^(-kt)
C.
y = -Ce^(kt)
D.
y = -Ce^(-kt)
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Solution
This is a separable equation. Integrating gives y = Ce^(-kt).
Correct Answer:
B
— y = Ce^(-kt)
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Q. What is the solution to the differential equation dy/dx = -y/x?
A.
y = Cx
B.
y = C/x
C.
y = Cx^2
D.
y = Cx^(-1)
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Solution
This is a separable equation. Separating variables and integrating gives y = C/x.
Correct Answer:
B
— y = C/x
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Q. What is the solution to the differential equation y' = 5y + 3?
A.
y = (3/5) + Ce^(5x)
B.
y = (5/3) + Ce^(5x)
C.
y = Ce^(5x) - 3
D.
y = Ce^(3x) + 5
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Solution
Using the integrating factor method, we find the solution to be y = (3/5) + Ce^(5x).
Correct Answer:
A
— y = (3/5) + Ce^(5x)
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Q. What is the solution to the equation dy/dx = -5y?
A.
y = Ce^(-5x)
B.
y = -5Ce^x
C.
y = Ce^(5x)
D.
y = 5Ce^(-x)
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Solution
This is a separable differential equation. The solution is y = Ce^(-5x), where C is a constant.
Correct Answer:
A
— y = Ce^(-5x)
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Q. What is the solution to the equation dy/dx = y^2? (2022)
A.
y = 1/(C - x)
B.
y = C/(x - 1)
C.
y = Cx^2
D.
y = ln(Cx)
Show solution
Solution
This is a separable equation. Integrating gives y = 1/(C - x).
Correct Answer:
A
— y = 1/(C - x)
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Q. What is the solution to the equation y' + 2y = 0?
A.
y = Ce^(-2x)
B.
y = Ce^(2x)
C.
y = 2Ce^x
D.
y = Ce^x
Show solution
Solution
This is a separable equation. The solution is y = Ce^(-2x).
Correct Answer:
A
— y = Ce^(-2x)
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Q. What is the solution to the equation y' + 3y = 0?
A.
y = Ce^(-3x)
B.
y = Ce^(3x)
C.
y = 3Ce^(-x)
D.
y = Ce^(-x/3)
Show solution
Solution
This is a first-order linear differential equation. The solution is y = Ce^(-3x).
Correct Answer:
A
— y = Ce^(-3x)
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Q. What is the solution to the equation y' = 3y + 6?
A.
y = Ce^(3x) - 2
B.
y = Ce^(3x) + 2
C.
y = 2e^(3x)
D.
y = 3Ce^(x)
Show solution
Solution
This is a first-order linear equation. The integrating factor is e^(3x), leading to the solution y = Ce^(3x) + 2.
Correct Answer:
B
— y = Ce^(3x) + 2
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Q. What is the solution to the equation y'' + 4y = 0?
A.
y = C1 cos(2x) + C2 sin(2x)
B.
y = C1 e^(2x) + C2 e^(-2x)
C.
y = C1 e^(4x) + C2 e^(-4x)
D.
y = C1 sin(4x) + C2 cos(4x)
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Solution
The characteristic equation is r^2 + 4 = 0, giving complex roots. The general solution is y = C1 cos(2x) + C2 sin(2x).
Correct Answer:
A
— y = C1 cos(2x) + C2 sin(2x)
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Q. What is the solution to the equation y'' - 3y' + 2y = 0?
A.
y = C1 e^(2x) + C2 e^(x)
B.
y = C1 e^(x) + C2 e^(2x)
C.
y = C1 e^(-x) + C2 e^(-2x)
D.
y = C1 + C2x
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Solution
The characteristic equation r^2 - 3r + 2 = 0 has roots 1 and 2, leading to y = C1 e^(x) + C2 e^(2x).
Correct Answer:
B
— y = C1 e^(x) + C2 e^(2x)
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Q. What is the square of the modulus of the complex number 1 + 2i? (2014)
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Solution
The modulus is √(1^2 + 2^2) = √(1 + 4) = √5. The square of the modulus is 5.
Correct Answer:
A
— 5
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Q. What is the square of the modulus of the complex number 1 + i? (2020)
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Solution
The modulus is √(1^2 + 1^2) = √2, and the square of the modulus is 2.
Correct Answer:
A
— 2
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Q. What is the square root of 64? (2020)
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Solution
The square root of 64 is 8.
Correct Answer:
C
— 8
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Q. What is the square root of the complex number -1? (2021)
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Solution
The square root of -1 is defined as i.
Correct Answer:
A
— i
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Q. What is the square root of the complex number -4? (2020)
A.
2i
B.
-2i
C.
4i
D.
-4i
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Solution
The square root of -4 is √(-1) * √4 = 2i.
Correct Answer:
A
— 2i
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Q. What is the sum of the coefficients in the expansion of (2 + 3)^4? (2022)
A.
81
B.
64
C.
100
D.
125
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Solution
The sum of the coefficients is (2 + 3)^4 = 5^4 = 625.
Correct Answer:
A
— 81
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Q. What is the sum of the coefficients in the expansion of (3x - 2)^4? (2023)
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Solution
To find the sum of the coefficients, substitute x = 1. Thus, (3(1) - 2)^4 = (3 - 2)^4 = 1^4 = 1.
Correct Answer:
B
— 81
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Q. What is the sum of the coefficients in the expansion of (x + 2)^5? (2021)
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Solution
The sum of the coefficients is found by substituting x=1. So, (1 + 2)^5 = 3^5 = 243.
Correct Answer:
B
— 64
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Q. What is the sum of the complex numbers 1 + 2i and 3 - 4i? (2023)
A.
4 - 2i
B.
4 + 2i
C.
2 - 2i
D.
2 + 2i
Show solution
Solution
(1 + 2i) + (3 - 4i) = (1 + 3) + (2 - 4)i = 4 - 2i.
Correct Answer:
A
— 4 - 2i
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Q. What is the sum of the complex numbers 3 + 2i and 1 - 4i? (2023)
A.
4 - 2i
B.
2 - 2i
C.
4 + 2i
D.
2 + 2i
Show solution
Solution
(3 + 2i) + (1 - 4i) = (3 + 1) + (2 - 4)i = 4 - 2i.
Correct Answer:
A
— 4 - 2i
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Q. What is the sum of the roots of the equation 2x² - 4x + 1 = 0? (2023)
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Solution
The sum of the roots is given by -b/a = 4/2 = 2.
Correct Answer:
A
— 2
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Q. What is the sum of the roots of the equation 3x² + 12x + 9 = 0? (2021)
Show solution
Solution
The sum of the roots is given by -b/a = -12/3 = -4.
Correct Answer:
A
— -4
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Q. What is the term containing x^2 in the expansion of (3x - 4)^6?
A.
-1440
B.
720
C.
-720
D.
1440
Show solution
Solution
The term containing x^2 is given by C(6,2) * (3x)^2 * (-4)^(6-2) = 15 * 9 * 256 = -1440.
Correct Answer:
A
— -1440
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Q. What is the term containing x^2 in the expansion of (x + 4)^6?
A.
240
B.
360
C.
480
D.
600
Show solution
Solution
The term containing x^2 is given by C(6,2) * (4)^4 * (x)^2 = 15 * 256 * x^2 = 3840.
Correct Answer:
C
— 480
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Q. What is the term containing x^5 in the expansion of (2x + 3)^6?
A.
540
B.
720
C.
810
D.
900
Show solution
Solution
The term containing x^5 occurs when k = 5. Using the binomial theorem, the term is C(6,5) * (2x)^5 * 3^1 = 6 * 32 * 3 = 576.
Correct Answer:
B
— 720
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Q. What is the term containing x^5 in the expansion of (2x - 3)^8?
A.
-6720
B.
6720
C.
-13440
D.
13440
Show solution
Solution
The term containing x^5 occurs when k = 5. Using the binomial theorem, the term is C(8,5) * (2x)^5 * (-3)^3 = 56 * 32 * (-27) = -48384.
Correct Answer:
A
— -6720
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Q. What is the term independent of x in the expansion of (2x - 3)^8?
A.
-256
B.
256
C.
-512
D.
512
Show solution
Solution
The term independent of x is given by C(8,4) * (2x)^4 * (-3)^4 = 70 * 16 * 81 = -256.
Correct Answer:
A
— -256
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Q. What is the term independent of x in the expansion of (3x - 2)^6?
Show solution
Solution
The term independent of x occurs when k = 3. Using the binomial theorem, the term is C(6,3) * (3x)^3 * (-2)^(6-3) = 20 * 27 * -8 = -4320.
Correct Answer:
C
— 40
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Showing 871 to 900 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!
