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 distance between the points P(3, 4) and Q(7, 1)?
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Solution
Using the distance formula, d = √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the distance from the center of a circle to a chord if the radius is 13 cm and the chord length is 10 cm?
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Solution
Using the formula d = √(r² - (c/2)²): d = √(13² - (10/2)²) = √(169 - 25) = √144 = 12.
Correct Answer:
B
— 6
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Q. What is the distance from the center of a circle to a tangent line if the radius is 4 cm?
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Solution
The distance from the center to the tangent line is equal to the radius of the circle, which is 4 cm.
Correct Answer:
B
— 4
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Q. What is the distance from the point (1, 1) to the line x + y = 2? (2023)
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Solution
Distance = |1 + 1 - 2| / √(1² + 1²) = 0 / √2 = 0.
Correct Answer:
A
— 1
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Q. What is the distance from the point (1, 2) to the line 3x + 4y - 10 = 0?
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Solution
Distance = |3(1) + 4(2) - 10| / √(3² + 4²) = |3 + 8 - 10| / 5 = 1.
Correct Answer:
B
— 2
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Q. What is the distance from the point (1, 2) to the line x + y - 3 = 0? (2023)
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Solution
Distance = |1 + 2 - 3| / √(1² + 1²) = |0| / √2 = 0, closest option is 1.
Correct Answer:
B
— 2
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Q. What is the distance from the point (1, 2) to the line x + y = 5? (2020)
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Solution
Distance = |1 + 2 - 5| / √(1² + 1²) = | -2 | / √2 = 2/√2 = √2.
Correct Answer:
A
— 3
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Q. What is the distance from the point (2, 3) to the line x + y - 5 = 0? (2022)
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Solution
Distance = |(1*2 + 1*3 - 5)| / √(1² + 1²) = |5 - 5| / √2 = 0
Correct Answer:
A
— 1
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Q. What is the distance from the point (2, 3) to the line x + y = 5? (2020)
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Solution
Distance = |(1*2 + 1*3 - 5)| / √(1² + 1²) = |5 - 5| / √2 = 0/√2 = 0
Correct Answer:
B
— 2
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Q. What is the distance from the point (3, 4) to the line 2x + 3y - 6 = 0?
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Solution
Distance = |2(3) + 3(4) - 6| / √(2² + 3²) = |6 + 12 - 6| / √13 = 12/√13.
Correct Answer:
A
— 1
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Q. What is the distance from the point (3, 4) to the line x + y = 5? (2022)
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Solution
Distance = |3 + 4 - 5| / √(1² + 1²) = |2| / √2 = 2/√2 = √2.
Correct Answer:
B
— 2
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Q. What is the divisibility rule for 3?
A.
The last digit must be 0
B.
The sum of the digits must be divisible by 3
C.
The number must be even
D.
The number must end in 3 or 6
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Solution
A number is divisible by 3 if the sum of its digits is divisible by 3.
Correct Answer:
B
— The sum of the digits must be divisible by 3
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Q. What is the divisibility rule for 9?
A.
The number must be even
B.
The sum of the digits must be divisible by 9
C.
The last digit must be 0
D.
The number must be a multiple of 3
Show solution
Solution
A number is divisible by 9 if the sum of its digits is divisible by 9.
Correct Answer:
B
— The sum of the digits must be divisible by 9
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Q. What is the domain of the function f(x) = 1/(x - 2)?
A.
x ≠ 2
B.
x > 2
C.
x < 2
D.
All real numbers
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Solution
The function is undefined at x = 2, so the domain is all real numbers except 2.
Correct Answer:
A
— x ≠ 2
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Q. What is the domain of the function f(x) = 1/(x-3)?
A.
x ≠ 3
B.
x > 3
C.
x < 3
D.
All real numbers
Show solution
Solution
The function is undefined at x = 3, so the domain is x ≠ 3.
Correct Answer:
A
— x ≠ 3
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Q. What is the domain of the function f(x) = sqrt(x - 1)?
A.
x >= 1
B.
x > 1
C.
x <= 1
D.
x < 1
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Solution
The expression under the square root must be non-negative, so x - 1 >= 0, hence x >= 1.
Correct Answer:
A
— x >= 1
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Q. What is the Doppler effect?
A.
Change in frequency due to motion
B.
Change in amplitude due to distance
C.
Change in speed due to temperature
D.
Change in wavelength due to pressure
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Solution
The Doppler effect refers to the change in frequency of a wave in relation to an observer moving relative to the wave source.
Correct Answer:
A
— Change in frequency due to motion
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Q. What is the dot product of vectors (1, 2) and (3, 4)?
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Solution
Dot product = 1*3 + 2*4 = 3 + 8 = 11
Correct Answer:
A
— 11
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Q. What is the dot product of vectors A = (2, 3, 4) and B = (1, 0, -1)?
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Solution
A . B = 2*1 + 3*0 + 4*(-1) = 2 + 0 - 4 = -2.
Correct Answer:
B
— 5
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Q. What is the dot product of vectors A = 2i + 3j and B = 4i - j? (2022)
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Solution
A · B = (2)(4) + (3)(-1) = 8 - 3 = 5.
Correct Answer:
B
— 10
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Q. What is the eccentricity of a hyperbola defined by the equation x^2/a^2 - y^2/b^2 = 1?
A.
1
B.
√2
C.
√(1 + b^2/a^2)
D.
√(1 - b^2/a^2)
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Solution
The eccentricity e of a hyperbola is given by e = √(1 + b^2/a^2).
Correct Answer:
C
— √(1 + b^2/a^2)
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Q. What is the effect called when sound waves spread out after passing through a narrow opening? (2019)
A.
Reflection
B.
Refraction
C.
Diffraction
D.
Interference
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Solution
The spreading out of sound waves after passing through a narrow opening is known as diffraction.
Correct Answer:
C
— Diffraction
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Q. What is the effect called when two sound waves of slightly different frequencies interfere?
A.
Doppler effect
B.
Beats
C.
Resonance
D.
Echo
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Solution
The phenomenon of two sound waves of slightly different frequencies interfering is called beats.
Correct Answer:
B
— Beats
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Q. What is the effect of -NO2 group on the stability of benzene derivatives?
A.
Stabilizing
B.
Destabilizing
C.
No effect
D.
Enhancing acidity
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Solution
-NO2 is a strong electron-withdrawing group and destabilizes benzene derivatives.
Correct Answer:
B
— Destabilizing
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Q. What is the effect of a -CF3 group on the stability of a benzene ring?
A.
Stabilizing
B.
Destabilizing
C.
No effect
D.
Depends on substituents
Show solution
Solution
-CF3 is a strong electron-withdrawing group, which destabilizes the benzene ring.
Correct Answer:
B
— Destabilizing
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Q. What is the effect of a -CH3 group on the stability of a carbocation?
A.
Destabilizes
B.
No effect
C.
Stabilizes
D.
Increases acidity
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Solution
The -CH3 group is an electron-donating group and stabilizes the carbocation through hyperconjugation.
Correct Answer:
C
— Stabilizes
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Q. What is the effect of a -COOH group on the stability of a benzene ring?
A.
Stabilizing
B.
Destabilizing
C.
No effect
D.
Depends on substituents
Show solution
Solution
The -COOH group is a strong electron-withdrawing group, thus it destabilizes the benzene ring.
Correct Answer:
B
— Destabilizing
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Q. What is the effect of a -I group on the acidity of a carboxylic acid?
A.
Increases acidity
B.
Decreases acidity
C.
No effect
D.
Only affects basicity
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Solution
A -I group increases the acidity of a carboxylic acid by stabilizing the negative charge on the conjugate base.
Correct Answer:
A
— Increases acidity
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Q. What is the effect of a -I group on the acidity of carboxylic acids?
A.
Increases acidity
B.
Decreases acidity
C.
No effect
D.
Depends on the solvent
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Solution
A -I group increases the acidity of carboxylic acids by stabilizing the negative charge on the conjugate base.
Correct Answer:
A
— Increases acidity
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Q. What is the effect of a -NO2 group on the stability of a benzene ring?
A.
Stabilizing
B.
Destabilizing
C.
No effect
D.
Enhances reactivity
Show solution
Solution
The -NO2 group is a strong electron-withdrawing group, which destabilizes the benzene ring.
Correct Answer:
B
— Destabilizing
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