Q. In the equation 5x - 2y = 10, what is the value of y when x = 0?
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Solution
Substituting x = 0 into the equation gives -2y = 10, leading to y = -5.
Correct Answer:
B
— 5
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Q. In the equation x^2 - 4x + 4 = 0, what is the nature of the roots? (2021)
A.
Real and distinct
B.
Real and equal
C.
Complex
D.
None of the above
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Solution
The discriminant is 0, which indicates that the roots are real and equal.
Correct Answer:
B
— Real and equal
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Q. In the equation y = mx + b, what does 'm' represent?
A.
The y-intercept
B.
The slope of the line
C.
The x-intercept
D.
The constant term
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Solution
'm' represents the slope of the line, indicating how steep the line is.
Correct Answer:
B
— The slope of the line
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Q. In the equilibrium constant expression Kc, what is the unit for Kc if the reaction is A(g) + B(g) ⇌ C(g)?
A.
mol/L
B.
L/mol
C.
dimensionless
D.
mol^2/L^2
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Solution
The equilibrium constant Kc is dimensionless because it is a ratio of concentrations raised to their stoichiometric coefficients.
Correct Answer:
C
— dimensionless
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Q. In the equilibrium reaction 2SO2(g) + O2(g) ⇌ 2SO3(g), if SO2 is added, what will be the effect on the equilibrium?
A.
Shift to the right
B.
Shift to the left
C.
No change
D.
Increase in pressure
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Solution
Adding SO2 will shift the equilibrium to the right to produce more SO3, according to Le Chatelier's principle.
Correct Answer:
A
— Shift to the right
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Q. In the equilibrium reaction 2SO2(g) + O2(g) ⇌ 2SO3(g), what happens if SO3 is removed?
A.
Shift to the right
B.
Shift to the left
C.
No change
D.
Increase in pressure
Show solution
Solution
Removing SO3 will shift the equilibrium to the right to produce more SO3.
Correct Answer:
A
— Shift to the right
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Q. In the expansion of (1 + x)^10, what is the coefficient of x^5?
A.
252
B.
210
C.
120
D.
300
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Solution
The coefficient of x^5 is C(10,5) = 10! / (5!5!) = 252.
Correct Answer:
A
— 252
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Q. In the expansion of (1 + x)^n, what is the term containing x^4?
A.
C(n, 4)x^4
B.
C(n, 3)x^4
C.
C(n, 5)x^4
D.
C(n, 2)x^4
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Solution
The term containing x^4 in the expansion of (1 + x)^n is C(n, 4)x^4.
Correct Answer:
A
— C(n, 4)x^4
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Q. In the expansion of (2 + 3x)^4, what is the coefficient of x?
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Solution
The coefficient of x is C(4,1) * 2^3 * 3 = 4 * 8 * 3 = 96.
Correct Answer:
A
— 12
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Q. In the expansion of (2 + 3x)^4, what is the coefficient of x^2?
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Solution
The coefficient of x^2 is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.
Correct Answer:
B
— 54
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Q. In the expansion of (2 + 3x)^5, what is the coefficient of x?
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Solution
The coefficient of x is given by C(5, 1) * (2)^4 * (3) = 5 * 16 * 3 = 240.
Correct Answer:
A
— 15
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Q. In the expansion of (2 + 3x)^5, what is the coefficient of x^2?
A.
90
B.
180
C.
270
D.
360
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Solution
The coefficient of x^2 is given by 5C2 * (3^2) * (2^3) = 10 * 9 * 8 = 720.
Correct Answer:
B
— 180
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Q. In the expansion of (2 - x)^5, what is the coefficient of x^3?
A.
-80
B.
-60
C.
60
D.
80
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Solution
The coefficient of x^3 in (2 - x)^5 is given by 5C3 * 2^2 * (-1)^3 = 10 * 4 * (-1) = -40.
Correct Answer:
A
— -80
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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 + 3)^4, what is the coefficient of x^1?
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Solution
The coefficient of x^1 is C(4,1) * (2)^1 * (3)^3 = 4 * 2 * 27 = 216.
Correct Answer:
B
— 48
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Q. In the expansion of (2x + 3)^4, what is the coefficient of x^2?
A.
108
B.
72
C.
36
D.
144
Show solution
Solution
The coefficient of x^2 is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.
Correct Answer:
B
— 72
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Q. In the expansion of (2x + 3)^6, what is the coefficient of x^4?
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:
B
— 720
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Q. In the expansion of (2x + 3y)^4, what is the coefficient of x^2y^2?
A.
108
B.
72
C.
36
D.
144
Show solution
Solution
The coefficient is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.
Correct Answer:
A
— 108
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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)^3, what is the coefficient of x^2?
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Solution
The coefficient of x^2 in (2x + 5)^3 is given by 3C2 * (2x)^2 * 5^1 = 3 * 4 * 5 = 60.
Correct Answer:
B
— 60
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Q. In the expansion of (2x + 5)^4, what is the coefficient of x^2?
A.
300
B.
600
C.
450
D.
500
Show solution
Solution
The coefficient of x^2 is C(4,2) * (2)^2 * (5)^2 = 6 * 4 * 25 = 600.
Correct Answer:
A
— 300
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Q. In the expansion of (2x - 3)^3, what is the coefficient of x?
A.
-9
B.
-18
C.
-27
D.
-6
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Solution
The coefficient of x is C(3,1) * (2)^1 * (-3)^2 = 3 * 2 * 9 = -54.
Correct Answer:
B
— -18
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Q. In the expansion of (2x - 3)^4, what is the coefficient of x^3? (2023)
A.
-108
B.
-72
C.
72
D.
108
Show solution
Solution
The coefficient of x^3 in (2x - 3)^4 is given by 4C1 * (2)^3 * (-3)^1 = 4 * 8 * (-3) = -96. The coefficient is -108.
Correct Answer:
A
— -108
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Q. In the expansion of (2x - 3)^5, what is the coefficient of x^1?
A.
-15
B.
-30
C.
30
D.
15
Show solution
Solution
The coefficient of x^1 is C(5,1) * (2)^1 * (-3)^4 = 5 * 2 * 81 = 810.
Correct Answer:
B
— -30
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Q. In the expansion of (2x - 3)^5, what is the coefficient of x^2?
A.
-90
B.
-120
C.
-150
D.
-180
Show solution
Solution
The coefficient of x^2 is C(5,2) * (2)^2 * (-3)^3 = 10 * 4 * (-27) = -1080.
Correct Answer:
B
— -120
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Q. In the expansion of (2x - 3)^5, what is the coefficient of x^3?
A.
-540
B.
-720
C.
-960
D.
-1080
Show solution
Solution
The coefficient of x^3 is C(5,3) * (2)^3 * (-3)^2 = 10 * 8 * 9 = -720.
Correct Answer:
C
— -960
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Q. In the expansion of (2x - 3)^5, what is the coefficient of x^4?
A.
-90
B.
-120
C.
-150
D.
-180
Show solution
Solution
The coefficient of x^4 is C(5,4) * (2)^4 * (-3)^1 = 5 * 16 * (-3) = -240.
Correct Answer:
B
— -120
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Q. In the expansion of (2x - 3)^6, what is the term containing x^4?
A.
-540x^4
B.
540x^4
C.
-810x^4
D.
810x^4
Show solution
Solution
The term containing x^4 is given by 6C4 * (2^4) * (-3)^2 = 15 * 16 * 9 = -2160.
Correct Answer:
A
— -540x^4
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Q. In the expansion of (2x - 3y)^5, what is the coefficient of x^3y^2?
A.
-720
B.
-540
C.
540
D.
720
Show solution
Solution
The coefficient is C(5,3) * (2)^3 * (-3)^2 = 10 * 8 * 9 = 720.
Correct Answer:
C
— 540
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Major Competitive Exams MCQ & Objective Questions
Major Competitive Exams play a crucial role in shaping the academic and professional futures of students in India. These exams not only assess knowledge but also test problem-solving skills and time management. Practicing MCQs and objective questions is essential for scoring better, as they help in familiarizing students with the exam format and identifying important questions that frequently appear in tests.
What You Will Practise Here
Key concepts and theories related to major subjects
Important formulas and their applications
Definitions of critical terms and terminologies
Diagrams and illustrations to enhance understanding
Practice questions that mirror actual exam patterns
Strategies for solving objective questions efficiently
Time management techniques for competitive exams
Exam Relevance
The topics covered under Major Competitive Exams are integral to various examinations such as CBSE, State Boards, NEET, and JEE. Students can expect to encounter a mix of conceptual and application-based questions that require a solid understanding of the subjects. Common question patterns include multiple-choice questions that test both knowledge and analytical skills, making it essential to be well-prepared with practice MCQs.
Common Mistakes Students Make
Rushing through questions without reading them carefully
Overlooking the negative marking scheme in MCQs
Confusing similar concepts or terms
Neglecting to review previous years’ question papers
Failing to manage time effectively during the exam
FAQs
Question: How can I improve my performance in Major Competitive Exams?Answer: Regular practice of MCQs and understanding key concepts will significantly enhance your performance.
Question: What types of questions should I focus on for these exams?Answer: Concentrate on important Major Competitive Exams questions that frequently appear in past papers and mock tests.
Question: Are there specific strategies for tackling objective questions?Answer: Yes, practicing under timed conditions and reviewing mistakes can help develop effective strategies.
Start your journey towards success by solving practice MCQs today! Test your understanding and build confidence for your upcoming exams. Remember, consistent practice is the key to mastering Major Competitive Exams!
