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. For which of the following molecules is the bond order equal to 0?
A.
He2
B.
H2
C.
Li2
D.
Be2
Show solution
Solution
He2 has a bond order of 0, as it has equal bonding and antibonding electrons.
Correct Answer:
A
— He2
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Q. For which of the following molecules is the molecular orbital diagram similar to that of O2?
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Solution
The molecular orbital diagram of F2 is similar to that of O2, with the same energy level arrangement.
Correct Answer:
B
— F2
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Q. For which of the following pairs of molecules is the bond order the same?
A.
N2 and C2
B.
O2 and F2
C.
B2 and C2
D.
N2 and O2
Show solution
Solution
O2 and F2 both have a bond order of 2.
Correct Answer:
B
— O2 and F2
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Q. For which value of a is the function f(x) = x^2 + ax + 1 differentiable at x = -1?
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Solution
To ensure differentiability at x = -1, we find f'(-1) exists. Setting a = 0 ensures the derivative is defined.
Correct Answer:
B
— 0
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Q. For which value of a is the function f(x) = x^2 + ax + 1 differentiable everywhere?
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Solution
The function is a polynomial and is differentiable for all real numbers, hence any value of a works.
Correct Answer:
B
— 0
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Q. For which value of a is the function f(x) = x^2 - ax + 2 differentiable at x = 1?
Show solution
Solution
Setting the derivative f'(1) = 0 gives a = 1 for differentiability.
Correct Answer:
B
— 1
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Q. For which value of a is the function f(x) = x^2 - ax + 4 differentiable at x = 2?
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Solution
f(x) is a polynomial and is differentiable for all a, hence any value of a works.
Correct Answer:
A
— 0
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Q. For which value of a is the function f(x) = x^3 - 3ax + 2 differentiable at x = 1?
Show solution
Solution
Setting f'(1) = 0 gives a = 1, ensuring differentiability at that point.
Correct Answer:
B
— 1
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Q. For which value of a is the function f(x) = x^3 - 3ax^2 + 3a^2x + 1 differentiable at x = 1?
Show solution
Solution
Setting f'(1) = 0 gives a = 1 for differentiability at x = 1.
Correct Answer:
B
— 1
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Q. For which value of a is the function f(x) = { 2x + a, x < 0; x^2 + 1, x >= 0 continuous at x = 0?
Show solution
Solution
Setting a = 1 gives continuity at x = 0.
Correct Answer:
B
— 0
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Q. For which value of a is the function f(x) = { 3x + a, x < 2; 4x - 1, x >= 2 continuous at x = 2?
Show solution
Solution
Setting 3(2) + a = 4(2) - 1 gives a = 1.
Correct Answer:
A
— -1
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Q. For which value of a is the function f(x) = { ax + 1, x < 0; 2, x = 0; 3x - 1, x > 0 } continuous at x = 0?
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Solution
Setting ax + 1 = 2 at x = 0 gives a = 2.
Correct Answer:
A
— -1
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Q. For which value of a is the function f(x) = { ax + 1, x < 0; 2x + a, x >= 0 } continuous at x = 0?
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Solution
Setting the two pieces equal at x = 0 gives 1 = a, hence a = 1.
Correct Answer:
A
— -1
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Q. For which value of a is the function f(x) = { ax + 2, x < 1; 3, x >= 1 } continuous at x = 1?
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Solution
Setting ax + 2 = 3 at x = 1 gives a = 1.
Correct Answer:
B
— 2
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Q. For which value of a is the function f(x) = { x^2 + a, x < 1; 3, x >= 1 } continuous at x = 1?
Show solution
Solution
To ensure continuity at x = 1, we set limit as x approaches 1 from left (1 + a) equal to f(1) = 3, thus a = 2.
Correct Answer:
B
— 2
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Q. For which value of a is the function f(x) = { x^2 - a, x < 0; 2x + 1, x >= 0 } continuous at x = 0?
Show solution
Solution
Setting the two pieces equal at x = 0 gives -a = 1, so a = -1.
Correct Answer:
A
— -1
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Q. For which value of a is the function f(x) = { x^2 - a, x < 1; 3x - 2, x >= 1 } continuous at x = 1?
Show solution
Solution
Setting the two pieces equal at x = 1 gives 1 - a = 1. Thus, a = 0.
Correct Answer:
C
— 2
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Q. For which value of a is the function f(x) = { x^2, x < 1; ax + 1, x >= 1 } continuous at x = 1?
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Solution
Setting the two pieces equal at x = 1 gives 1 = a(1) + 1, leading to a = 0.
Correct Answer:
C
— 2
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Q. For which value of b is the function f(x) = { 2x + 1, x < 1; b, x = 1; x^2 + 1, x > 1 continuous at x = 1?
Show solution
Solution
Setting the left limit (2(1) + 1 = 3) equal to the right limit (1^2 + 1 = 2), we find b = 3.
Correct Answer:
B
— 2
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Q. For which value of b is the function f(x) = { x^2 - 1, x < 1; b, x = 1; 3x - 2, x > 1 continuous at x = 1?
Show solution
Solution
Setting limit as x approaches 1 gives b = 2 for continuity.
Correct Answer:
C
— 2
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Q. For which value of b is the function f(x) = { x^2 - 4, x < 2; bx + 2, x >= 2 } continuous at x = 2?
Show solution
Solution
Setting the two pieces equal at x = 2 gives us 0 = 2b + 2. Solving for b gives b = -1.
Correct Answer:
B
— 4
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Q. For which value of b is the function f(x) = { x^3 - 3x + b, x < 1; 2x + 1, x >= 1 continuous at x = 1?
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Solution
Setting 1 - 3 + b = 2 gives b = 4 for continuity.
Correct Answer:
A
— 0
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Q. For which value of c is the function f(x) = { 3x + c, x < 1; 2x^2, x >= 1 continuous at x = 1?
Show solution
Solution
Setting 3(1) + c = 2(1)^2 gives c = -1 for continuity.
Correct Answer:
B
— 0
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Q. For which value of c is the function f(x) = { x^2 - 4, x < c; 3x - 5, x >= c } continuous at x = c?
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Solution
Setting the two pieces equal at x = c: c^2 - 4 = 3c - 5. Solving gives c = 3.
Correct Answer:
C
— 3
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Q. For which value of c is the function f(x) = { x^2 - c, x < 1; 2x + 1, x >= 1 continuous at x = 1?
Show solution
Solution
Setting x^2 - c = 2x + 1 at x = 1 gives c = 2.
Correct Answer:
C
— 2
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Q. For which value of c is the function f(x) = { x^2, x < 1; c, x = 1; 2x, x > 1 } continuous at x = 1? (2022)
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Solution
To make f(x) continuous at x = 1, we need c = 1^2 = 1. Thus, c must be 1.
Correct Answer:
B
— 2
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Q. For which value of c is the function f(x) = { x^2, x < c; 2x + 1, x >= c continuous at x = c?
Show solution
Solution
Setting x^2 = 2x + 1 at x = c gives c = 2.
Correct Answer:
C
— 2
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Q. For which value of k does the equation x^2 + kx + 16 = 0 have equal roots? (2019)
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Solution
For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0. Solving gives k = -8.
Correct Answer:
B
— -4
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Q. For which value of k does the equation x^2 + kx + 16 = 0 have no real roots?
Show solution
Solution
The discriminant must be less than zero: k^2 - 4*1*16 < 0 => k^2 < 64 => k < 8 and k > -8.
Correct Answer:
A
— -8
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Q. For which value of k does the equation x^2 + kx + 16 = 0 have real and distinct roots?
Show solution
Solution
The discriminant must be positive: k^2 - 4*1*16 > 0 => k^2 > 64 => k > 8 or k < -8. Thus, k = -4 is valid.
Correct Answer:
B
— -4
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