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!
Q. What is the equation of the line parallel to y = 3x - 4 that passes through the point (2, 1)? (2020)
A.
y = 3x - 5
B.
y = 3x + 1
C.
y = 3x - 1
D.
y = 3x + 4
Show solution
Solution
Since parallel lines have the same slope, the equation is y - 1 = 3(x - 2) which simplifies to y = 3x - 5.
Correct Answer:
C
— y = 3x - 1
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Q. What is the equation of the line parallel to y = 3x - 5 and passing through (2, 1)?
A.
y = 3x - 8
B.
y = 3x + 5
C.
y = 3x - 1
D.
y = 3x + 1
Show solution
Solution
Parallel lines have the same slope. The slope is 3. Using point-slope form: y - 1 = 3(x - 2) gives y = 3x - 8.
Correct Answer:
A
— y = 3x - 8
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Q. What is the equation of the line parallel to y = 3x - 5 that passes through the point (2, 1)?
A.
y = 3x - 8
B.
y = 3x + 5
C.
y = 3x - 1
D.
y = 3x + 1
Show solution
Solution
Since the lines are parallel, they have the same slope. Using point-slope form: y - 1 = 3(x - 2) gives y = 3x - 8.
Correct Answer:
A
— y = 3x - 8
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Q. What is the equation of the line parallel to y = 4x - 5 and passing through (2, 3)?
A.
y = 4x - 5
B.
y = 4x - 1
C.
y = 4x + 5
D.
y = 4x + 3
Show solution
Solution
Parallel lines have the same slope. Using point-slope form: y - 3 = 4(x - 2) => y = 4x - 5.
Correct Answer:
B
— y = 4x - 1
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Q. What is the equation of the line parallel to y = 4x - 5 that passes through the point (2, 3)?
A.
y = 4x - 5
B.
y = 4x - 1
C.
y = 4x + 5
D.
y = 4x + 3
Show solution
Solution
Parallel lines have the same slope. Using point-slope form: y - 3 = 4(x - 2) => y = 4x - 8 + 3 => y = 4x - 5.
Correct Answer:
B
— y = 4x - 1
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Q. What is the equation of the line parallel to y = 5x - 2 and passing through the point (2, 3)?
A.
y = 5x - 7
B.
y = 5x + 7
C.
y = 5x - 2
D.
y = 5x + 2
Show solution
Solution
Parallel lines have the same slope. Using point-slope form: y - 3 = 5(x - 2) gives y = 5x - 7.
Correct Answer:
A
— y = 5x - 7
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Q. What is the equation of the line passing through (0, 0) and (2, 4)? (2019)
A.
y = 2x
B.
y = x
C.
y = 4x
D.
y = 3x
Show solution
Solution
Slope = (4-0)/(2-0) = 2, so the equation is y = 2x.
Correct Answer:
A
— y = 2x
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Q. What is the equation of the line passing through (0, 0) with a slope of 3? (2021)
A.
y = 3x
B.
y = x/3
C.
y = 3/x
D.
y = 1/3x
Show solution
Solution
Equation of line: y = mx + c; here m = 3, c = 0 => y = 3x
Correct Answer:
A
— y = 3x
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Q. What is the equation of the line passing through (2, 3) with a slope of 2? (2021)
A.
y = 2x - 1
B.
y = 2x + 1
C.
y = 2x + 3
D.
y = 2x - 3
Show solution
Solution
Using point-slope form: y - 3 = 2(x - 2) => y = 2x - 4 + 3 => y = 2x - 1.
Correct Answer:
B
— y = 2x + 1
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Q. What is the equation of the line passing through the points (1, 2) and (3, 4)?
A.
y = x + 1
B.
y = 2x
C.
y = x + 2
D.
y = 2x - 2
Show solution
Solution
The slope m = (4 - 2) / (3 - 1) = 1. Using point-slope form, y - 2 = 1(x - 1) gives y = x + 1.
Correct Answer:
A
— y = x + 1
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Q. What is the equation of the line passing through the points (1, 2) and (3, 6)?
A.
y = 2x
B.
y = 3x - 1
C.
y = x + 1
D.
y = 4x - 2
Show solution
Solution
The slope m = (6 - 2) / (3 - 1) = 2. Using point-slope form, y - 2 = 2(x - 1) gives y = 2x.
Correct Answer:
A
— y = 2x
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Q. What is the equation of the line passing through the points (1, 2, 3) and (4, 5, 6)?
A.
x = 1 + 3t, y = 2 + 3t, z = 3 + 3t
B.
x = 1 + t, y = 2 + t, z = 3 + t
C.
x = 1 + t, y = 2 + 2t, z = 3 + 3t
D.
x = 1 + 3t, y = 2 + 2t, z = 3 + t
Show solution
Solution
Direction ratios = (3, 3, 3), hence the line equation is x = 1 + 3t, y = 2 + 3t, z = 3 + 3t.
Correct Answer:
A
— x = 1 + 3t, y = 2 + 3t, z = 3 + 3t
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Q. What is the equation of the line perpendicular to y = 3x + 1 that passes through (2, 3)?
A.
y = -1/3x + 4
B.
y = 3x - 3
C.
y = -3x + 9
D.
y = 1/3x + 2
Show solution
Solution
The slope of the perpendicular line is -1/3. Using point-slope form, we find y - 3 = -1/3(x - 2) which simplifies to y = -1/3x + 4.
Correct Answer:
A
— y = -1/3x + 4
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Q. What is the equation of the line that is perpendicular to y = 3x + 1 and passes through the point (2, 3)?
A.
y = -1/3x + 4
B.
y = 3x - 3
C.
y = -3x + 9
D.
y = 1/3x + 2
Show solution
Solution
The slope of the given line is 3, so the perpendicular slope is -1/3. Using point-slope form: y - 3 = -1/3(x - 2) gives y = -1/3x + 4.
Correct Answer:
A
— y = -1/3x + 4
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Q. What is the equation of the line that is perpendicular to y = 3x + 2 and passes through the point (2, 3)?
A.
y = -1/3x + 4
B.
y = 3x - 3
C.
y = -3x + 9
D.
y = 1/3x + 2
Show solution
Solution
The slope of the perpendicular line is -1/3. Using point-slope form: y - 3 = -1/3(x - 2) gives y = -1/3x + 4.
Correct Answer:
A
— y = -1/3x + 4
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Q. What is the equation of the line that is perpendicular to y = 3x + 2 and passes through the point (1, 1)? (2022)
A.
y = -1/3x + 4/3
B.
y = 3x - 2
C.
y = -3x + 4
D.
y = 1/3x + 2/3
Show solution
Solution
The slope of the perpendicular line is -1/3. Using point-slope form: y - 1 = -1/3(x - 1) gives y = -1/3x + 4/3.
Correct Answer:
A
— y = -1/3x + 4/3
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Q. What is the equation of the line that is perpendicular to y = 3x + 4 and passes through the origin?
A.
y = -1/3x
B.
y = 3x
C.
y = -3x
D.
y = 1/3x
Show solution
Solution
The slope of the given line is 3. The slope of the perpendicular line is -1/3. Thus, the equation is y = -1/3x.
Correct Answer:
A
— y = -1/3x
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Q. What is the equation of the line that is perpendicular to y = 3x + 4 and passes through the point (1, 1)? (2022)
A.
y - 1 = -1/3(x - 1)
B.
y - 1 = 3(x - 1)
C.
y - 1 = 3/1(x - 1)
D.
y - 1 = -3(x - 1)
Show solution
Solution
The slope of the perpendicular line is -1/3. Using point-slope form: y - 1 = -1/3(x - 1).
Correct Answer:
A
— y - 1 = -1/3(x - 1)
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Q. What is the equation of the line that passes through the origin and has a slope of -1?
A.
y = -x
B.
y = x
C.
y = -2x
D.
y = 2x
Show solution
Solution
The equation of a line through the origin with slope m is y = mx. Thus, y = -1x or y = -x.
Correct Answer:
A
— y = -x
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Q. What is the equation of the line that passes through the origin and has a slope of -4? (2023)
A.
y = -4x
B.
y = 4x
C.
y = -x/4
D.
y = 1/4x
Show solution
Solution
Using the slope-intercept form y = mx + b, with m = -4 and b = 0, the equation is y = -4x.
Correct Answer:
A
— y = -4x
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Q. What is the equation of the line that passes through the origin and has a slope of -5?
A.
y = -5x
B.
y = 5x
C.
y = -x/5
D.
y = 5/x
Show solution
Solution
The equation of a line through the origin with slope m is y = mx. Thus, y = -5x.
Correct Answer:
A
— y = -5x
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Q. What is the equation of the line that passes through the origin and has a slope of -3? (2022)
A.
y = -3x
B.
y = 3x
C.
y = -x/3
D.
y = 1/3x
Show solution
Solution
The equation of a line through the origin with slope m is y = mx. Thus, y = -3x.
Correct Answer:
A
— y = -3x
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Q. What is the equation of the line that passes through the point (2, 3) and has a slope of -1?
A.
y = -x + 5
B.
y = -x + 3
C.
y = x + 1
D.
y = -x + 2
Show solution
Solution
Using point-slope form: y - 3 = -1(x - 2) => y = -x + 5.
Correct Answer:
A
— y = -x + 5
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Q. What is the equation of the line with slope 2 passing through the point (1, 2)?
A.
y = 2x + 1
B.
y = 2x - 2
C.
y = 2x + 2
D.
y = 2x - 1
Show solution
Solution
Using point-slope form: y - 2 = 2(x - 1) => y = 2x - 2 + 2 => y = 2x - 1.
Correct Answer:
D
— y = 2x - 1
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Q. What is the equation of the line with slope 3 passing through the point (1, 2)?
A.
y = 3x + 2
B.
y = 3x - 1
C.
y = 3x + 1
D.
y = 3x - 2
Show solution
Solution
Using point-slope form: y - 2 = 3(x - 1) => y = 3x - 1.
Correct Answer:
C
— y = 3x + 1
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Q. What is the equation of the line with slope 3 that passes through the point (1, 2)?
A.
y = 3x + 2
B.
y = 3x - 1
C.
y - 2 = 3(x - 1)
D.
y = 2x + 1
Show solution
Solution
Using point-slope form: y - y1 = m(x - x1) => y - 2 = 3(x - 1).
Correct Answer:
C
— y - 2 = 3(x - 1)
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Q. What is the equation of the line with slope 5 that passes through the point (1, 2)?
A.
y = 5x - 3
B.
y = 5x + 2
C.
y = 5x + 1
D.
y = 5x - 2
Show solution
Solution
Using point-slope form: y - 2 = 5(x - 1) gives y = 5x - 3.
Correct Answer:
C
— y = 5x + 1
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Q. What is the equation of the parabola that opens upwards with vertex at the origin and passes through the point (2, 8)?
A.
y = 2x^2
B.
y = x^2
C.
y = 4x^2
D.
y = 8x^2
Show solution
Solution
The vertex form of a parabola is y = ax^2. Since it passes through (2, 8), we have 8 = a(2^2) => 8 = 4a => a = 2. Thus, the equation is y = 4x^2.
Correct Answer:
C
— y = 4x^2
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Q. What is the equation of the parabola with focus at (0, 2) and directrix y = -2?
A.
x^2 = 8y
B.
x^2 = -8y
C.
y^2 = 8x
D.
y^2 = -8x
Show solution
Solution
The distance from the focus to the directrix is 4, so the equation is y = (1/4)(x - 0)^2 + 0, which simplifies to x^2 = 8y.
Correct Answer:
A
— x^2 = 8y
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Q. What is the equation of the parabola with focus at (0, 3) and directrix y = -3?
A.
x^2 = 12y
B.
y^2 = 12x
C.
y = 3x^2
D.
x = 3y^2
Show solution
Solution
The distance from the focus to the directrix is 6, so p = 3. The equation is y^2 = 4px = 12y.
Correct Answer:
A
— x^2 = 12y
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