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. For an electron in a 3p orbital, what are the possible values of m_s?

A. -1/2, +1/2
B. 0, +1
C. 1, 2
D. -1, 0, +1

Solution

The spin quantum number (m_s) can take values of -1/2 and +1/2.

Correct Answer: A — -1/2, +1/2

Q. For an electron in a 3p orbital, what are the possible values of the magnetic quantum number (m_l)?

A. -1, 0, +1
B. 0, +1, +2
C. -2, -1, 0
D. 1, 2, 3

Solution

For a p orbital (l=1), m_l can take values -1, 0, +1.

Correct Answer: A — -1, 0, +1

Q. For an electron in a 5d orbital, what are the possible values of m_l?

A. -2, -1, 0, 1, 2
B. -3, -2, -1, 0, 1, 2, 3
C. 0, 1, 2
D. -1, 0, 1

Solution

For l=2 (d orbital), m_l can take values from -2 to +2, which are -2, -1, 0, 1, 2.

Correct Answer: A — -2, -1, 0, 1, 2

Q. For an ideal gas, if the temperature is increased, what happens to the RMS speed?

A. Increases
B. Decreases
C. Remains constant
D. Depends on the gas

Solution

The RMS speed increases with temperature as v_rms = sqrt(3RT/M) shows that it is directly proportional to the square root of temperature T.

Correct Answer: A — Increases

Q. For an ideal gas, if the volume is halved while keeping the temperature constant, what happens to the pressure?

A. It remains the same
B. It doubles
C. It halves
D. It quadruples

Solution

According to Boyle's law, for a given mass of gas at constant temperature, the pressure is inversely proportional to the volume. Halving the volume will double the pressure.

Correct Answer: B — It doubles

Q. For an ideal gas, the equation of state is given by:

A. PV = nRT
B. PV = NkT
C. PV = mRT
D. PV = kT

Solution

The equation of state for an ideal gas is given by PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

Correct Answer: A — PV = nRT

Q. For an ideal gas, the work done during an isobaric process is given by which formula? (2022)

A. W = PΔV
B. W = nRT
C. W = ΔU + Q
D. W = 0

Solution

In an isobaric process, the work done is calculated using the formula W = PΔV, where P is pressure and ΔV is the change in volume.

Correct Answer: A — W = PΔV

Q. For an ideal gas, which equation relates pressure, volume, and temperature?

A. PV = nRT
B. PV = nR
C. PV = RT
D. PV = nT

Solution

The ideal gas law is given by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

Correct Answer: A — PV = nRT

Q. For an ideal gas, which law relates pressure, volume, and temperature? (2023) 2023

A. Boyle's Law
B. Charles's Law
C. Ideal Gas Law
D. Avogadro's Law

Solution

The Ideal Gas Law (PV = nRT) relates pressure (P), volume (V), and temperature (T) for an ideal gas.

Correct Answer: C — Ideal Gas Law

Q. For an ideal gas, which of the following equations is correct?

A. PV = nRT
B. PV = nR/T
C. PV = nT/R
D. PV = nRT^2

Solution

The ideal gas law is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

Correct Answer: A — PV = nRT

Q. For an ideal gas, which of the following is true at constant temperature?

A. PV = nRT
B. P1V1 = P2V2
C. P/T = constant
D. V/T = constant

Solution

At constant temperature, Boyle's law states that the product of pressure and volume (PV) is constant, hence P1V1 = P2V2.

Correct Answer: B — P1V1 = P2V2

Q. For an ideal solution, if the mole fraction of the solvent is 0.75, what is the vapor pressure of the solution if the vapor pressure of the pure solvent is 100 mmHg?

A. 75 mmHg
B. 100 mmHg
C. 25 mmHg
D. 50 mmHg

Solution

According to Raoult's Law, the vapor pressure of the solution is 0.75 * 100 mmHg = 75 mmHg.

Correct Answer: A — 75 mmHg

Q. For an infinite plane sheet of charge with surface charge density σ, what is the electric field at any point?

A. σ/2ε₀
B. σ/ε₀
C. 0
D. σ/4πε₀

Solution

The electric field due to an infinite plane sheet of charge is constant and given by E = σ/2ε₀ on either side of the sheet.

Correct Answer: A — σ/2ε₀

Q. For an infinite plane sheet of charge with surface charge density σ, what is the electric field at a point near the sheet?

A. σ/2ε₀
B. σ/ε₀
C. 0
D. σ/4πε₀

Solution

Using Gauss's law, the electric field due to an infinite plane sheet of charge is E = σ/2ε₀ on either side of the sheet.

Correct Answer: A — σ/2ε₀

Q. For destructive interference to occur in a thin film, the path difference must be equal to:

A. nλ/2 (n is an integer)
B. nλ (n is an integer)
C. λ/4
D. λ/2

Solution

Destructive interference occurs when the path difference is an odd multiple of λ/2 (i.e., (2n+1)λ/2).

Correct Answer: A — nλ/2 (n is an integer)

Q. For f(x) = { x^2, x < 1; 2x - 1, x ≥ 1 }, is f differentiable at x = 1?

A. Yes
B. No
C. Only left
D. Only right

Solution

f'(1) from left = 2, from right = 2; hence f is differentiable at x = 1.

Correct Answer: B — No

Q. For the cubic equation x^3 - 3x^2 + 3x - 1 = 0, which of the following is a root?

A. -1
B. 0
C. 1
D. 2

Solution

By substituting x = 1 into the equation, we find that it satisfies the equation, hence 1 is a root.

Correct Answer: C — 1

Q. For the cubic equation x^3 - 3x^2 + 3x - 1 = 0, which of the following is true about its roots?

A. All roots are real
B. All roots are complex
C. One root is real and two are complex
D. Two roots are real and one is complex

Solution

The roots can be found using the Rational Root Theorem and synthetic division, confirming that all roots are real.

Correct Answer: A — All roots are real

Q. For the data set 10, 20, 30, 40, 50, what is the mean deviation?

A. 10
B. 15
C. 20
D. 25

Solution

Mean = 30; Mean Deviation = (|10-30| + |20-30| + |30-30| + |40-30| + |50-30|) / 5 = 10.

Correct Answer: B — 15

Q. For the data set 2, 3, 3, 4, 4, 4, 5, 5, what is the mode?

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

Solution

The mode is 4, as it appears 3 times, more than any other number.

Correct Answer: C — 4

Q. For the data set {10, 12, 23, 23, 16, 23, 21}, what is the mode?

A. 10
B. 12
C. 23
D. 21

Solution

The mode is the number that appears most frequently, which is 23.

Correct Answer: C — 23

Q. For the data set {12, 15, 20, 22, 25}, what is the mode?

A. 12
B. 15
C. 20
D. No mode

Solution

There is no mode as all values appear only once.

Correct Answer: D — No mode

Q. For the data set {2, 4, 6, 8, 10}, what is the mean deviation?

A. 2
B. 1.6
C. 3
D. 2.5

Solution

Mean = 6; Mean deviation = (|2-6| + |4-6| + |6-6| + |8-6| + |10-6|)/5 = (4 + 2 + 0 + 2 + 4)/5 = 12/5 = 2.4.

Correct Answer: B — 1.6

Q. For the data set {4, 8, 6, 5, 3}, what is the mean?

A. 4.5
B. 5.5
C. 6.0
D. 5.0

Solution

Mean = (4 + 8 + 6 + 5 + 3) / 5 = 26 / 5 = 5.0.

Correct Answer: D — 5.0

Q. For the data set: 1, 2, 3, 4, 5, what is the interquartile range?

A. 1
B. 2
C. 3
D. 4

Solution

Q1 = 2, Q3 = 4; Interquartile Range = Q3 - Q1 = 4 - 2 = 2.

Correct Answer: B — 2

Q. For the data set: 1, 2, 3, 4, 5, what is the variance? (2022)

A. 2
B. 1.5
C. 1
D. 0.5

Solution

Mean = (1 + 2 + 3 + 4 + 5) / 5 = 3. Variance = [(1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²] / 5 = 2.

Correct Answer: B — 1.5

Q. For the data set: 10, 12, 14, 16, 18, calculate the variance. (2020)

A. 8
B. 10
C. 12
D. 14

Solution

Mean = (10 + 12 + 14 + 16 + 18) / 5 = 14. Variance = [(10-14)² + (12-14)² + (14-14)² + (16-14)² + (18-14)²] / 5 = 8.

Correct Answer: A — 8

Q. For the data set: 10, 12, 14, 16, what is the variance? (2019)

A. 2
B. 4
C. 6
D. 8

Solution

Mean = (10 + 12 + 14 + 16) / 4 = 13. Variance = [(10-13)² + (12-13)² + (14-13)² + (16-13)²] / 4 = 2.

Correct Answer: B — 4

Q. For the data set: 2, 4, 6, 8, 10, what is the variance? (2023)

A. 6
B. 8
C. 10
D. 12

Solution

Mean = (2 + 4 + 6 + 8 + 10) / 5 = 6. Variance = [(2-6)² + (4-6)² + (6-6)² + (8-6)² + (10-6)²] / 5 = 8.

Correct Answer: A — 6

Q. For the data set: 3, 3, 3, 3, 3, what is the variance? (2023)

A. 0
B. 1
C. 2
D. 3

Solution

All values are the same, so variance = 0.

Correct Answer: A — 0

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