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 scalar product of the vectors G = (2, -3, 1) and H = (4, 0, -2).

A. -2
B. 0
C. 2
D. 8

Solution

G · H = 2*4 + (-3)*0 + 1*(-2) = 8 + 0 - 2 = 6.

Correct Answer: A — -2

Q. Find the scalar product of the vectors G = (5, -3, 2) and H = (1, 1, 1).

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

Solution

G · H = 5*1 + (-3)*1 + 2*1 = 5 - 3 + 2 = 4.

Correct Answer: D — 3

Q. Find the scalar product of vectors A = 7i + 1j + 2k and B = 3i + 4j + 5k.

A. 43
B. 37
C. 35
D. 41

Solution

A · B = (7)(3) + (1)(4) + (2)(5) = 21 + 4 + 10 = 35.

Correct Answer: A — 43

Q. Find the scalar projection of vector A = (3, 4) onto vector B = (1, 0).

A. 3
B. 4
C. 1
D. 0

Solution

Scalar projection = (A · B) / |B| = (3*1 + 4*0) / 1 = 3.

Correct Answer: A — 3

Q. Find the scalar triple product of vectors A = (1, 2, 3), B = (4, 5, 6), and C = (7, 8, 9).

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

Solution

Scalar triple product = A · (B × C) = 0, as vectors are coplanar.

Correct Answer: A — 0

Q. Find the second derivative of f(x) = 4x^4 - 2x^3 + x. (2019)

A. 48x^2 - 12x + 1
B. 48x^3 - 6
C. 12x^2 - 6
D. 12x^3 - 6x

Solution

First derivative f'(x) = 16x^3 - 6x^2 + 1. Second derivative f''(x) = 48x^2 - 12x.

Correct Answer: A — 48x^2 - 12x + 1

Q. Find the second derivative of f(x) = e^x at x = 0.

A. 0
B. 1
C. e
D. e^2

Solution

f''(x) = e^x, thus f''(0) = e^0 = 1.

Correct Answer: B — 1

Q. Find the second derivative of f(x) = ln(x^2 + 1).

A. -2/(x^2 + 1)^2
B. 2/(x^2 + 1)^2
C. 0
D. -1/(x^2 + 1)

Solution

First derivative f'(x) = (2x)/(x^2 + 1). Second derivative f''(x) = (2(x^2 + 1) - 4x^2)/(x^2 + 1)^2 = -2/(x^2 + 1)^2.

Correct Answer: A — -2/(x^2 + 1)^2

Q. Find the second derivative of f(x) = x^3 - 3x^2 + 4. (2020)

A. 6x - 6
B. 6x + 6
C. 3x^2 - 6
D. 3x^2 + 6

Solution

First derivative f'(x) = 3x^2 - 6x; second derivative f''(x) = 6x - 6.

Correct Answer: A — 6x - 6

Q. Find the second derivative of f(x) = x^3 - 6x^2 + 9x.

A. 6
B. 0
C. 12
D. 3

Solution

f'(x) = 3x^2 - 12x + 9; f''(x) = 6x - 12. At x = 2, f''(2) = 6(2) - 12 = 0.

Correct Answer: A — 6

Q. Find the second derivative of f(x) = x^4 - 4x^3 + 6x^2.

A. 12x - 24
B. 12x^2 - 24
C. 24x - 12
D. 24x^2 - 12

Solution

First derivative f'(x) = 4x^3 - 12x^2 + 12. Second derivative f''(x) = 12x^2 - 24.

Correct Answer: A — 12x - 24

Q. Find the second derivative of the function f(x) = x^3 - 3x^2 + 4. (2020)

A. 6x - 6
B. 6x + 6
C. 3x^2 - 6
D. 3x^2 + 6

Solution

First derivative f'(x) = 3x^2 - 6x; Second derivative f''(x) = 6x - 6.

Correct Answer: A — 6x - 6

Q. Find the slope of the line passing through the points (2, 3) and (4, 7).

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

Solution

The slope m is given by (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Correct Answer: A — 2

Q. Find the slope of the line represented by the equation 2x - 3y + 6 = 0.

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

Solution

Rearranging gives y = (2/3)x + 2, so slope = 2/3.

Correct Answer: B — -2/3

Q. Find the slope of the line that passes through the points (0, 0) and (5, 5).

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

Solution

The slope m = (5 - 0) / (5 - 0) = 1.

Correct Answer: B — 1

Q. Find the slope of the tangent line to f(x) = 2x^3 - 3x^2 + 4 at x = 1. (2021)

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

Solution

f'(x) = 6x^2 - 6. f'(1) = 6(1)^2 - 6 = 0.

Correct Answer: B — 2

Q. Find the slope of the tangent line to f(x) = x^2 + 2x at x = 1. (2022)

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

Solution

f'(x) = 2x + 2. At x = 1, f'(1) = 4.

Correct Answer: A — 2

Q. Find the slope of the tangent line to the curve y = sin(x) at x = π/4.

A. 1
B. √2/2
C. √3/2
D. 0

Solution

The derivative f'(x) = cos(x). At x = π/4, f'(π/4) = cos(π/4) = √2/2.

Correct Answer: B — √2/2

Q. Find the slopes of the lines represented by the equation 5x^2 + 6xy + 2y^2 = 0.

A. -1, -2
B. -3, -1
C. 1, 2
D. 2, 3

Solution

The slopes can be found by solving the quadratic equation for m in terms of x and y.

Correct Answer: B — -3, -1

Q. Find the slopes of the lines represented by the equation 6x^2 - 5xy + y^2 = 0.

A. -1/6, 5
B. 1/6, -5
C. 5/6, -1
D. 1, -1

Solution

The slopes can be calculated from the quadratic equation, yielding slopes of 5/6 and -1.

Correct Answer: C — 5/6, -1

Q. Find the solution for the inequality 2(x - 1) ≥ 3.

A. x ≥ 2.5
B. x ≤ 2.5
C. x ≥ 1.5
D. x ≤ 1.5

Solution

2(x - 1) ≥ 3 => x - 1 ≥ 1.5 => x ≥ 2.5.

Correct Answer: C — x ≥ 1.5

Q. Find the solution for the inequality 2x + 3 ≤ 5.

A. x ≤ 1
B. x ≥ 1
C. x ≤ 2
D. x ≥ 2

Solution

2x + 3 ≤ 5 => 2x ≤ 2 => x ≤ 1.

Correct Answer: A — x ≤ 1

Q. Find the solution for the inequality 2x + 5 > 3x - 1.

A. x < 6
B. x > 6
C. x < 4
D. x > 4

Solution

2x + 5 > 3x - 1 => 5 + 1 > 3x - 2x => 6 > x => x < 6.

Correct Answer: D — x > 4

Q. Find the solution for the inequality 3x + 2 ≥ 11.

A. x ≥ 3
B. x ≤ 3
C. x ≥ 2
D. x ≤ 2

Solution

3x + 2 ≥ 11 => 3x ≥ 9 => x ≥ 3.

Correct Answer: A — x ≥ 3

Q. Find the solution for the inequality 3x - 5 ≥ 4.

A. x ≥ 3
B. x ≤ 3
C. x ≥ 2
D. x ≤ 2

Solution

3x - 5 ≥ 4 => 3x ≥ 9 => x ≥ 3.

Correct Answer: A — x ≥ 3

Q. Find the solution for the inequality 6x - 4 ≤ 2x + 8.

A. x ≤ 3
B. x ≥ 3
C. x ≤ 2
D. x ≥ 2

Solution

6x - 4 ≤ 2x + 8 => 4x ≤ 12 => x ≥ 3.

Correct Answer: B — x ≥ 3

Q. Find the solution for the inequality: -x + 4 ≤ 2.

A. x ≥ 2
B. x ≤ 2
C. x ≥ 4
D. x ≤ 4

Solution

-x + 4 ≤ 2 => -x ≤ -2 => x ≥ 2.

Correct Answer: B — x ≤ 2

Q. Find the solution for the inequality: 8x - 3 > 5.

A. x > 1
B. x < 1
C. x > 0.5
D. x < 0.5

Solution

8x - 3 > 5 => 8x > 8 => x > 1.

Correct Answer: A — x > 1

Q. Find the solution of the differential equation dy/dx = y^2.

A. y = 1/(C - x)
B. y = C/(x - 1)
C. y = Cx
D. y = e^(x)

Solution

This is a separable equation. Integrating gives y = 1/(C - x).

Correct Answer: A — y = 1/(C - x)

Q. Find the solution of the differential equation y' = 2y + 3.

A. y = Ce^(2x) - 3/2
B. y = Ce^(-2x) + 3/2
C. y = 3/2 - Ce^(2x)
D. y = 3/2 + Ce^(-2x)

Solution

This is a linear first-order equation. The general solution is y = 3/2 + Ce^(-2x).

Correct Answer: D — y = 3/2 + Ce^(-2x)

Showing 5761 to 5790 of 31669 (1056 Pages)

School

College

Degree

Competitve

Skills

eBooks

Soulshift Feedback ×

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

Not likely Very likely