Major Competitive Exams

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Major Competitive Exams

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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!

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Q. If a player scores 30 points in a game and the winning score is 50 points, what percentage of the winning score did the player achieve?

A. 60%
B. 50%
C. 70%
D. 40%

Solution

To find the percentage, divide the player's score by the winning score and multiply by 100. (30/50) * 100 = 60%.

Correct Answer: A — 60%

Q. If a point charge Q is placed at the center of a spherical Gaussian surface of radius R, what is the electric flux through the surface?

A. 0
B. Q/ε₀
C. Q/2ε₀
D. Q/4ε₀

Solution

The electric flux through a closed surface is given by Φ = Q_enc/ε₀. Here, Q_enc = Q, so Φ = Q/ε₀.

Correct Answer: B — Q/ε₀

Q. If a point charge Q is placed at the center of a spherical Gaussian surface of radius R, what is the total electric flux through the surface?

A. 0
B. Q/ε₀
C. Q/4πε₀R²
D. Q/4πε₀

Solution

The total electric flux through the Gaussian surface is given by Φ = Q/ε₀, where Q is the charge enclosed.

Correct Answer: B — Q/ε₀

Q. If a point charge Q is placed at the center of a spherical Gaussian surface, what is the total electric flux through the surface?

A. 0
B. Q/ε₀
C. Q/4πε₀
D. 4πQ/ε₀

Solution

According to Gauss's law, the total electric flux through a closed surface is equal to the charge enclosed divided by ε₀, thus Φ = Q/ε₀.

Correct Answer: B — Q/ε₀

Q. If a political party needs 50% of the total seats in the Lok Sabha to form a government, how many seats does it need if there are 545 total seats?

A. 272
B. 273
C. 274
D. 275

Solution

Seats needed = (545/2) + 1 = 273 seats.

Correct Answer: B — 273

Q. If a politician misuses $50,000 of public funds and is ordered to return 80% of it, how much must he return?

A. $30,000
B. $35,000
C. $40,000
D. $45,000

Solution

80% of $50,000 is $40,000.

Correct Answer: C — $40,000

Q. If a polygon has 10 sides, what is the measure of each interior angle in a regular decagon? (2023)

A. 144 degrees
B. 120 degrees
C. 108 degrees
D. 135 degrees

Solution

The measure of each interior angle in a regular polygon is given by the formula [(n-2) * 180] / n. For a decagon (n=10), it is [(10-2) * 180] / 10 = 144 degrees.

Correct Answer: A — 144 degrees

Q. If a polygon has 10 sides, what is the measure of each interior angle in a regular polygon? (2023)

A. 144 degrees
B. 156 degrees
C. 180 degrees
D. 120 degrees

Solution

The measure of each interior angle in a regular polygon can be calculated using the formula [(n-2) * 180] / n. For n=10, it is 144 degrees.

Correct Answer: A — 144 degrees

Q. If a polygon has 12 sides, how many diagonals can be drawn from one vertex?

A. 9
B. 10
C. 11
D. 12

Solution

The number of diagonals that can be drawn from one vertex of an n-sided polygon is given by (n-3). For a dodecagon (12-sided polygon), it is 12-3 = 9.

Correct Answer: B — 10

Q. If a polygon has 12 sides, what is the measure of each exterior angle in a regular dodecagon?

A. 30 degrees
B. 36 degrees
C. 15 degrees
D. 45 degrees

Solution

The measure of each exterior angle of a regular polygon can be calculated using the formula 360/n, where n is the number of sides. For a dodecagon (12 sides), it is 360/12 = 30 degrees.

Correct Answer: B — 36 degrees

Q. If a polygon has 12 sides, what is the measure of each exterior angle in a regular polygon?

A. 30 degrees
B. 36 degrees
C. 60 degrees
D. 90 degrees

Solution

The measure of each exterior angle of a regular polygon is calculated as 360/n, where n is the number of sides. For a dodecagon (12 sides), it is 360/12 = 30 degrees.

Correct Answer: B — 36 degrees

Q. If a polygon has 8 sides, how many diagonals does it have?

A. 20
B. 24
C. 28
D. 32

Solution

Using the formula n(n-3)/2, for an octagon (n=8), the number of diagonals is 8(8-3)/2 = 20.

Correct Answer: A — 20

Q. If a polygon has 8 sides, what is the measure of each interior angle in a regular octagon?

A. 135 degrees
B. 120 degrees
C. 108 degrees
D. 150 degrees

Solution

The measure of each interior angle of a regular polygon can be calculated using the formula [(n-2) * 180] / n. For an octagon (n=8), it is [(8-2) * 180] / 8 = 135 degrees.

Correct Answer: C — 108 degrees

Q. If a polygon has 8 sides, what is the sum of its interior angles?

A. 720 degrees
B. 1080 degrees
C. 900 degrees
D. 1440 degrees

Solution

The sum of the interior angles of an octagon (8-sided polygon) is calculated using the formula (n-2) * 180, which gives (8-2) * 180 = 1080 degrees.

Correct Answer: B — 1080 degrees

Q. If a polynomial is expressed as P(x) = 2x^3 - 4x^2 + 3x - 5, what is the coefficient of the x^2 term?

A. 2
B. -4
C. 3
D. -5

Solution

In the polynomial P(x), the coefficient of the x^2 term is -4.

Correct Answer: B — -4

Q. If a polynomial is expressed as P(x) = 2x^3 - 4x^2 + 3x - 5, what is the coefficient of x^2?

A. 2
B. -4
C. 3
D. -5

Solution

In the polynomial P(x), the coefficient of x^2 is -4.

Correct Answer: B — -4

Q. If a polynomial p(x) is expressed as p(x) = x^2 - 5x + 6, what are its roots?

A. 2 and 3
B. 1 and 6
C. 0 and 6
D. 5 and 1

Solution

The roots of the polynomial can be found by factoring it as (x - 2)(x - 3) = 0, giving roots 2 and 3.

Correct Answer: A — 2 and 3

Q. If a polynomial p(x) is given by p(x) = x^2 - 5x + 6, what are its roots?

A. 2 and 3
B. 1 and 6
C. 0 and 6
D. 5 and 1

Solution

The roots of the polynomial can be found by factoring it as (x - 2)(x - 3) = 0, giving roots 2 and 3.

Correct Answer: A — 2 and 3

Q. If a polynomial p(x) is given by p(x) = x^2 - 5x + 6, what are the roots of the polynomial?

A. 2 and 3
B. 1 and 6
C. 0 and 6
D. 5 and 1

Solution

The roots of the polynomial can be found by factoring it as (x - 2)(x - 3) = 0, giving roots 2 and 3.

Correct Answer: A — 2 and 3

Q. If a polynomial p(x) is given by p(x) = x^3 - 6x^2 + 11x - 6, what can be inferred about its roots?

A. It has three distinct real roots.
B. It has one real root and two complex roots.
C. It has no real roots.
D. It has two distinct real roots.

Solution

By applying the Rational Root Theorem and synthetic division, we can find that p(x) has three distinct real roots.

Correct Answer: A — It has three distinct real roots.

Q. If a population increases from 2000 to 2500, what is the percentage increase?

A. 20%
B. 25%
C. 30%
D. 35%

Solution

Percentage increase = ((2500 - 2000) / 2000) * 100 = 25%.

Correct Answer: B — 25%

Q. If a population of 1,000 has a disease prevalence of 3%, how many individuals are expected to be affected? (2019)

A. 30
B. 25
C. 35
D. 40

Solution

Expected affected individuals = Prevalence × Population = 0.03 × 1000 = 30.

Correct Answer: A — 30

Q. If a population of a town increases by 10% every year, what will be the population after 2 years if the current population is 1,000? (2023)

A. 1,100
B. 1,210
C. 1,300
D. 1,400

Solution

Population after 2 years = 1000 * (1 + 0.10)^2 = 1000 * 1.21 = 1210.

Correct Answer: B — 1,210

Q. If a population of a town increases by 15% every year, what will be the population after 2 years if the current population is 1000? (2023)

A. 1150
B. 1300
C. 1325
D. 1440

Solution

After 1 year, the population will be 1000 * 1.15 = 1150. After 2 years, it will be 1150 * 1.15 = 1322.5, rounded to 1325.

Correct Answer: C — 1325

Q. If a population of a town increases by 15% in one year and then decreases by 10% the next year, what is the net percentage change in the population over the two years?

A. 5%
B. 3.5%
C. 4.5%
D. 6%

Solution

Let the initial population be 100. After a 15% increase, it becomes 115. After a 10% decrease, it becomes 115 - 11.5 = 103.5. The net change is (103.5 - 100) / 100 * 100% = 3.5%.

Correct Answer: C — 4.5%

Q. If a population of a town increases by 5% every year, what will be the population after 2 years if the current population is 1,000?

A. 1,050
B. 1,102.5
C. 1,100
D. 1,120

Solution

Population after 1 year = 1,000 * 1.05 = 1,050. After 2 years = 1,050 * 1.05 = 1,102.5.

Correct Answer: B — 1,102.5

Q. If a potentiometer is used to compare two cells, what is the effect of increasing the length of the wire?

A. It increases the accuracy of the measurement
B. It decreases the accuracy of the measurement
C. It has no effect on the measurement
D. It makes the cells equal

Solution

Increasing the length of the wire increases the potential gradient, which can improve the accuracy of the measurement by allowing for finer adjustments.

Correct Answer: A — It increases the accuracy of the measurement

Q. If a potentiometer is used to compare two emfs, what is the key requirement for the two circuits?

A. They must have the same resistance
B. They must have the same length of wire
C. They must be connected in series
D. They must have the same potential gradient

Solution

For accurate comparison of two emfs using a potentiometer, both circuits must have the same potential gradient to ensure that the readings are directly comparable.

Correct Answer: D — They must have the same potential gradient

Q. If a potentiometer is used to measure a voltage of 12 V and the length of the wire used is 6 m, what is the potential gradient?

A. 2 V/m
B. 4 V/m
C. 6 V/m
D. 8 V/m

Solution

The potential gradient is calculated as the potential difference divided by the length of the wire: 12 V / 6 m = 2 V/m.

Correct Answer: A — 2 V/m

Q. If a potentiometer is used to measure the EMF of a cell and the balance point is found at 3 m, what can be inferred about the cell's EMF if the potential gradient is 1.5 V/m?

A. 1.5 V
B. 3 V
C. 4.5 V
D. 6 V

Solution

The EMF of the cell can be calculated as EMF = potential gradient × length = 1.5 V/m × 3 m = 4.5 V.

Correct Answer: C — 4.5 V

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