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. If the polynomial P(x) = x^2 + bx + c has roots 3 and -2, what is the value of b?
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Solution
Using Vieta's formulas, the sum of the roots (3 + (-2)) = 1, hence b = -1.
Correct Answer:
B
— 5
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Q. If the polynomial P(x) = x^2 - 5x + 6 has roots r1 and r2, what is the value of r1 + r2?
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Solution
According to Vieta's formulas, the sum of the roots r1 + r2 of the polynomial x^2 - 5x + 6 is equal to the coefficient of x (which is -(-5)) = 5.
Correct Answer:
A
— 5
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Q. If the polynomial P(x) = x^2 - 5x + 6 is factored, what are the roots of the polynomial?
A.
2 and 3
B.
1 and 6
C.
3 and 2
D.
0 and 5
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Solution
Factoring the polynomial gives (x - 2)(x - 3), so the roots are 2 and 3.
Correct Answer:
A
— 2 and 3
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Q. If the polynomial P(x) = x^2 - 5x + 6 is factored, what are the roots?
A.
2 and 3
B.
1 and 6
C.
3 and 2
D.
0 and 6
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Solution
Factoring the polynomial P(x) gives (x - 2)(x - 3), so the roots are 2 and 3.
Correct Answer:
A
— 2 and 3
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Q. If the polynomial P(x) = x^3 - 3x^2 + 4 has a local maximum at x = 1, what is the value of P(1)?
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Solution
Calculating P(1) gives 1^3 - 3(1^2) + 4 = 1 - 3 + 4 = 2.
Correct Answer:
A
— 2
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Q. If the polynomial P(x) = x^3 - 6x^2 + 11x - 6 has a root at x = 1, what is P(2)?
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Solution
P(2) = 2^3 - 6(2^2) + 11(2) - 6 = 8 - 24 + 22 - 6 = 0.
Correct Answer:
D
— 3
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Q. If the population of a city increases by 10% every year, what will be the population after 2 years if the current population is 1000? (2021)
A.
1210
B.
1100
C.
1020
D.
1200
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Solution
Population after 1 year = 1000 * 1.10 = 1100. Population after 2 years = 1100 * 1.10 = 1210.
Correct Answer:
A
— 1210
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Q. If the population of a city is 1 million and it grows at a rate of 2% per year, what will be the population after one year? (2023)
A.
1.02 million
B.
1.05 million
C.
1.1 million
D.
1.1 million
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Solution
Population after one year = Current Population * (1 + Growth Rate) = 1 million * (1 + 0.02) = 1 million * 1.02 = 1.02 million.
Correct Answer:
A
— 1.02 million
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Q. If the population of a city is 1 million and the average carbon footprint per person is 4 tons per year, what is the total carbon footprint of the city?
A.
2 million tons
B.
3 million tons
C.
4 million tons
D.
5 million tons
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Solution
1,000,000 people * 4 tons/person = 4 million tons
Correct Answer:
C
— 4 million tons
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Q. If the population of a city is 80,000 and it is expected to grow at a rate of 3% per year, what will be the population after 3 years?
A.
85000
B.
90000
C.
88400
D.
80000
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Solution
Population after 3 years = 80000 * (1 + 0.03)^3 = 80000 * 1.092727 = 87418.16, approximately 88400.
Correct Answer:
C
— 88400
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Q. If the population of a country grows from 1 million to 1.2 million in 5 years, what is the annual growth rate?
A.
3.8%
B.
4%
C.
5%
D.
6%
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Solution
Annual Growth Rate = ((Final Population / Initial Population)^(1/Number of Years) - 1) * 100 = ((1.2 million / 1 million)^(1/5) - 1) * 100 ≈ 4%.
Correct Answer:
B
— 4%
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Q. If the population of a country increases by 5% every year, what will be the population after 2 years if the current population is 100,000?
A.
110,250
B.
105,000
C.
120,000
D.
102,500
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Solution
Population after 2 years = 100,000 * (1 + 0.05)^2 = 100,000 * 1.1025 = 110,250.
Correct Answer:
A
— 110,250
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Q. If the population of a town increases by 10% every year, what will be the population after 2 years if the current population is 1000? (2021)
A.
1210
B.
1100
C.
1020
D.
1200
Show solution
Solution
Population after 1 year = 1000 * 1.10 = 1100. Population after 2 years = 1100 * 1.10 = 1210.
Correct Answer:
A
— 1210
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Q. If the population of a town increases from 20,000 to 25,000 in 5 years, what is the annual growth rate?
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Solution
The growth rate is calculated as ((25000 - 20000) / 20000) / 5 * 100 = 5%.
Correct Answer:
B
— 5%
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Q. If the position vector of a point is (5, 12), what is its distance from the origin?
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Solution
Distance = √(5^2 + 12^2) = √(25 + 144) = √169 = 13
Correct Answer:
A
— 13
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Q. If the position vector of a point is given by r = (2t, 3t, 4t), what is the velocity vector?
A.
(2, 3, 4)
B.
(4, 6, 8)
C.
(2t, 3t, 4t)
D.
(0, 0, 0)
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Solution
Velocity vector = dr/dt = (2, 3, 4)
Correct Answer:
A
— (2, 3, 4)
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Q. If the position vector of a point P is (2, 3, 4), what is the distance from the origin to point P?
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Solution
Distance = √(2^2 + 3^2 + 4^2) = √(4 + 9 + 16) = √29 ≈ 5.385.
Correct Answer:
B
— 6
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Q. If the position vector of a point P is (x, y, z) and the vector a = (1, 2, 3), what is the projection of P onto a?
A.
(1, 2, 3)
B.
(2, 4, 6)
C.
(0, 0, 0)
D.
(x, y, z)
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Solution
Projection of P onto a = ((P · a) / |a|^2) * a.
Correct Answer:
D
— (x, y, z)
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Q. If the position vector of a point P is given by r = (2t, 3t, 4t), find the coordinates of P when t = 1.
A.
(2, 3, 4)
B.
(1, 1, 1)
C.
(0, 0, 0)
D.
(2, 4, 6)
Show solution
Solution
Substituting t = 1, r = (2*1, 3*1, 4*1) = (2, 3, 4).
Correct Answer:
A
— (2, 3, 4)
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Q. If the position vector of point P is (3, -2) and Q is (1, 4), what is the vector PQ?
A.
(-2, 6)
B.
(2, -6)
C.
(4, -6)
D.
(6, 2)
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Solution
Vector PQ = Q - P = (1 - 3, 4 - (-2)) = (-2, 6).
Correct Answer:
A
— (-2, 6)
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Q. If the position vector of point P is (3, 4) and Q is (1, 2), what is the vector PQ?
A.
(2, 2)
B.
(4, 6)
C.
(2, 4)
D.
(1, 1)
Show solution
Solution
Vector PQ = Q - P = (1 - 3, 2 - 4) = (-2, -2).
Correct Answer:
A
— (2, 2)
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Q. If the position vector of point P is given by r = 2i + 3j + 4k, what is the distance from the origin to point P?
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Solution
Distance = |r| = √(2^2 + 3^2 + 4^2) = √(4 + 9 + 16) = √29.
Correct Answer:
B
— 6
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Q. If the position vector of point P is given by r = 2i + 3j + 4k, what is the x-coordinate of point P? (2020)
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Solution
The x-coordinate of point P is the coefficient of i in the position vector, which is 2.
Correct Answer:
A
— 2
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Q. If the position vector of point P is given by r = 2i + 3j + 4k, what is the x-component of r?
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Solution
The x-component of r is 2.
Correct Answer:
A
— 2
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Q. If the position vector of point P is given by r = 3i + 4j, what is the distance of point P from the origin?
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Solution
Distance = |r| = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.
Correct Answer:
A
— 5
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Q. If the potential at a point is 5 V and the electric field is 2 V/m, what is the distance from the reference point? (2023)
A.
2.5 m
B.
10 m
C.
7.5 m
D.
5 m
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Solution
Distance (d) = Potential (V) / Electric field (E) = 5 V / 2 V/m = 2.5 m.
Correct Answer:
B
— 10 m
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Q. If the potential difference across a capacitor is halved, what happens to the energy stored in the capacitor? (2019)
A.
Halved
B.
Doubled
C.
Remains the same
D.
Quadrupled
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Solution
The energy stored in a capacitor is given by U = 1/2 CV^2. If V is halved, the energy becomes U' = 1/2 C(V/2)^2 = 1/8 CV^2, which is halved.
Correct Answer:
A
— Halved
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Q. If the potential difference across a capacitor is increased, what happens to the charge stored in it? (2020)
A.
It decreases
B.
It remains the same
C.
It increases
D.
It becomes zero
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Solution
The charge (Q) stored in a capacitor is directly proportional to the potential difference (V) across it, given by Q = CV.
Correct Answer:
C
— It increases
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Q. If the potential difference between two points is 10 V and the work done to move a charge of 2 C between these points is: (2020)
A.
5 J
B.
10 J
C.
20 J
D.
40 J
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Solution
Work done (W) = Charge (Q) × Potential difference (V) = 2 C × 10 V = 20 J.
Correct Answer:
C
— 20 J
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Q. If the poverty line is set at an income of $1,500 per month, how much does a person earning $1,200 fall short by?
A.
$200
B.
$300
C.
$400
D.
$500
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Solution
The person earns $1,200 and the poverty line is $1,500. They fall short by 1500 - 1200 = $300.
Correct Answer:
A
— $200
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