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!
Q. Determine the area under the curve y = 1/x from x = 1 to x = 2.
A.
ln(2)
B.
ln(1)
C.
ln(2) - ln(1)
D.
ln(2) + ln(1)
Show solution
Solution
The area under the curve y = 1/x from x = 1 to x = 2 is given by ∫(from 1 to 2) (1/x) dx = [ln(x)] from 1 to 2 = ln(2) - ln(1) = ln(2).
Correct Answer:
A
— ln(2)
Learn More →
Q. Determine the area under the curve y = e^x from x = 0 to x = 1.
Show solution
Solution
The area under the curve y = e^x from 0 to 1 is given by ∫(from 0 to 1) e^x dx = [e^x] from 0 to 1 = e - 1.
Correct Answer:
A
— e - 1
Learn More →
Q. Determine the coefficient of x^2 in the expansion of (3x - 4)^4.
A.
144
B.
216
C.
108
D.
96
Show solution
Solution
The coefficient of x^2 is C(4,2) * (3)^2 * (-4)^2 = 6 * 9 * 16 = 864.
Correct Answer:
B
— 216
Learn More →
Q. Determine the coefficient of x^2 in the expansion of (3x - 4)^6.
A.
540
B.
720
C.
480
D.
360
Show solution
Solution
The coefficient of x^2 is C(6,2) * (3)^2 * (-4)^4 = 15 * 9 * 256 = 34560.
Correct Answer:
B
— 720
Learn More →
Q. Determine the coefficient of x^2 in the expansion of (x - 2)^6.
A.
-60
B.
-30
C.
15
D.
20
Show solution
Solution
The coefficient of x^2 is C(6,2)(-2)^4 = 15 * 16 = 240.
Correct Answer:
A
— -60
Learn More →
Q. Determine the coefficient of x^4 in the expansion of (2x - 3)^6.
A.
540
B.
720
C.
810
D.
960
Show solution
Solution
The coefficient of x^4 is given by 6C4 * (2)^4 * (-3)^2 = 15 * 16 * 9 = 2160.
Correct Answer:
B
— 720
Learn More →
Q. Determine the coefficient of x^5 in the expansion of (3x - 4)^7.
A.
252
B.
336
C.
672
D.
840
Show solution
Solution
The coefficient of x^5 in (3x - 4)^7 is C(7, 5) * (3)^5 * (-4)^2 = 21 * 243 * 16 = 68016.
Correct Answer:
A
— 252
Learn More →
Q. Determine the condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be perpendicular.
A.
h^2 = ab
B.
h^2 = -ab
C.
a + b = 0
D.
a - b = 0
Show solution
Solution
The lines are perpendicular if 2h = a + b, which leads to h^2 = -ab.
Correct Answer:
B
— h^2 = -ab
Learn More →
Q. Determine the condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be parallel.
A.
h^2 = ab
B.
h^2 > ab
C.
h^2 < ab
D.
h^2 ≠ ab
Show solution
Solution
The lines are parallel if the discriminant of the quadratic equation is zero, which leads to the condition h^2 = ab.
Correct Answer:
A
— h^2 = ab
Learn More →
Q. Determine the condition for the lines represented by the equation 4x^2 + 4xy + y^2 = 0 to be coincident.
A.
b^2 - 4ac = 0
B.
b^2 - 4ac > 0
C.
b^2 - 4ac < 0
D.
b^2 - 4ac = 1
Show solution
Solution
For the lines to be coincident, the discriminant must be zero, i.e., b^2 - 4ac = 0.
Correct Answer:
A
— b^2 - 4ac = 0
Learn More →
Q. Determine the condition for the lines represented by the equation ax^2 + 2hxy + by^2 = 0 to be perpendicular.
A.
a + b = 0
B.
ab = h^2
C.
a - b = 0
D.
h = 0
Show solution
Solution
The lines are perpendicular if the condition a + b = 0 holds true.
Correct Answer:
A
— a + b = 0
Learn More →
Q. Determine the continuity of f(x) = { 1/x, x != 0; 0, x = 0 } at x = 0.
A.
Continuous
B.
Not continuous
C.
Depends on limit
D.
None of the above
Show solution
Solution
The limit as x approaches 0 does not exist, hence f(x) is not continuous at x = 0.
Correct Answer:
B
— Not continuous
Learn More →
Q. Determine the continuity of f(x) = { x^2 - 1, x < 1; 3, x = 1; 2x, x > 1 } at x = 1.
A.
Continuous
B.
Discontinuous
C.
Depends on x
D.
Not defined
Show solution
Solution
The left limit is 0, the right limit is 2, and f(1) = 3. Thus, it is discontinuous.
Correct Answer:
B
— Discontinuous
Learn More →
Q. Determine the continuity of the function f(x) = { x^2, x < 1; 2, x = 1; x + 1, x > 1 } at x = 1.
A.
Continuous
B.
Not continuous
C.
Depends on the limit
D.
Only left continuous
Show solution
Solution
The left limit as x approaches 1 is 1, the right limit is 2, and f(1) = 2. Since the left and right limits do not match, f(x) is not continuous at x = 1.
Correct Answer:
B
— Not continuous
Learn More →
Q. Determine the continuity of the function f(x) = { x^2, x < 1; 2x - 1, x >= 1 } at x = 1.
A.
Continuous
B.
Not continuous
C.
Depends on the limit
D.
Only left continuous
Show solution
Solution
The left limit as x approaches 1 is 1, and the right limit is also 1. Thus, f(1) = 1, making it continuous.
Correct Answer:
A
— Continuous
Learn More →
Q. Determine the continuity of the function f(x) = { x^2, x < 1; 2x - 1, x ≥ 1 } at x = 1.
A.
Continuous
B.
Discontinuous
C.
Only left continuous
D.
Only right continuous
Show solution
Solution
At x = 1, f(1) = 2(1) - 1 = 1 and lim x→1- f(x) = 1, lim x→1+ f(x) = 1. Thus, f(x) is continuous at x = 1.
Correct Answer:
A
— Continuous
Learn More →
Q. Determine the continuity of the function f(x) = |x| at x = 0. (2020)
A.
Continuous
B.
Not continuous
C.
Depends on the limit
D.
Only left continuous
Show solution
Solution
The function f(x) = |x| is continuous at x = 0 since both the left-hand limit and right-hand limit equal f(0) = 0.
Correct Answer:
A
— Continuous
Learn More →
Q. Determine the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(4, 0, 0), C(0, 3, 0). (2023)
A.
(1, 1, 0)
B.
(2, 1, 0)
C.
(4/3, 1, 0)
D.
(0, 1, 0)
Show solution
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)
Learn More →
Q. Determine the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(6, 0, 0), and C(0, 8, 0). (2023)
A.
(2, 2, 0)
B.
(2, 3, 0)
C.
(3, 2, 0)
D.
(0, 0, 0)
Show solution
Solution
Centroid = ((0+6+0)/3, (0+0+8)/3, (0+0+0)/3) = (2, 2.67, 0).
Correct Answer:
A
— (2, 2, 0)
Learn More →
Q. Determine the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(0, 4, 0), and C(3, 0, 0). (2021)
A.
(1, 1.33, 0)
B.
(1, 2, 0)
C.
(0, 1.33, 0)
D.
(0, 2, 0)
Show solution
Solution
Centroid = ((0+0+3)/3, (0+4+0)/3, (0+0+0)/3) = (1, 1.33, 0).
Correct Answer:
B
— (1, 2, 0)
Learn More →
Q. Determine the coordinates of the centroid of the triangle with vertices A(1, 2, 3), B(4, 5, 6), and C(7, 8, 9). (2021)
A.
(4, 5, 6)
B.
(3, 4, 5)
C.
(5, 6, 7)
D.
(6, 7, 8)
Show solution
Solution
Centroid G = ((1+4+7)/3, (2+5+8)/3, (3+6+9)/3) = (4, 5, 6).
Correct Answer:
B
— (3, 4, 5)
Learn More →
Q. Determine 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)
Show solution
Solution
Centroid = ((0+6+3)/3, (0+0+6)/3) = (3, 2).
Correct Answer:
B
— (3, 3)
Learn More →
Q. Determine the coordinates of the foot of the perpendicular from the point (1, 2, 3) to the plane x + 2y + 3z = 14. (2023)
A.
(2, 3, 4)
B.
(1, 2, 4)
C.
(2, 1, 3)
D.
(3, 2, 1)
Show solution
Solution
Using the formula for the foot of the perpendicular, we find the coordinates to be (1, 2, 4).
Correct Answer:
B
— (1, 2, 4)
Learn More →
Q. Determine the critical points of f(x) = 3x^4 - 8x^3 + 6. (2021)
A.
(0, 6)
B.
(1, 1)
C.
(2, 0)
D.
(3, -1)
Show solution
Solution
f'(x) = 12x^3 - 24x^2. Setting f'(x) = 0 gives x = 0, 2. Check f(1) = 1.
Correct Answer:
B
— (1, 1)
Learn More →
Q. Determine the critical points of f(x) = e^x - 2x. (2021)
Show solution
Solution
f'(x) = e^x - 2. Setting f'(x) = 0 gives e^x = 2, so x = ln(2).
Correct Answer:
B
— 1
Learn More →
Q. Determine the critical points of f(x) = x^3 - 3x + 2.
A.
-1, 1
B.
0, 2
C.
1, -2
D.
2, -1
Show solution
Solution
Setting f'(x) = 3x^2 - 3 = 0 gives x^2 = 1, so critical points are x = -1 and x = 1.
Correct Answer:
A
— -1, 1
Learn More →
Q. Determine the critical points of f(x) = x^3 - 3x^2 + 4.
A.
(0, 4)
B.
(1, 2)
C.
(2, 1)
D.
(3, 0)
Show solution
Solution
f'(x) = 3x^2 - 6x. Setting f'(x) = 0 gives x = 0 and x = 2. Critical points are (0, 4) and (2, 1).
Correct Answer:
B
— (1, 2)
Learn More →
Q. Determine the critical points of f(x) = x^3 - 6x^2 + 9x.
A.
x = 0, 3
B.
x = 1, 2
C.
x = 2, 3
D.
x = 1, 3
Show solution
Solution
Setting f'(x) = 0 gives critical points at x = 0 and x = 3.
Correct Answer:
A
— x = 0, 3
Learn More →
Q. Determine the critical points of f(x) = x^4 - 4x^3 + 6.
A.
x = 0, 3
B.
x = 1, 2
C.
x = 2, 3
D.
x = 1, 3
Show solution
Solution
Setting f'(x) = 0 gives critical points at x = 1 and x = 2.
Correct Answer:
B
— x = 1, 2
Learn More →
Q. Determine the critical points of f(x) = x^4 - 8x^2 + 16.
A.
x = 0, ±2
B.
x = ±4
C.
x = ±1
D.
x = 2
Show solution
Solution
Setting f'(x) = 0 gives critical points at x = 0, ±2.
Correct Answer:
A
— x = 0, ±2
Learn More →
Showing 4891 to 4920 of 31669 (1056 Pages)
