Q. In how many ways can 5 different letters be arranged if 2 letters are always together? (2019)
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Solution
Treat the 2 letters as one unit. So, we have 4 units to arrange: 4! * 2! = 48.
Correct Answer:
B
— 60
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Q. In how many ways can 6 different books be arranged on a shelf?
A.
720
B.
600
C.
360
D.
480
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Solution
The number of arrangements of 6 different books is 6! = 720.
Correct Answer:
A
— 720
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Q. In how many ways can 6 different colored balls be arranged in a line?
A.
720
B.
120
C.
60
D.
30
Show solution
Solution
The number of arrangements of 6 different colored balls is 6! = 720.
Correct Answer:
A
— 720
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Q. In how many ways can 6 different colored balls be arranged in a row? (2018)
A.
720
B.
600
C.
480
D.
360
Show solution
Solution
The number of arrangements of 6 distinct balls is 6! = 720.
Correct Answer:
A
— 720
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Q. In how many ways can 6 different flags be arranged on a pole?
A.
720
B.
600
C.
480
D.
540
Show solution
Solution
The number of arrangements is 6! = 720.
Correct Answer:
A
— 720
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Q. In how many ways can 6 people be seated in a row?
A.
720
B.
600
C.
480
D.
360
Show solution
Solution
The number of arrangements of 6 people is 6! = 720.
Correct Answer:
A
— 720
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Q. In how many ways can 7 people be divided into 3 groups if one group must have 3 people?
A.
210
B.
300
C.
420
D.
560
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Solution
Choose 3 people from 7: C(7, 3) = 35. The remaining 4 can be divided into 2 groups in 2 ways. Total = 35 * 2 = 70.
Correct Answer:
B
— 300
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Q. In how many ways can the letters of the word 'BOOK' be arranged? (2022)
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Solution
The word 'BOOK' has 4 letters with 'O' repeating. The number of arrangements is 4! / 2! = 12.
Correct Answer:
C
— 16
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Q. In the expansion of (2x + 3)^4, what is the coefficient of x? (2020)
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Solution
The coefficient of x is given by 4C1 * (2)^1 * (3)^3 = 4 * 2 * 27 = 216.
Correct Answer:
B
— 36
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Q. In the expansion of (2x + 3)^4, what is the coefficient of x^0?
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Solution
The coefficient of x^0 is given by 4C4 * (2x)^0 * (3)^4 = 1 * 81 = 81.
Correct Answer:
A
— 81
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Q. In the expansion of (2x + 5)^3, what is the coefficient of x?
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Solution
The coefficient of x is given by 3C1 * (2)^1 * (5)^2 = 3 * 2 * 25 = 150.
Correct Answer:
B
— 45
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Q. In the expansion of (2x - 5)^5, what is the coefficient of x^2? (2021)
A.
-300
B.
-600
C.
600
D.
300
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Solution
The coefficient of x^2 is C(5,2) * (2)^2 * (-5)^3 = 10 * 4 * (-125) = -5000.
Correct Answer:
A
— -300
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Q. In the expansion of (2x - 5)^5, what is the coefficient of x^3? (2021)
A.
150
B.
300
C.
450
D.
600
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Solution
The coefficient of x^3 is C(5,3) * (2)^3 * (-5)^2 = 10 * 8 * 25 = 2000.
Correct Answer:
C
— 450
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Q. In the expansion of (2x - 5)^6, what is the coefficient of x^2? (2021)
A.
-150
B.
-300
C.
300
D.
150
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Solution
The coefficient of x^2 is C(6,2) * (2)^2 * (-5)^4 = 15 * 4 * 625 = -37500.
Correct Answer:
A
— -150
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Q. In the expansion of (2x - 5)^6, what is the coefficient of x^3? (2020)
A.
-600
B.
-720
C.
720
D.
600
Show solution
Solution
The coefficient of x^3 is C(6,3)(2)^3(-5)^3 = 20 * 8 * -125 = -20000.
Correct Answer:
B
— -720
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Q. In the expansion of (3 + 2x)^4, what is the coefficient of x^2? (2023)
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Solution
The coefficient of x^2 is C(4,2) * (3)^2 * (2)^2 = 6 * 9 * 4 = 216.
Correct Answer:
B
— 48
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Q. In the expansion of (3x - 2)^6, what is the coefficient of x^4? (2022)
A.
540
B.
810
C.
729
D.
486
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Solution
The coefficient of x^4 is given by 6C4 * (3)^4 * (-2)^2 = 15 * 81 * 4 = 4860.
Correct Answer:
A
— 540
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Q. In the expansion of (3x - 4)^4, what is the coefficient of x^2? (2023)
A.
-144
B.
-216
C.
216
D.
144
Show solution
Solution
The coefficient of x^2 is C(4,2)(3)^2(-4)^2 = 6 * 9 * 16 = -864.
Correct Answer:
B
— -216
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Q. In the expansion of (x + 3)^4, what is the coefficient of x^3? (2023)
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Solution
The coefficient of x^3 is C(4,3) * (3)^1 = 4 * 3 = 12.
Correct Answer:
A
— 36
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Q. In the expansion of (x + 4)^5, what is the coefficient of x^3? (2021)
A.
240
B.
320
C.
80
D.
160
Show solution
Solution
The coefficient of x^3 is C(5,3) * (4)^2 = 10 * 16 = 160.
Correct Answer:
A
— 240
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Q. In the expansion of (x - 1)^5, what is the coefficient of x^3?
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Solution
The coefficient of x^3 is C(5,3) * (-1)^2 = 10.
Correct Answer:
A
— -10
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Q. Solve the differential equation dy/dx = 2x + 1.
A.
y = x^2 + x + C
B.
y = x^2 + 2x + C
C.
y = 2x^2 + x + C
D.
y = x^2 + C
Show solution
Solution
Integrating both sides, we get y = ∫(2x + 1)dx = x^2 + x + C.
Correct Answer:
A
— y = x^2 + x + C
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Q. Solve the differential equation dy/dx = 2y + 3. (2023)
A.
y = Ce^(2x) - 3/2
B.
y = Ce^(-2x) + 3/2
C.
y = 3e^(2x)
D.
y = 2e^(2x) + C
Show solution
Solution
Using an integrating factor, we find the solution is y = Ce^(2x) - 3/2.
Correct Answer:
A
— y = Ce^(2x) - 3/2
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Q. Solve the differential equation dy/dx = 6x^2y.
A.
y = Ce^(2x^3)
B.
y = Ce^(3x^2)
C.
y = Ce^(6x^2)
D.
y = Ce^(x^6)
Show solution
Solution
This is a separable equation. Integrating gives y = Ce^(2x^3).
Correct Answer:
A
— y = Ce^(2x^3)
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Q. Solve the differential equation dy/dx = y/x. (2023)
A.
y = Cx
B.
y = Cx^2
C.
y = C/x
D.
y = C ln(x)
Show solution
Solution
This is a separable equation. Integrating gives y = Cx.
Correct Answer:
A
— y = Cx
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Q. Solve the differential equation y' = 5 - 2y.
A.
y = 5/2 + Ce^(-2x)
B.
y = 5 + Ce^(-2x)
C.
y = 2 + Ce^(2x)
D.
y = 5/2 - Ce^(-2x)
Show solution
Solution
This is a linear first-order equation. The solution is y = 5/2 + Ce^(-2x).
Correct Answer:
A
— y = 5/2 + Ce^(-2x)
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Q. Solve 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
Show solution
Solution
Using the integrating factor method, we find the solution y = (3/5) + Ce^(5x).
Correct Answer:
A
— y = (3/5) + Ce^(5x)
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Q. Solve the differential equation y'' - 3y' + 2y = 0.
A.
y = C1e^(2x) + C2e^(x)
B.
y = C1e^(x) + C2e^(2x)
C.
y = C1e^(-x) + C2e^(-2x)
D.
y = C1e^(3x) + C2e^(x)
Show solution
Solution
The characteristic equation is r^2 - 3r + 2 = 0, which factors to (r - 1)(r - 2) = 0. The general solution is y = C1e^(x) + C2e^(2x).
Correct Answer:
B
— y = C1e^(x) + C2e^(2x)
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Q. Solve the equation y' = 6y + 12.
A.
y = 2 - Ce^(-6x)
B.
y = Ce^(6x) - 2
C.
y = 2 + Ce^(6x)
D.
y = 6Ce^(-x)
Show solution
Solution
This is a first-order linear equation. The integrating factor method gives the solution y = 2 - Ce^(-6x).
Correct Answer:
A
— y = 2 - Ce^(-6x)
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Q. Solve the first-order differential equation dy/dx = y/x.
A.
y = Cx
B.
y = Cx^2
C.
y = C/x
D.
y = C ln(x)
Show solution
Solution
This is a separable equation. Separating variables and integrating gives y = Cx.
Correct Answer:
A
— y = Cx
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Showing 571 to 600 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!
