Major Competitive Exams

My Learning Cart

Major Competitive Exams

Download Q&A

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!

Civil Services Defence Exams Engineering & Architecture Admissions Government Jobs Management Admissions Undergraduate

Q. Find the coefficient of x^4 in the expansion of (x + 3)^6.

A. 81
B. 162
C. 243
D. 729

Solution

The coefficient of x^4 is C(6,4) * (3)^2 = 15 * 9 = 135.

Correct Answer: C — 243

Q. Find the coefficient of x^4 in the expansion of (x + 5)^7.

A. 210
B. 1260
C. 1750
D. 2450

Solution

The coefficient of x^4 is given by C(7,4) * 5^3 = 35 * 125 = 4375.

Correct Answer: B — 1260

Q. Find the coefficient of x^4 in the expansion of (x - 1)^5.

A. -5
B. 10
C. -10
D. 5

Solution

The coefficient of x^4 is C(5,4) * (-1)^1 = 5 * (-1) = -5.

Correct Answer: C — -10

Q. Find the coefficient of x^4 in the expansion of (x - 5)^6.

A. 150
B. 200
C. 250
D. 300

Solution

The coefficient of x^4 is given by C(6,4) * (-5)^2 = 15 * 25 = 375.

Correct Answer: B — 200

Q. Find the coefficient of x^5 in the expansion of (2x - 3)^6. (2022)

A. -540
B. 540
C. -720
D. 720

Solution

The coefficient of x^5 is C(6,5) * (2)^5 * (-3)^1 = 6 * 32 * (-3) = -576.

Correct Answer: A — -540

Q. Find the coefficient of x^5 in the expansion of (2x - 3)^7. (2023)

A. 168
B. 252
C. 336
D. 504

Solution

The coefficient of x^5 is C(7,5) * (2)^5 * (-3)^2 = 21 * 32 * 9 = 6048.

Correct Answer: B — 252

Q. Find the coefficient of x^5 in the expansion of (2x - 3)^8.

A. -6720
B. 6720
C. -3360
D. 3360

Solution

The coefficient of x^5 is C(8,5) * (2)^5 * (-3)^3 = 56 * 32 * (-27) = -6720.

Correct Answer: A — -6720

Q. Find the coefficient of x^5 in the expansion of (3x + 2)^6.

A. 486
B. 729
C. 729
D. 486

Solution

The coefficient of x^5 in (3x + 2)^6 is C(6, 5)(3)^5(2)^1 = 6 * 243 * 2 = 2916.

Correct Answer: A — 486

Q. Find the coefficient of x^5 in the expansion of (x + 1)^7.

A. 7
B. 21
C. 35
D. 42

Solution

The coefficient of x^5 is C(7,5) = 21.

Correct Answer: C — 35

Q. Find the coefficient of x^5 in the expansion of (x + 1)^8.

A. 56
B. 70
C. 80
D. 90

Solution

The coefficient of x^5 is C(8,5) = 56.

Correct Answer: B — 70

Q. Find the coefficient of x^5 in the expansion of (x + 2)^7.

A. 21
B. 42
C. 56
D. 70

Solution

The coefficient of x^5 is C(7,5) * 2^2 = 21 * 4 = 84.

Correct Answer: C — 56

Q. Find the coefficient of x^5 in the expansion of (x + 3)^8.

A. 56
B. 168
C. 336
D. 672

Solution

The coefficient of x^5 is C(8,5) * (3)^3 = 56 * 27 = 1512.

Correct Answer: B — 168

Q. Find the coefficient of x^5 in the expansion of (x - 3)^7.

A. -1890
B. -2187
C. -2401
D. -2430

Solution

The coefficient of x^5 is C(7,5) * (-3)^2 = 21 * 9 = -1890.

Correct Answer: A — -1890

Q. Find the coefficient of x^6 in the expansion of (x + 1)^10. (2023)

A. 10
B. 45
C. 120
D. 210

Solution

The coefficient of x^6 is given by 10C6 = 210.

Correct Answer: D — 210

Q. Find the condition for the lines represented by the equation 2x^2 + 3xy + y^2 = 0 to be parallel.

A. D = 0
B. D > 0
C. D < 0
D. D = 1

Solution

For the lines to be parallel, the discriminant D must be equal to 0.

Correct Answer: A — D = 0

Q. Find the condition for the lines represented by the equation ax^2 + 2hxy + by^2 = 0 to be parallel.

A. h^2 = ab
B. h^2 > ab
C. h^2 < ab
D. h^2 = 0

Solution

The condition for the lines to be parallel is given by h^2 = ab.

Correct Answer: A — h^2 = ab

Q. Find the condition for the lines represented by the equation ax^2 + 2hxy + by^2 = 0 to be perpendicular.

A. ab + h^2 = 0
B. ab - h^2 = 0
C. a + b = 0
D. a - b = 0

Solution

The condition for the lines to be perpendicular is given by the relation ab + h^2 = 0.

Correct Answer: A — ab + h^2 = 0

Q. Find the conjugate of the complex number z = 2 - 5i.

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

Solution

The conjugate of z = 2 - 5i is z* = 2 + 5i.

Correct Answer: A — 2 + 5i

Q. Find the conjugate of the complex number z = 5 - 6i.

A. 5 + 6i
B. 5 - 6i
C. -5 + 6i
D. -5 - 6i

Solution

The conjugate of z = 5 - 6i is z̅ = 5 + 6i.

Correct Answer: A — 5 + 6i

Q. Find the constant term in the expansion of (3x - 4/x)^5.

A. -64
B. 0
C. 32
D. 48

Solution

The constant term occurs when the power of x is zero. The term is given by 5C2 * (3x)^2 * (-4/x)^3 = 10 * 9 * (-64) = -5760.

Correct Answer: A — -64

Q. Find the constant term in the expansion of (x - 2/x)^6. (2022)

A. -64
B. 32
C. 0
D. -32

Solution

The constant term occurs when the power of x is zero. Setting 6 - 2k = 0 gives k = 3. The term is C(6,3)(-2)^3 = -64.

Correct Answer: A — -64

Q. Find the coordinates of the centroid of the triangle with vertices (0, 0), (6, 0), and (0, 8). (2022)

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

Solution

Centroid = ((0+6+0)/3, (0+0+8)/3) = (2, 2).

Correct Answer: A — (2, 2)

Q. Find the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(4, 0, 0), C(0, 3, 0). (2021)

A. (4/3, 1, 0)
B. (2, 1, 0)
C. (1, 1, 0)
D. (0, 0, 0)

Solution

Centroid G = ((0+4+0)/3, (0+0+3)/3, (0+0+0)/3) = (4/3, 1, 0).

Correct Answer: B — (2, 1, 0)

Q. Find the coordinates of the centroid of the triangle with vertices at (0, 0), (6, 0), and (3, 6).

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

Solution

Centroid = ((x1+x2+x3)/3, (y1+y2+y3)/3) = (9/3, 6/3) = (3, 2).

Correct Answer: B — (3, 3)

Q. Find the coordinates of the centroid of the triangle with vertices at (0, 0), (6, 0), and (0, 8).

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

Solution

Centroid = ((0+6+0)/3, (0+0+8)/3) = (2, 2).

Correct Answer: A — (2, 2)

Q. Find the coordinates of the centroid of the triangle with vertices at (1, 2), (3, 4), and (5, 6).

A. (3, 4)
B. (2, 3)
C. (4, 5)
D. (5, 6)

Solution

Centroid = ((1+3+5)/3, (2+4+6)/3) = (3, 4).

Correct Answer: B — (2, 3)

Q. Find the coordinates of the focus of the parabola y^2 = -12x.

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

Solution

The equation y^2 = -12x can be rewritten as (y - 0)^2 = 4p(x - 0) with p = -3, so the focus is at (-3, 0).

Correct Answer: A — (-3, 0)

Q. Find the coordinates of the foot of the perpendicular from the point (1, 2) to the line 2x - 3y + 6 = 0.

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

Solution

Using the formula for foot of perpendicular, we find the coordinates to be (1, 1).

Correct Answer: B — (1, 1)

Q. Find the coordinates of the foot of the perpendicular from the point (3, 4) to the line 2x + 3y - 6 = 0.

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

Solution

Using the formula for foot of perpendicular, we find the coordinates to be (3, 2).

Correct Answer: D — (3, 2)

Q. Find the coordinates of the midpoint of the line segment joining A(2, -1, 3) and B(4, 3, 5). (2022)

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

Solution

Midpoint M = ((2+4)/2, (-1+3)/2, (3+5)/2) = (3, 1, 4).

Correct Answer: A — (3, 1, 4)

Showing 5371 to 5400 of 31669 (1056 Pages)

School

College

Degree

Competitve

Skills

Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely