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 data set: 5, 7, 8, 9, 10, what is the mean absolute deviation?

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

Solution

Mean = 7.5; MAD = (|5-7.5| + |7-7.5| + |8-7.5| + |9-7.5| + |10-7.5|) / 5 = 1.

Correct Answer: B — 2

Q. For the data set: 5, 7, 8, 9, 10, what is the standard deviation?

A. 1.5
B. 2
C. 2.5
D. 3

Solution

Mean = 7.5; Variance = [(5-7.5)^2 + (7-7.5)^2 + (8-7.5)^2 + (9-7.5)^2 + (10-7.5)^2] / 5 = 2; Standard Deviation = sqrt(2) = 1.41

Correct Answer: B — 2

Q. For the data set: 5, 7, 9, 11, 13, what is the variance?

A. 4
B. 6
C. 8
D. 10

Solution

Mean = 9. Variance = [(5-9)² + (7-9)² + (9-9)² + (11-9)² + (13-9)²] / 5 = 8.

Correct Answer: A — 4

Q. For the data set: 5, 8, 12, 15, 20, what is the median? (2020)

A. 12
B. 15
C. 10
D. 8

Solution

Arranging the numbers: 5, 8, 12, 15, 20. The median is the middle number, which is 12.

Correct Answer: A — 12

Q. For the data set: 6, 7, 8, 8, 9, 9, 9, 10, what is the mode?

A. 6
B. 7
C. 8
D. 9

Solution

The mode is 9, as it appears most frequently (three times) in the data set.

Correct Answer: D — 9

Q. For the ellipse defined by the equation 9x^2 + 16y^2 = 144, what are the lengths of the semi-major and semi-minor axes?

A. 3, 4
B. 4, 3
C. 6, 8
D. 8, 6

Solution

The semi-major axis is 4 and the semi-minor axis is 3 after rewriting the equation in standard form.

Correct Answer: A — 3, 4

Q. For the equation x^2 + 2x + 1 = 0, what is the nature of the roots?

A. Real and distinct
B. Real and equal
C. Complex
D. None of the above

Solution

The discriminant is 2^2 - 4(1)(1) = 0, indicating that the roots are real and equal.

Correct Answer: B — Real and equal

Q. For the equation x^2 + 2x + k = 0 to have one root equal to 1, what is the value of k?

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

Solution

Substituting x = 1 into the equation gives 1^2 + 2*1 + k = 0 => 1 + 2 + k = 0 => k = -3.

Correct Answer: B — 1

Q. For the equation x^2 + 4x + k = 0 to have real roots, what must be the condition on k? (2023)

A. k >= 0
B. k <= 0
C. k >= 16
D. k <= 16

Solution

The discriminant must be non-negative: 4^2 - 4*1*k >= 0 leads to 16 - 4k >= 0, thus k <= 4.

Correct Answer: C — k >= 16

Q. For the equation x^2 + 6x + k = 0 to have no real roots, what must be the condition on k?

A. k < 0
B. k > 0
C. k = 0
D. k ≤ 0

Solution

The condition for no real roots is that the discriminant must be less than zero: 6^2 - 4*1*k < 0 => 36 < 4k => k > 9.

Correct Answer: D — k ≤ 0

Q. For the equation x^2 + kx + 9 = 0 to have real roots, what must be true about k?

A. k < 6
B. k > 6
C. k < 0
D. k > 0

Solution

The discriminant must be non-negative: k^2 - 4*1*9 >= 0 => k^2 >= 36 => k <= -6 or k >= 6.

Correct Answer: A — k < 6

Q. For the equation x^2 + px + q = 0, if the roots are -2 and -3, what is the value of p?

A. 5
B. 6
C. 7
D. 8

Solution

The sum of the roots is -(-2) + -(-3) = 5, hence p = 5.

Correct Answer: A — 5

Q. For the equation x^3 - 3x^2 + 3x - 1 = 0, how many real roots does it have?

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

Solution

The equation can be factored as (x-1)^3 = 0, which has one real root (x = 1) with multiplicity 3.

Correct Answer: A — 1

Q. For the equation x^3 - 4x^2 + 5x - 2 = 0, which of the following is a root? (2023)

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

Solution

By substituting x = 2 into the equation, we find that it satisfies the equation, thus x = 2 is a root.

Correct Answer: B — 2

Q. For the equation x^3 - 6x^2 + 11x - 6 = 0, what is the product of the roots? (2019)

A. 6
B. 11
C. 1
D. 0

Solution

The product of the roots of the cubic equation ax^3 + bx^2 + cx + d = 0 is given by -d/a. Here, d = -6 and a = 1, so the product is -(-6)/1 = 6.

Correct Answer: A — 6

Q. For the equation x^3 - 6x^2 + 11x - 6 = 0, which of the following is a root?

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

Solution

By substituting x = 2 into the equation, we find that 2 is a root since 2^3 - 6(2^2) + 11(2) - 6 = 0.

Correct Answer: B — 2

Q. For the equation x² + 4x + k = 0 to have real roots, what must be the minimum value of k? (2023)

A. -4
B. 0
C. 4
D. 8

Solution

The discriminant must be non-negative: 4² - 4*1*k ≥ 0, thus k ≤ 4.

Correct Answer: A — -4

Q. For the equation x² + 6x + k = 0 to have real roots, what is the minimum value of k? (2021)

A. -9
B. -6
C. 0
D. 6

Solution

The discriminant must be non-negative: 6² - 4*1*k ≥ 0, which gives k ≤ 9, so the minimum value is -9.

Correct Answer: A — -9

Q. For the equation x² + 6x + k = 0 to have real roots, what must be the minimum value of k? (2023)

A. -9
B. -6
C. -12
D. -15

Solution

The discriminant must be non-negative: 6² - 4*1*k ≥ 0, thus k ≤ 9.

Correct Answer: A — -9

Q. For the equilibrium 2A(g) ⇌ B(g) + C(g), how many moles of gas are on the reactant side?

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

Solution

There are 2 moles of gas on the reactant side (2A).

Correct Answer: B — 2

Q. For the equilibrium 2A(g) ⇌ B(g) + C(g), if the concentration of B is increased, what will happen to the concentration of A?

A. Increase
B. Decrease
C. Remain the same
D. Cannot be determined

Solution

According to Le Chatelier's principle, increasing the concentration of B will shift the equilibrium to the left, resulting in a decrease in the concentration of A.

Correct Answer: B — Decrease

Q. For the equilibrium 2A(g) ⇌ B(g) + C(g), if the volume of the container is decreased, what will happen?

A. Shift to the left
B. Shift to the right
C. No change
D. Depends on the temperature

Solution

Decreasing the volume increases the pressure, and the equilibrium will shift towards the side with fewer moles of gas, which is the right side in this case.

Correct Answer: B — Shift to the right

Q. For the equilibrium 2A(g) ⇌ B(g) + C(g), if the volume of the container is decreased, what will happen to the equilibrium? (2020)

A. Shift to the left
B. Shift to the right
C. No change
D. Depends on temperature

Solution

Decreasing the volume increases the pressure, and the equilibrium will shift towards the side with fewer moles of gas, which is the right side in this case.

Correct Answer: B — Shift to the right

Q. For the equilibrium 2A(g) ⇌ B(g) + C(g), if the volume of the container is doubled, what will happen to the equilibrium position?

A. Shift to the left
B. Shift to the right
C. No change
D. Depends on the temperature

Solution

Doubling the volume decreases the pressure, which shifts the equilibrium towards the side with more moles of gas, in this case, the right side.

Correct Answer: B — Shift to the right

Q. For the equilibrium 2A(g) ⇌ B(g) + C(g), if the volume of the container is doubled, what will happen to the equilibrium concentrations?

A. Concentrations of A will increase
B. Concentrations of B and C will increase
C. Equilibrium will not change
D. Concentrations of A will decrease

Solution

Doubling the volume decreases the pressure, which shifts the equilibrium towards the side with more moles of gas (B and C).

Correct Answer: B — Concentrations of B and C will increase

Q. For the equilibrium reaction 2SO2(g) + O2(g) ⇌ 2SO3(g), what is the effect of decreasing the volume of the container? (2021)

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

Solution

Decreasing the volume increases the pressure, and according to Le Chatelier's principle, the equilibrium will shift towards the side with fewer moles of gas, which is the right side in this case.

Correct Answer: B — Shift to the right

Q. For the equilibrium reaction 4HCl(g) ⇌ 2H2(g) + 2Cl2(g), how will the equilibrium shift if the temperature is decreased?

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

Solution

Decreasing the temperature for an endothermic reaction will shift the equilibrium to the left, favoring the formation of HCl.

Correct Answer: B — Shift to the left

Q. For the equilibrium reaction A ⇌ B, if the concentration of B is increased, what will be the effect on the equilibrium? (2023)

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

Solution

Increasing the concentration of B will shift the equilibrium to the left to produce more A, according to Le Chatelier's principle.

Correct Answer: B — Shift to the left

Q. For the equilibrium reaction CO(g) + 2H2(g) ⇌ CH3OH(g), if the temperature is decreased, what will be the effect?

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

Solution

Decreasing the temperature for an exothermic reaction will shift the equilibrium to the right, favoring the formation of products.

Correct Answer: A — Shift to the right

Q. For the equilibrium reaction N2(g) + 3H2(g) ⇌ 2NH3(g), how will the equilibrium shift if H2 is added?

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

Solution

Adding H2 will shift the equilibrium to the right to produce more NH3.

Correct Answer: A — Shift to the right

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