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 sum of the complex numbers 3 + 2i and 1 - 4i? (2023)

A. 4 - 2i
B. 2 - 2i
C. 4 + 2i
D. 2 + 2i

Solution

(3 + 2i) + (1 - 4i) = (3 + 1) + (2 - 4)i = 4 - 2i.

Correct Answer: A — 4 - 2i

Q. What is the sum of the complex numbers z1 = 2 + 2i and z2 = 3 - 4i?

A. 5 - 2i
B. 5 + 2i
C. 1 - 2i
D. 1 + 2i

Solution

To find the sum, we add the real parts and the imaginary parts: (2 + 3) + (2 - 4)i = 5 - 2i.

Correct Answer: A — 5 - 2i

Q. What is the sum of the complex numbers z1 = 2 + 3i and z2 = 4 - 2i?

A. 6 + i
B. 6 + i
C. 2 + 5i
D. 8 + i

Solution

The sum of two complex numbers z1 + z2 = (2 + 3i) + (4 - 2i) = (2 + 4) + (3 - 2)i = 6 + i.

Correct Answer: A — 6 + i

Q. What is the sum of the decimal equivalents of '101' and '110' in binary?

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

Solution

'101' is 5 and '110' is 6 in decimal. Their sum is 5 + 6 = 11.

Correct Answer: C — 7

Q. What is the sum of the digits in the number '1011' in binary?

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

Solution

The sum of the digits in '1011' is 1 + 0 + 1 + 1 = 3.

Correct Answer: C — 4

Q. What is the sum of the digits of the number '123' in base 4?

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

Solution

The digits are 1, 2, and 3. Their sum is 1 + 2 + 3 = 6.

Correct Answer: A — 6

Q. What is the sum of the first 10 prime numbers?

A. 28
B. 52
C. 129
D. 41

Solution

The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Their sum is 129.

Correct Answer: C — 129

Q. What is the sum of the first 15 terms of an arithmetic progression where the first term is 2 and the common difference is 4?

A. 120
B. 130
C. 140
D. 150

Solution

The sum of the first n terms S_n = n/2 * (2a + (n-1)d). Here, S_15 = 15/2 * (2*2 + 14*4) = 15/2 * (4 + 56) = 15/2 * 60 = 450.

Correct Answer: A — 120

Q. What is the sum of the first 15 terms of an arithmetic progression where the first term is 10 and the common difference is 2?

A. 150
B. 160
C. 170
D. 180

Solution

The sum of the first n terms S_n = n/2 * (2a + (n-1)d). Here, S_15 = 15/2 * (2*10 + 14*2) = 15/2 * (20 + 28) = 15/2 * 48 = 360.

Correct Answer: B — 160

Q. What is the sum of the first 5 natural numbers?

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

Solution

Sum = 1 + 2 + 3 + 4 + 5 = 15.

Correct Answer: B — 15

Q. What is the sum of the first 5 terms of a GP where the first term is 2 and the common ratio is 3?

A. 242
B. 364
C. 486
D. 728

Solution

The sum of the first n terms of a GP is given by S_n = a(1 - r^n) / (1 - r). Here, S_5 = 2(1 - 3^5) / (1 - 3) = 2(1 - 243) / (-2) = 242.

Correct Answer: A — 242

Q. What is the sum of the first 5 terms of the series 1, 1/2, 1/4, ...?

A. 1.5
B. 2
C. 1
D. 3

Solution

S_5 = 1 + 1/2 + 1/4 + 1/8 + 1/16 = 1.5.

Correct Answer: A — 1.5

Q. What is the sum of the first 50 natural numbers?

A. 2450
B. 2550
C. 2600
D. 2700

Solution

The sum of the first n natural numbers is given by the formula n(n + 1)/2. For n = 50, the sum is 50(50 + 1)/2 = 50 * 51 / 2 = 1275.

Correct Answer: A — 2450

Q. What is the sum of the first 6 terms of the arithmetic series 10, 15, 20, ...?

A. 90
B. 100
C. 110
D. 120

Solution

The sum S_n = n/2 * (2a + (n-1)d) = 6/2 * (2*10 + 5*5) = 3 * (20 + 25) = 135.

Correct Answer: A — 90

Q. What is the sum of the first five prime numbers?

A. 28
B. 26
C. 30
D. 24

Solution

The first five prime numbers are 2, 3, 5, 7, and 11. Their sum is 2 + 3 + 5 + 7 + 11 = 28.

Correct Answer: A — 28

Q. What is the sum of the first n terms of the arithmetic series 2, 5, 8, ...?

A. n/2 * (2 + (n-1) * 3)
B. n * (2 + 3n)/2
C. 3n^2/2 + n/2
D. n * (n + 1)

Solution

The first term a = 2, common difference d = 3. The sum of the first n terms S_n = n/2 * (2a + (n-1)d) = n/2 * (2 + (n-1) * 3).

Correct Answer: A — n/2 * (2 + (n-1) * 3)

Q. What is the sum of the first three prime numbers?

A. 10
B. 12
C. 15
D. 17

Solution

The first three prime numbers are 2, 3, and 5. Their sum is 2 + 3 + 5 = 10.

Correct Answer: A — 10

Q. What is the sum of the infinite geometric series 1 + 1/2 + 1/4 + ...?

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

Solution

The sum S = a/(1 - r) = 1/(1 - 1/2) = 1/(1/2) = 2.

Correct Answer: A — 2

Q. What is the sum of the interior angles of a hexagon? (2022)

A. 720 degrees
B. 540 degrees
C. 360 degrees
D. 180 degrees

Solution

Sum of interior angles = (n-2) * 180° = (6-2) * 180° = 720 degrees

Correct Answer: A — 720 degrees

Q. What is the sum of the interior angles of a pentagon?

A. 360°
B. 540°
C. 720°
D. 180°

Solution

The sum of the interior angles of a polygon is given by (n-2) * 180°, where n is the number of sides. For a pentagon, n = 5, so (5-2) * 180° = 540°.

Correct Answer: B — 540°

Q. What is the sum of the interior angles of a quadrilateral? (2023)

A. 180 degrees
B. 360 degrees
C. 540 degrees
D. 720 degrees

Solution

The sum of the interior angles of any quadrilateral is 360 degrees.

Correct Answer: B — 360 degrees

Q. What is the sum of the interior angles of a triangle formed by three intersecting lines?

A. 180 degrees
B. 360 degrees
C. 90 degrees
D. 270 degrees

Solution

The sum of the interior angles of any triangle is always 180 degrees.

Correct Answer: A — 180 degrees

Q. What is the sum of the interior angles of a triangle? (2019)

A. 90 degrees
B. 180 degrees
C. 270 degrees
D. 360 degrees

Solution

The sum of the interior angles of any triangle is always 180 degrees.

Correct Answer: B — 180 degrees

Q. What is the sum of the numbers '101' and '110' in binary?

A. 1011
B. 111
C. 1001
D. 1100

Solution

In binary, '101' + '110' = '1011'.

Correct Answer: A — 1011

Q. What is the sum of the numbers '12' and '21' in base-3?

A. 100
B. 110
C. 120
D. 200

Solution

'12' in base-3 is 3 and '21' is 7. Their sum is 10, which is '100' in base-3.

Correct Answer: A — 100

Q. What is the sum of the numbers 1010 (binary) and 1101 (binary) in decimal?

A. 23
B. 20
C. 25
D. 22

Solution

First convert to decimal: 1010 = 10 and 1101 = 13. The sum is 10 + 13 = 23.

Correct Answer: B — 20

Q. What is the sum of the roots of the equation 2x^2 - 3x + 1 = 0?

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

Solution

The sum of the roots is given by -b/a = 3/2.

Correct Answer: B — 3/2

Q. What is the sum of the roots of the equation 2x^2 - 4x + 1 = 0?

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

Solution

The sum of the roots is given by -b/a = 4/2 = 2.

Correct Answer: B — 1

Q. What is the sum of the roots of the equation 2x^2 - 8x + 6 = 0? (2022)

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

Solution

Using Vieta's formulas, the sum of the roots is -(-8)/2 = 4.

Correct Answer: A — 4

Q. What is the sum of the roots of the equation 2x² - 4x + 1 = 0? (2023)

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

Solution

The sum of the roots is given by -b/a = 4/2 = 2.

Correct Answer: A — 2

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