Q. Determine the point at which the function f(x) = |x - 3| is not differentiable.
A.
x = 1
B.
x = 2
C.
x = 3
D.
x = 4
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Solution
The function f(x) = |x - 3| is not differentiable at x = 3 because it has a sharp corner.
Correct Answer:
C
— x = 3
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Q. Determine the point at which the function f(x) = |x^2 - 4| is differentiable.
A.
x = -2
B.
x = 0
C.
x = 2
D.
x = -4
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Solution
f(x) is not differentiable at x = -2 and x = 2, but is differentiable everywhere else.
Correct Answer:
A
— x = -2
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Q. Determine the point of inflection for the function f(x) = x^4 - 4x^3 + 6.
A.
(1, 3)
B.
(2, 2)
C.
(3, 1)
D.
(0, 6)
Show solution
Solution
f''(x) = 12x^2 - 24x. Setting f''(x) = 0 gives x = 0 and x = 2. The point of inflection is at (1, 3).
Correct Answer:
A
— (1, 3)
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Q. Determine the point of inflection for the function f(x) = x^4 - 4x^3 + 6x^2.
A.
(1, 3)
B.
(2, 2)
C.
(3, 1)
D.
(0, 0)
Show solution
Solution
Find f''(x) = 12x^2 - 24x + 12. Setting f''(x) = 0 gives x = 1 and x = 2. Testing intervals shows a change in concavity at x = 1.
Correct Answer:
A
— (1, 3)
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Q. Determine the point of intersection of the lines y = 2x + 1 and y = -x + 4.
A.
(1, 3)
B.
(2, 5)
C.
(3, 7)
D.
(4, 9)
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Solution
Setting 2x + 1 = -x + 4 gives 3x = 3, hence x = 1. Substituting back gives y = 3.
Correct Answer:
A
— (1, 3)
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Q. Determine the points where f(x) = x^3 - 3x is not differentiable.
A.
x = 0
B.
x = 1
C.
x = -1
D.
Nowhere
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Solution
The function is a polynomial and is differentiable everywhere, hence nowhere.
Correct Answer:
D
— Nowhere
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Q. Determine the points where the function f(x) = x^4 - 4x^3 is not differentiable.
A.
x = 0
B.
x = 1
C.
x = 2
D.
None
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Solution
The function is a polynomial and is differentiable everywhere. Thus, there are no points where it is not differentiable.
Correct Answer:
D
— None
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Q. Determine the scalar product of the vectors (0, 1, 2) and (3, 4, 5).
Show solution
Solution
Scalar product = 0*3 + 1*4 + 2*5 = 0 + 4 + 10 = 14.
Correct Answer:
B
— 11
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Q. Determine the scalar product of the vectors A = (1, 1, 1) and B = (2, 2, 2).
Show solution
Solution
A · B = 1*2 + 1*2 + 1*2 = 2 + 2 + 2 = 6.
Correct Answer:
C
— 6
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Q. Determine the scalar product of the vectors A = (2, 2, 2) and B = (3, 3, 3).
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Solution
A · B = 2*3 + 2*3 + 2*3 = 6 + 6 + 6 = 18.
Correct Answer:
A
— 12
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Q. Determine the solution for the inequality -2x + 6 > 0.
A.
x < 3
B.
x > 3
C.
x < -3
D.
x > -3
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Solution
-2x + 6 > 0 => -2x > -6 => x < 3.
Correct Answer:
B
— x > 3
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Q. Determine the solution for the inequality -2x + 6 ≥ 0.
A.
x ≤ 3
B.
x ≥ 3
C.
x ≤ -3
D.
x ≥ -3
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Solution
-2x + 6 ≥ 0 => -2x ≥ -6 => x ≤ 3.
Correct Answer:
B
— x ≥ 3
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Q. Determine the solution for the inequality -3x + 1 ≤ 4.
A.
x ≥ -1
B.
x ≤ -1
C.
x ≥ 1
D.
x ≤ 1
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Solution
-3x + 1 ≤ 4 => -3x ≤ 3 => x ≥ -1.
Correct Answer:
B
— x ≤ -1
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Q. Determine the solution for the inequality -3x + 4 ≤ 1.
A.
x ≥ 1
B.
x ≤ 1
C.
x ≥ -1
D.
x ≤ -1
Show solution
Solution
-3x + 4 ≤ 1 => -3x ≤ -3 => x ≥ 1.
Correct Answer:
B
— x ≤ 1
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Q. Determine the solution for the inequality 2x + 3 ≤ 7.
A.
x ≤ 2
B.
x ≥ 2
C.
x ≤ 3
D.
x ≥ 3
Show solution
Solution
2x + 3 ≤ 7 => 2x ≤ 4 => x ≤ 2.
Correct Answer:
A
— x ≤ 2
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Q. Determine the solution for the inequality 6 - x > 2.
A.
x < 4
B.
x > 4
C.
x < 6
D.
x > 6
Show solution
Solution
6 - x > 2 => -x > -4 => x < 4.
Correct Answer:
A
— x < 4
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Q. Determine the solution for the inequality 6 - x ≤ 3.
A.
x ≥ 3
B.
x ≤ 3
C.
x ≥ 6
D.
x ≤ 6
Show solution
Solution
6 - x ≤ 3 => -x ≤ -3 => x ≥ 3.
Correct Answer:
B
— x ≤ 3
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Q. Determine the solution for the inequality 7 - 3x < 1.
A.
x < 2
B.
x > 2
C.
x ≤ 2
D.
x ≥ 2
Show solution
Solution
7 - 3x < 1 => -3x < -6 => x > 2.
Correct Answer:
A
— x < 2
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Q. Determine the solution for the inequality 7x - 2 ≤ 5x + 6.
A.
x ≤ 4
B.
x ≥ 4
C.
x ≤ 3
D.
x ≥ 3
Show solution
Solution
7x - 2 ≤ 5x + 6 => 2x ≤ 8 => x ≤ 4.
Correct Answer:
A
— x ≤ 4
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Q. Determine the solution set for the inequality 2(x - 1) ≥ 3.
A.
x ≤ 2
B.
x ≥ 2
C.
x ≤ 3
D.
x ≥ 3
Show solution
Solution
2(x - 1) ≥ 3 => x - 1 ≥ 1.5 => x ≥ 2.
Correct Answer:
B
— x ≥ 2
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Q. Determine the solution set for the inequality 2x + 3 > 5.
A.
x < 1
B.
x > 1
C.
x < 2
D.
x > 2
Show solution
Solution
2x + 3 > 5 => 2x > 2 => x > 1.
Correct Answer:
B
— x > 1
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Q. Determine the solution set for the inequality 2x + 3 > 7.
A.
x < 2
B.
x > 2
C.
x < 3
D.
x > 3
Show solution
Solution
2x + 3 > 7 => 2x > 4 => x > 2.
Correct Answer:
B
— x > 2
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Q. Determine the solution set for the inequality 2x + 3 ≤ 7.
A.
x ≤ 2
B.
x ≥ 2
C.
x < 2
D.
x > 2
Show solution
Solution
2x + 3 ≤ 7 => 2x ≤ 4 => x ≤ 2.
Correct Answer:
A
— x ≤ 2
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Q. Determine the solution set for the inequality 3x - 4 < 2x + 5.
A.
x < 9
B.
x > 9
C.
x ≤ 9
D.
x ≥ 9
Show solution
Solution
3x - 4 < 2x + 5 => x < 9.
Correct Answer:
A
— x < 9
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Q. Determine the solution set for the inequality 4x - 1 > 3.
A.
x < 1
B.
x > 1
C.
x ≤ 1
D.
x ≥ 1
Show solution
Solution
4x - 1 > 3 => 4x > 4 => x > 1.
Correct Answer:
B
— x > 1
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Q. Determine the solution set for the inequality 4x - 1 > 3x + 2.
A.
x < 3
B.
x > 3
C.
x < 1
D.
x > 1
Show solution
Solution
4x - 1 > 3x + 2 => x > 3.
Correct Answer:
B
— x > 3
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Q. Determine the solution set for the inequality 4x - 1 < 3.
A.
x < 1
B.
x > 1
C.
x ≤ 1
D.
x ≥ 1
Show solution
Solution
4x - 1 < 3 => 4x < 4 => x < 1.
Correct Answer:
A
— x < 1
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Q. Determine the solution set for the inequality 4x - 8 < 0.
A.
x < 2
B.
x > 2
C.
x ≤ 2
D.
x ≥ 2
Show solution
Solution
4x - 8 < 0 => 4x < 8 => x < 2.
Correct Answer:
A
— x < 2
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Q. Determine the solution set for the inequality 5 - 2x ≤ 3.
A.
x < 1
B.
x > 1
C.
x ≤ 1
D.
x ≥ 1
Show solution
Solution
5 - 2x ≤ 3 => -2x ≤ -2 => x ≥ 1.
Correct Answer:
C
— x ≤ 1
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Q. Determine the solution set for the inequality 5 - x ≥ 2.
A.
x ≤ 3
B.
x < 3
C.
x ≥ 3
D.
x > 3
Show solution
Solution
5 - x ≥ 2 => -x ≥ -3 => x ≤ 3.
Correct Answer:
C
— x ≥ 3
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Mathematics Syllabus (JEE Main) MCQ & Objective Questions
The Mathematics Syllabus for JEE Main is crucial for students aiming to excel in competitive exams. Understanding this syllabus not only helps in grasping key concepts but also enhances your ability to tackle objective questions effectively. Practicing MCQs and important questions from this syllabus is essential for solid exam preparation, ensuring you are well-equipped to score better in your exams.
What You Will Practise Here
Sets, Relations, and Functions
Complex Numbers and Quadratic Equations
Permutations and Combinations
Binomial Theorem
Sequences and Series
Limits and Derivatives
Statistics and Probability
Exam Relevance
The Mathematics Syllabus (JEE Main) is not only relevant for JEE but also appears in CBSE and State Board examinations. Students can expect a variety of question patterns, including direct MCQs, numerical problems, and conceptual questions. Mastery of this syllabus will prepare you for similar topics in NEET and other competitive exams, making it vital for your overall academic success.
Common Mistakes Students Make
Misinterpreting the questions, especially in word problems.
Overlooking the importance of units and dimensions in problems.
Confusing formulas related to sequences and series.
Neglecting to practice derivations, leading to errors in calculus.
Failing to apply the correct methods for solving probability questions.
FAQs
Question: What are the key topics in the Mathematics Syllabus for JEE Main? Answer: Key topics include Sets, Complex Numbers, Permutations, Binomial Theorem, and Calculus.
Question: How can I improve my performance in Mathematics MCQs? Answer: Regular practice of MCQs and understanding the underlying concepts are essential for improvement.
Now is the time to take charge of your exam preparation! Dive into solving practice MCQs and test your understanding of the Mathematics Syllabus (JEE Main). Your success is just a question away!
