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. What is the value of the integral ∫(0 to 1) (3x^2)dx?

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

Solution

The integral evaluates to [x^3] from 0 to 1 = 1^3 - 0^3 = 1.

Correct Answer: A — 1

Q. What is the value of the integral ∫(0 to 1) x^2 dx?

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

Solution

The integral ∫(0 to 1) x^2 dx = [x^3/3] from 0 to 1 = 1/3.

Correct Answer: A — 1/3

Q. What is the value of the integral ∫(1 to 2) (3x^2 - 2)dx?

A. 3
B. 4
C. 5
D. 6

Solution

The integral evaluates to [x^3 - 2x] from 1 to 2 = (8 - 4) - (1 - 2) = 3.

Correct Answer: B — 4

Q. What is the value of the integral ∫(1 to 2) (x^2 + 2x)dx?

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

Solution

The integral evaluates to 7.

Correct Answer: A — 7

Q. What is the value of the integral ∫(1/(x^2 + 1))dx?

A. tan^-1(x) + C
B. sin^-1(x) + C
C. cos^-1(x) + C
D. ln(x) + C

Solution

The integral evaluates to tan^-1(x) + C.

Correct Answer: A — tan^-1(x) + C

Q. What is the value of the integral ∫(2x + 3)dx from 0 to 1?

A. 2.5
B. 3
C. 4
D. 5

Solution

The integral ∫(2x + 3)dx = [x^2 + 3x] from 0 to 1 = (1^2 + 3*1) - (0 + 0) = 1 + 3 = 4.

Correct Answer: B — 3

Q. What is the value of the integral ∫(2x)dx from 0 to 1?

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

Solution

∫(2x)dx = x^2 from 0 to 1 = 1^2 - 0^2 = 1.

Correct Answer: A — 1

Q. What is the value of the integral ∫(2x)dx from 0 to 2?

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

Solution

∫(2x)dx = x^2 from 0 to 2 = 2^2 - 0^2 = 4.

Correct Answer: A — 4

Q. What is the value of the integral ∫(2x^3 - 3x^2 + 4)dx from 1 to 2?

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

Solution

The integral evaluates to [0.5x^4 - x^3 + 4x] from 1 to 2 = (8 - 8 + 8) - (0.5 - 1 + 4) = 8 - 2.5 = 5.5.

Correct Answer: B — 6

Q. What is the value of the integral ∫(2x^3 - 3x^2 + 4)dx from 1 to 3?

A. 10
B. 20
C. 30
D. 40

Solution

The integral evaluates to 20.

Correct Answer: B — 20

Q. What is the value of the integral ∫_0^1 (3x^2 + 2x) dx?

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

Solution

Evaluating the integral gives [x^3 + x^2]_0^1 = (1 + 1) - (0 + 0) = 2.

Correct Answer: B — 2

Q. What is the value of the limit lim (x -> 0) (sin(5x)/x)?

A. 0
B. 1
C. 5
D. 10

Solution

Using L'Hôpital's rule, the limit evaluates to 5.

Correct Answer: C — 5

Q. What is the value of the limit lim (x -> 1) (x^2 - 1)/(x - 1)?

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

Solution

Using L'Hôpital's Rule, the limit evaluates to 2.

Correct Answer: C — 2

Q. What is the value of the limit lim(x->0) (sin(x)/x)?

A. 0
B. 1
C. ∞
D. undefined

Solution

The limit lim(x->0) (sin(x)/x) = 1.

Correct Answer: B — 1

Q. What is the value of the limit lim(x→0) (sin(5x)/x)?

A. 0
B. 1
C. 5
D. 10

Solution

Using L'Hôpital's rule, the limit evaluates to 5.

Correct Answer: C — 5

Q. What is the value of the limit lim(x→0) (sin(x)/x)?

A. 0
B. 1
C. ∞
D. undefined

Solution

The limit lim(x→0) (sin(x)/x) = 1.

Correct Answer: B — 1

Q. What is the value of the limit: lim (x -> ∞) (1/x)?

A. 0
B. 1
C. Infinity
D. Undefined

Solution

As x approaches infinity, 1/x approaches 0.

Correct Answer: A — 0

Q. What is the value of the polynomial p(x) = 3x^2 - 2x + 1 at x = 2?

A. 5
B. 7
C. 9
D. 11

Solution

Substituting x = 2 into the polynomial gives p(2) = 3(2^2) - 2(2) + 1 = 12 - 4 + 1 = 9.

Correct Answer: C — 9

Q. What is the value of the polynomial p(x) = 3x^2 - 4x + 1 at x = 2?

A. 3
B. 1
C. 5
D. 7

Solution

Substituting x = 2 into the polynomial gives p(2) = 3(2^2) - 4(2) + 1 = 12 - 8 + 1 = 5.

Correct Answer: C — 5

Q. What is the value of the polynomial P(x) = 4x^2 - 3x + 7 when x = 2?

A. 25
B. 27
C. 23
D. 21

Solution

Substituting x = 2 into the polynomial gives P(2) = 4(2^2) - 3(2) + 7 = 16 - 6 + 7 = 27.

Correct Answer: B — 27

Q. What is the value of the polynomial P(x) = 5x^2 - 3x + 7 at x = -1?

A. 15
B. 13
C. 9
D. 11

Solution

Substituting x = -1 gives P(-1) = 5(-1)^2 - 3(-1) + 7 = 5 + 3 + 7 = 15.

Correct Answer: B — 13

Q. What is the value of the principal quantum number (n) for an electron in the 4f subshell?

A. 3
B. 4
C. 5
D. 6

Solution

The principal quantum number n for the f subshell is 4.

Correct Answer: B — 4

Q. What is the value of the principal quantum number (n) for an electron in the 4s orbital?

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

Solution

The principal quantum number (n) indicates the energy level of the electron. For 4s, n=4.

Correct Answer: D — 4

Q. What is the value of the principal quantum number (n) for an electron in the ground state of a hydrogen atom?

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

Solution

In the ground state, the electron is in the first energy level, which corresponds to n=1.

Correct Answer: B — 1

Q. What is the value of the principal quantum number (n) for the outermost electrons in a sodium atom?

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

Solution

Sodium has an atomic number of 11, and its electron configuration is 1s² 2s² 2p⁶ 3s¹. The outermost electrons are in n=3.

Correct Answer: C — 3

Q. What is the value of the principal quantum number (n) for the outermost electron in potassium (K)?

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

Solution

Potassium has the electronic configuration [Ar] 4s1, so the outermost electron is in n=4.

Correct Answer: B — 4

Q. What is the value of the principal quantum number (n) for the outermost electron in a potassium atom?

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

Solution

Potassium (K) has an atomic number of 19, and its electron configuration ends in 4s, so the outermost electron has n=4.

Correct Answer: C — 3

Q. What is the value of the principal quantum number for an electron in the ground state of a hydrogen atom?

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

Solution

The ground state of hydrogen corresponds to n=1.

Correct Answer: A — 1

Q. What is the value of the principal quantum number for the outermost electrons in a sodium atom?

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

Solution

Sodium has an atomic number of 11, and its outermost electrons are in the n=3 shell.

Correct Answer: C — 3

Q. What is the value of the principal quantum number for the outermost electrons in potassium (K)?

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

Solution

Potassium has an atomic number of 19, and its outermost electrons are in the n=4 shell.

Correct Answer: D — 4

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