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. Calculate the vector product of A = (3, 2, 1) and B = (1, 0, 2).

A. (4, 5, -2)
B. (2, 5, -3)
C. (2, -5, 3)
D. (5, -2, 3)

Solution

A × B = |i  j  k|\n|3  2  1|\n|1  0  2| = (4, 5, -2)

Correct Answer: A — (4, 5, -2)

Q. Calculate the weight of a 10 kg object on the surface of Mars, where the acceleration due to gravity is 3.7 m/s².

A. 37 N
B. 74 N
C. 10 N
D. 100 N

Solution

Weight = mass * gravity = 10 kg * 3.7 m/s² = 37 N

Correct Answer: A — 37 N

Q. Calculate the weight of a 10 kg object on the surface of the Earth (g = 9.8 m/s²).

A. 98 N
B. 10 N
C. 9.8 N
D. 100 N

Solution

Weight W = m * g = 10 kg * 9.8 m/s² = 98 N.

Correct Answer: A — 98 N

Q. Calculate the weighted mean of the following data: (10, 2), (20, 3), (30, 5).

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

Solution

Weighted Mean = (10*2 + 20*3 + 30*5) / (2 + 3 + 5) = 220 / 10 = 22.

Correct Answer: B — 25

Q. Calculate the weighted mean of the following data: (2, 3), (4, 5), (6, 7) where the first number is the weight.

A. 4.5
B. 5
C. 5.5
D. 6

Solution

Weighted mean = (2*3 + 4*5 + 6*7) / (2 + 4 + 6) = (6 + 20 + 42) / 12 = 68 / 12 = 5.67.

Correct Answer: C — 5.5

Q. Calculate the weighted mean of the numbers 10, 20, and 30 with weights 1, 2, and 3 respectively.

A. 20
B. 25
C. 30
D. 15

Solution

Weighted mean = (10*1 + 20*2 + 30*3) / (1 + 2 + 3) = 140 / 6 = 23.33.

Correct Answer: B — 25

Q. Calculate the weighted mean of the scores 70, 80, and 90 with weights 1, 2, and 3 respectively.

A. 80
B. 85
C. 90
D. 75

Solution

Weighted mean = (70*1 + 80*2 + 90*3) / (1 + 2 + 3) = 85.

Correct Answer: B — 85

Q. Calculate ∫ from 0 to 1 of (1 - x^2) dx.

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

Solution

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

Correct Answer: B — 1/2

Q. Calculate ∫ from 0 to 1 of (1/x) dx.

A. 0
B. 1
C. ln(1)
D. ln(2)

Solution

The integral evaluates to [ln(x)] from 0 to 1 = ln(1) - ln(0) which diverges.

Correct Answer: C — ln(1)

Q. Calculate ∫ from 0 to 1 of (2x^2 + 3x + 1) dx.

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

Solution

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

Correct Answer: C — 3

Q. Calculate ∫ from 0 to 1 of (4x^3 - 2x^2 + x) dx.

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

Solution

The integral evaluates to [x^4 - (2/3)x^3 + (1/2)x^2] from 0 to 1 = (1 - 2/3 + 1/2) = 1/6.

Correct Answer: C — 1/2

Q. Calculate ∫ from 0 to 1 of (4x^3 - 3x^2 + 2x - 1) dx.

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

Solution

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

Correct Answer: B — 1

Q. Calculate ∫ from 0 to 1 of (4x^3 - 4x^2 + 1) dx.

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

Solution

The integral evaluates to [x^4 - (4/3)x^3 + x] from 0 to 1 = 1 - (4/3) + 1 = 2/3.

Correct Answer: A — 1

Q. Calculate ∫ from 0 to 1 of (6x^2 - 4x + 1) dx.

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

Solution

The integral evaluates to [2x^3 - 2x^2 + x] from 0 to 1 = (2 - 2 + 1) = 1.

Correct Answer: A — 1

Q. Calculate ∫ from 0 to 1 of (x^2 * e^x) dx.

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

Solution

Using integration by parts, the integral evaluates to (2/e - 1/e) = 1/e.

Correct Answer: B — 2/e

Q. Calculate ∫ from 0 to 1 of (x^2 + 1/x^2) dx.

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

Solution

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

Correct Answer: C — 3

Q. Calculate ∫ from 0 to 1 of (x^2 + 2x + 1) dx.

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

Solution

The integral evaluates to [x^3/3 + x^2 + x] from 0 to 1 = (1/3 + 1 + 1) - (0) = 7/3.

Correct Answer: C — 3

Q. Calculate ∫ from 0 to 1 of (x^2 + 4x + 4) dx.

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

Solution

The integral evaluates to [x^3/3 + 2x^2 + 4x] from 0 to 1 = (1/3 + 2 + 4) = 25/3.

Correct Answer: C — 5

Q. Calculate ∫ from 0 to 1 of (x^4 - 2x^2 + 1) dx.

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

Solution

The integral evaluates to [x^5/5 - 2x^3/3 + x] from 0 to 1 = (1/5 - 2/3 + 1) = (15/15 - 10/15 + 3/15) = 8/15.

Correct Answer: D — 2/3

Q. Calculate ∫ from 0 to 1 of (x^4 - 2x^3 + x^2) dx.

A. 0
B. 1/5
C. 1/3
D. 1/2

Solution

The integral evaluates to [x^5/5 - (2/4)x^4 + (1/3)x^3] from 0 to 1 = (1/5 - 1/2 + 1/3) = 1/30.

Correct Answer: B — 1/5

Q. Calculate ∫ from 0 to 2 of (x^3 - 3x^2 + 4) dx.

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

Solution

The integral evaluates to [x^4/4 - x^3 + 4x] from 0 to 2 = (4 - 8 + 8) - 0 = 4.

Correct Answer: C — 6

Q. Calculate ∫ from 0 to π of sin(x) dx.

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

Solution

The integral evaluates to [-cos(x)] from 0 to π = [1 - (-1)] = 2.

Correct Answer: C — 2

Q. Calculate ∫ from 0 to π/2 of sin(x) cos(x) dx.

A. 1/2
B. 1
C. π/4
D. π/2

Solution

Using the identity sin(2x) = 2sin(x)cos(x), the integral becomes 1/2 ∫ from 0 to π/2 of sin(2x) dx = 1/2 [-1/2 cos(2x)] from 0 to π/2 = 1/2 [0 - (-1/2)] = 1/4.

Correct Answer: A — 1/2

Q. Calculate ∫ from 0 to π/2 of sin^2(x) dx.

A. π/4
B. π/2
C. π/3
D. π/6

Solution

Using the identity sin^2(x) = (1 - cos(2x))/2, the integral evaluates to π/4.

Correct Answer: A — π/4

Q. Calculate ∫ from 1 to 3 of (2x + 1) dx.

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

Solution

The integral evaluates to [x^2 + x] from 1 to 3 = (9 + 3) - (1 + 1) = 10.

Correct Answer: B — 6

Q. Calculate ∫_0^1 (4x^3 - 3x^2 + 2) dx.

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

Solution

∫_0^1 (4x^3 - 3x^2 + 2) dx = [x^4 - x^3 + 2x] from 0 to 1 = (1 - 1 + 2) - (0) = 2.

Correct Answer: B — 2

Q. Calculate ∫_0^1 (e^x) dx.

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

Solution

∫_0^1 e^x dx = [e^x] from 0 to 1 = e - 1.

Correct Answer: A — e - 1

Q. Calculate ∫_0^1 (x^3 - 2x^2 + x) dx.

A. -1/12
B. 0
C. 1/12
D. 1/6

Solution

The integral evaluates to [x^4/4 - 2x^3/3 + x^2/2] from 0 to 1 = (1/4 - 2/3 + 1/2) = 1/12.

Correct Answer: C — 1/12

Q. Calculate ∫_0^π/2 cos^2(x) dx.

A. π/4
B. π/2
C. 1
D. 0

Solution

∫_0^π/2 cos^2(x) dx = π/4.

Correct Answer: A — π/4

Q. Calculate ∫_1^e (ln(x)) dx.

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

Solution

∫_1^e ln(x) dx = [x ln(x) - x] from 1 to e = (e - e) - (1 - 1) = 1.

Correct Answer: B — e - 1

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