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 the equilibrium reaction N2(g) + 3H2(g) ⇌ 2NH3(g), if the pressure is increased, what will be the effect on the equilibrium?

A. Shift to the right
B. Shift to the left
C. No change
D. Increase in temperature

Solution

Increasing the pressure will shift the equilibrium to the right, favoring the formation of NH3, which has fewer moles of gas.

Correct Answer: A — Shift to the right

Q. For the equilibrium reaction N2(g) + 3H2(g) ⇌ 2NH3(g), what happens if the volume of the container is decreased?

A. Shift to the right
B. Shift to the left
C. No change
D. Increase in temperature

Solution

Decreasing the volume increases the pressure, which shifts the equilibrium to the side with fewer moles of gas, favoring the production of NH3.

Correct Answer: A — Shift to the right

Q. For the equilibrium reaction: 2NO2(g) ⇌ N2O4(g), what is the effect of increasing the pressure? (2021)

A. Shift to the left
B. Shift to the right
C. No effect
D. Increase Kp

Solution

Increasing the pressure will shift the equilibrium to the side with fewer moles of gas, which is the right side (N2O4) in this case.

Correct Answer: A — Shift to the left

Q. For the equilibrium reaction: H2(g) + I2(g) ⇌ 2HI(g), what is the effect of adding more HI?

A. Shifts to the right
B. Shifts to the left
C. No change
D. Increases the rate of reaction

Solution

Adding more HI increases the concentration of products, which shifts the equilibrium to the left to form more reactants.

Correct Answer: B — Shifts to the left

Q. For the equilibrium reaction: H2(g) + I2(g) ⇌ 2HI(g), what is the effect of adding more I2?

A. Equilibrium shifts to the right
B. Equilibrium shifts to the left
C. No effect
D. Equilibrium constant changes

Solution

Adding more I2 increases its concentration, which shifts the equilibrium to the right to produce more HI.

Correct Answer: A — Equilibrium shifts to the right

Q. For the exothermic reaction A + B ⇌ C + D, what effect does increasing the temperature have on the equilibrium? (2020)

A. Shifts to the left
B. Shifts to the right
C. No change
D. Increases Kc

Solution

For an exothermic reaction, increasing the temperature shifts the equilibrium to the left, favoring the reactants.

Correct Answer: A — Shifts to the left

Q. For the exothermic reaction A + B ⇌ C + heat, what will happen if the temperature is increased? (2020)

A. Equilibrium will shift to the right
B. Equilibrium will shift to the left
C. No change in equilibrium
D. Equilibrium will shift to the center

Solution

For an exothermic reaction, increasing the temperature shifts the equilibrium to the left, favoring the reactants, as the system tries to absorb the added heat.

Correct Answer: B — Equilibrium will shift to the left

Q. For the exothermic reaction: N2(g) + 3H2(g) ⇌ 2NH3(g), what will happen if the temperature is increased? (2023)

A. The equilibrium will shift to the right
B. The equilibrium will shift to the left
C. No change in equilibrium
D. The reaction will stop

Solution

According to Le Chatelier's principle, increasing the temperature of an exothermic reaction shifts the equilibrium to the left, favoring the reactants.

Correct Answer: B — The equilibrium will shift to the left

Q. For the function f(x) = -x^2 + 4x + 1, find the maximum value. (2023)

A. 1
B. 5
C. 7
D. 9

Solution

The maximum occurs at x = -b/(2a) = -4/(-2) = 2. f(2) = -2^2 + 4(2) + 1 = 5.

Correct Answer: B — 5

Q. For the function f(x) = -x^2 + 4x + 1, find the x-coordinate of the vertex. (2023)

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

Solution

The vertex x-coordinate is given by -b/(2a) = -4/(2*-1) = 2.

Correct Answer: A — 2

Q. For the function f(x) = -x^2 + 6x, find the x-coordinate of the vertex. (2022)

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

Solution

The vertex x-coordinate is found using x = -b/(2a) = -6/(-2) = 3.

Correct Answer: A — 3

Q. For the function f(x) = 2x^2 - 8x + 10, find the minimum value. (2022)

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

Solution

The minimum occurs at x = 2. f(2) = 2(2^2) - 8(2) + 10 = 2.

Correct Answer: C — 4

Q. For the function f(x) = 2x^3 - 9x^2 + 12x, find the critical points. (2022)

A. (0, 0)
B. (1, 5)
C. (2, 0)
D. (3, 3)

Solution

Set f'(x) = 0. f'(x) = 6x^2 - 18x + 12 = 0. Critical points are x = 2.

Correct Answer: C — (2, 0)

Q. For the function f(x) = 2x^3 - 9x^2 + 12x, find the inflection point.

A. (1, 1)
B. (2, 2)
C. (3, 3)
D. (4, 4)

Solution

f''(x) = 12x - 18. Setting f''(x) = 0 gives x = 1.5. The inflection point is (1.5, f(1.5)).

Correct Answer: B — (2, 2)

Q. For the function f(x) = 2x^3 - 9x^2 + 12x, find the intervals of increase. (2022)

A. (-∞, 0)
B. (0, 3)
C. (3, ∞)
D. (0, 2)

Solution

f'(x) = 6x^2 - 18x + 12. The critical points are x = 1 and x = 2. Test intervals show increase in (0, 3).

Correct Answer: B — (0, 3)

Q. For the function f(x) = 2x^3 - 9x^2 + 12x, find the intervals where the function is increasing.

A. (-∞, 1)
B. (1, 3)
C. (3, ∞)
D. (0, 3)

Solution

f'(x) = 6x^2 - 18x + 12. Setting f'(x) = 0 gives x = 1 and x = 3. Testing intervals shows f is increasing on (1, 3).

Correct Answer: B — (1, 3)

Q. For the function f(x) = 2x^3 - 9x^2 + 12x, find the local maxima.

A. (1, 5)
B. (2, 0)
C. (3, 0)
D. (0, 0)

Solution

f'(x) = 6x^2 - 18x + 12. Setting f'(x) = 0 gives x = 1 and x = 2. f(1) = 5 is a local maximum.

Correct Answer: A — (1, 5)

Q. For the function f(x) = 2x^3 - 9x^2 + 12x, find the local maxima. (2023) 2023

A. (1, 5)
B. (2, 6)
C. (3, 3)
D. (0, 0)

Solution

Find f'(x) = 6x^2 - 18x + 12, set to 0. Local maxima at x = 2 gives f(2) = 6.

Correct Answer: B — (2, 6)

Q. For the function f(x) = 3x^2 - 12x + 7, find the coordinates of the minimum point. (2019)

A. (2, -5)
B. (2, -1)
C. (4, 1)
D. (4, -5)

Solution

The vertex is at x = -(-12)/(2*3) = 2. The minimum value is f(2) = 3(2^2) - 12(2) + 7 = -5. Thus, the coordinates are (2, -5).

Correct Answer: A — (2, -5)

Q. For the function f(x) = 3x^2 - 12x + 7, find the coordinates of the vertex.

A. (2, -5)
B. (2, -1)
C. (3, -2)
D. (1, 1)

Solution

The vertex is at x = -b/(2a) = 12/(2*3) = 2. f(2) = 3(2^2) - 12(2) + 7 = -1. So, the vertex is (2, -1).

Correct Answer: B — (2, -1)

Q. For the function f(x) = 3x^2 - 12x + 7, find the minimum value. (2022)

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

Solution

The vertex occurs at x = 2. f(2) = 3(2^2) - 12(2) + 7 = -5.

Correct Answer: B — -4

Q. For the function f(x) = 3x^2 - 12x + 7, find the x-coordinate of the vertex. (2022)

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

Solution

The x-coordinate of the vertex is given by x = -b/(2a) = 12/(2*3) = 2.

Correct Answer: B — 2

Q. For the function f(x) = 3x^2 - 12x + 9, find the coordinates of the vertex. (2020)

A. (2, 3)
B. (3, 0)
C. (1, 1)
D. (0, 9)

Solution

The vertex is at x = -b/(2a) = 2. f(2) = 3.

Correct Answer: A — (2, 3)

Q. For the function f(x) = 3x^2 - 12x + 9, find the vertex. (2021)

A. (2, 3)
B. (3, 0)
C. (0, 9)
D. (1, 6)

Solution

The vertex occurs at x = -b/(2a) = 12/(2*3) = 2. f(2) = 3(2^2) - 12(2) + 9 = 3.

Correct Answer: A — (2, 3)

Q. For the function f(x) = 3x^2 - 12x + 9, find the x-coordinate of the vertex. (2021)

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

Solution

The vertex x-coordinate is found using -b/(2a) = 12/(2*3) = 2.

Correct Answer: B — 2

Q. For the function f(x) = 3x^3 - 12x^2 + 9, find the x-coordinates of the inflection points.

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

Solution

f''(x) = 18x - 24. Setting f''(x) = 0 gives x = 4/3. This is the inflection point.

Correct Answer: B — 2

Q. For the function f(x) = 3x^3 - 12x^2 + 9x, the number of local maxima and minima is:

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

Solution

Finding f'(x) = 9x^2 - 24x + 9 and solving gives two critical points. The second derivative test confirms one maximum and one minimum.

Correct Answer: C — 2

Q. For the function f(x) = e^x - x^2, the point of inflection occurs at:

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

Solution

To find the point of inflection, we compute f''(x) = e^x - 2. Setting f''(x) = 0 gives e^x = 2, leading to x = ln(2). The closest integer is x = 1.

Correct Answer: B — x = 1

Q. For the function f(x) = e^x, what is f''(x)? (2021)

A. e^x
B. xe^x
C. 0
D. 1

Solution

The second derivative f''(x) = d/dx(e^x) = e^x.

Correct Answer: A — e^x

Q. For the function f(x) = ln(x), find the point where it is not differentiable.

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

Solution

f(x) = ln(x) is not defined for x ≤ 0, hence not differentiable at x = 0.

Correct Answer: A — x = 0

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