Q. The professor's lecture was filled with __________ insights that challenged the students to think critically about the subject matter.
A.
banal
B.
trivial
C.
profound
D.
irrelevant
Show solution
Solution
The context indicates that the insights were significant and thought-provoking, making 'profound' the correct choice.
Correct Answer:
C
— profound
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Q. The project was completed by the team. What is the active voice of this sentence? (2023)
A.
The team completes the project.
B.
The team is completing the project.
C.
The team completed the project.
D.
The project is completed by the team.
Show solution
Solution
The active voice emphasizes the team as the doer, leading to 'The team completed the project.'
Correct Answer:
C
— The team completed the project.
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Q. The Pulitzer Prize is awarded in which country? (1917)
A.
United Kingdom
B.
Canada
C.
United States
D.
Australia
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Solution
The Pulitzer Prize is an American award for achievements in newspaper, magazine and online journalism, literature, and musical composition.
Correct Answer:
C
— United States
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Q. The Pulitzer Prize is awarded in which field?
A.
Journalism
B.
Sports
C.
Music
D.
Film
Show solution
Solution
The Pulitzer Prize is awarded for achievements in journalism.
Correct Answer:
A
— Journalism
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Q. The quadratic equation 2x^2 - 4x + k = 0 has no real roots. What is the condition for k? (2022)
A.
k < 0
B.
k > 0
C.
k > 8
D.
k < 8
Show solution
Solution
The discriminant must be less than zero: (-4)^2 - 4*2*k < 0 leads to k > 8.
Correct Answer:
C
— k > 8
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Q. The quadratic equation 2x^2 - 4x + k = 0 has no real roots. What is the condition on k? (2022)
A.
k < 0
B.
k > 0
C.
k > 8
D.
k < 8
Show solution
Solution
The discriminant must be less than zero: (-4)^2 - 4*2*k < 0 leads to k > 8.
Correct Answer:
C
— k > 8
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Q. The quadratic equation 3x^2 + 12x + 12 = 0 can be simplified to what form? (2022)
A.
x^2 + 4x + 4 = 0
B.
x^2 + 3x + 4 = 0
C.
x^2 + 2x + 1 = 0
D.
x^2 + 6x + 4 = 0
Show solution
Solution
Dividing the entire equation by 3 gives x^2 + 4x + 4 = 0.
Correct Answer:
A
— x^2 + 4x + 4 = 0
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Q. The quadratic equation 4x^2 - 12x + 9 = 0 can be factored as: (2023)
A.
(2x - 3)(2x - 3)
B.
(4x - 3)(x - 3)
C.
(2x + 3)(2x + 3)
D.
(4x + 3)(x + 3)
Show solution
Solution
The equation can be factored as (2x - 3)(2x - 3) = 0, indicating a perfect square.
Correct Answer:
A
— (2x - 3)(2x - 3)
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Q. The quadratic equation 5x^2 + 3x - 2 = 0 has roots that can be expressed in which form? (2023)
A.
Rational
B.
Irrational
C.
Complex
D.
Imaginary
Show solution
Solution
The discriminant is 3^2 - 4*5*(-2) = 9 + 40 = 49, which is a perfect square, hence the roots are rational.
Correct Answer:
A
— Rational
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Q. The quadratic equation x^2 + 4x + 4 = 0 has:
A.
Two distinct real roots
B.
One real root
C.
No real roots
D.
Infinitely many roots
Show solution
Solution
The discriminant is 0, indicating one real root (a repeated root).
Correct Answer:
B
— One real root
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Q. The quadratic equation x^2 + 4x + k = 0 has roots that are both negative. What is the condition on k?
A.
k < 0
B.
k > 0
C.
k < 4
D.
k > 4
Show solution
Solution
For both roots to be negative, the sum of roots (4) must be positive and the product (k) must be positive, hence k > 0.
Correct Answer:
C
— k < 4
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Q. The quadratic equation x^2 + 6x + 9 = 0 can be expressed in the form of (x + a)^2. What is the value of a? (2022)
Show solution
Solution
The equation can be factored as (x + 3)^2 = 0, hence a = 3.
Correct Answer:
A
— 3
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Q. The quadratic equation x^2 + 6x + 9 = 0 can be expressed in which of the following forms? (2020)
A.
(x + 3)^2
B.
(x - 3)^2
C.
(x + 6)^2
D.
(x - 6)^2
Show solution
Solution
This is a perfect square trinomial: (x + 3)(x + 3) = 0.
Correct Answer:
A
— (x + 3)^2
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Q. The quadratic equation x^2 + 6x + 9 = 0 has roots that are:
A.
Real and equal
B.
Real and distinct
C.
Complex
D.
None of these
Show solution
Solution
The discriminant is 0, hence the roots are real and equal.
Correct Answer:
A
— Real and equal
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Q. The quadratic equation x^2 + 6x + k = 0 has equal roots. What is the value of k? (2020)
Show solution
Solution
For equal roots, b^2 - 4ac = 0. Here, 6^2 - 4(1)(k) = 0, so k = 9.
Correct Answer:
A
— 9
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Q. The quadratic equation x^2 + 6x + k = 0 has no real roots. What is the condition on k? (2020)
A.
k < 9
B.
k > 9
C.
k = 9
D.
k ≤ 9
Show solution
Solution
For no real roots, the discriminant must be less than zero: 6^2 - 4*1*k < 0, which gives k > 9.
Correct Answer:
B
— k > 9
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Q. The quadratic equation x^2 + 6x + k = 0 has roots that are both negative. What is the condition for k? (2020)
A.
k > 9
B.
k < 9
C.
k = 9
D.
k = 0
Show solution
Solution
For both roots to be negative, k must be greater than the square of half the coefficient of x, hence k > 9.
Correct Answer:
A
— k > 9
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Q. The quadratic equation x^2 + kx + 16 = 0 has equal roots. What is the value of k?
Show solution
Solution
For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0, solving gives k = -8.
Correct Answer:
A
— -8
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Q. The quadratic equation x^2 + px + q = 0 has roots 3 and -2. What is the value of p?
Show solution
Solution
Using the sum of roots: p = -(3 + (-2)) = -1.
Correct Answer:
B
— 5
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Q. The quadratic equation x^2 - 3x + 2 = 0 can be factored as?
A.
(x-1)(x-2)
B.
(x-2)(x-1)
C.
(x+1)(x+2)
D.
(x-3)(x+2)
Show solution
Solution
The equation factors to (x-1)(x-2) = 0.
Correct Answer:
A
— (x-1)(x-2)
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Q. The quadratic equation x^2 - 4x + 4 = 0 can be expressed in which of the following forms? (2022)
A.
(x - 2)^2
B.
(x + 2)^2
C.
(x - 4)^2
D.
(x + 4)^2
Show solution
Solution
The equation can be factored as (x - 2)(x - 2) = 0, which is (x - 2)^2.
Correct Answer:
A
— (x - 2)^2
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Q. The quadratic equation x^2 - 4x + 4 = 0 has how many distinct real roots?
Show solution
Solution
The discriminant is 0, indicating one distinct real root.
Correct Answer:
B
— 1
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Q. The quadratic equation x^2 - 6x + 9 = 0 can be expressed as which of the following? (2021)
A.
(x - 3)^2 = 0
B.
(x + 3)^2 = 0
C.
(x - 2)(x - 4) = 0
D.
(x + 2)(x + 4) = 0
Show solution
Solution
The equation can be factored as (x - 3)(x - 3) = 0, or (x - 3)^2 = 0.
Correct Answer:
A
— (x - 3)^2 = 0
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Q. The quadratic equation x^2 - 6x + 9 = 0 can be expressed in the form (x - a)^2 = 0. What is the value of a? (2021)
Show solution
Solution
The equation can be factored as (x - 3)^2 = 0, hence a = 3.
Correct Answer:
A
— 3
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Q. The quadratic equation x^2 - 6x + 9 = 0 has how many distinct real roots?
A.
0
B.
1
C.
2
D.
Infinite
Show solution
Solution
The discriminant is 0, indicating that there is exactly one distinct real root.
Correct Answer:
B
— 1
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Q. The quadratic equation x^2 - 6x + k = 0 has roots that are both positive. What is the condition on k?
A.
k > 0
B.
k < 0
C.
k > 9
D.
k < 9
Show solution
Solution
For both roots to be positive, k must be greater than the square of half the coefficient of x: k > (6/2)^2 = 9.
Correct Answer:
C
— k > 9
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Q. The quadratic equation x^2 - 6x + k = 0 has roots that differ by 2. What is the value of k?
Show solution
Solution
Let the roots be r and r+2. Then, r + (r+2) = 6 and r(r+2) = k. Solving gives k = 10.
Correct Answer:
B
— 10
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Q. The quadratic equation x² + 4x + 4 = 0 has how many distinct roots? (2021)
Show solution
Solution
The discriminant is 4² - 4*1*4 = 0, indicating one distinct root.
Correct Answer:
B
— 1
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Q. The Quit India Movement of 1942 was significant because it: (1942)
A.
Marked the first mass uprising against British rule
B.
Was a call for immediate independence from British rule
C.
Led to the formation of the Indian National Army
D.
Resulted in the Cripps Mission
Show solution
Solution
The Quit India Movement of 1942 was significant as it was a mass protest demanding an end to British rule in India.
Correct Answer:
B
— Was a call for immediate independence from British rule
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Q. The radius of a circle is increased by 50%. What is the percentage increase in the area of the circle? (2020)
A.
50%
B.
75%
C.
100%
D.
125%
Show solution
Solution
If r is the original radius, new radius = 1.5r. Area increases from πr² to π(1.5r)² = 2.25πr². Percentage increase = (2.25 - 1) × 100% = 125%.
Correct Answer:
C
— 100%
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Showing 17521 to 17550 of 31669 (1056 Pages)
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!
