Q. Solve the inequality 6 - 2x ≤ 4.
A.
x ≥ 1
B.
x < 1
C.
x > 1
D.
x ≤ 1
Show solution
Solution
6 - 2x ≤ 4 => -2x ≤ -2 => x ≥ 1.
Correct Answer:
D
— x ≤ 1
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Q. Solve the inequality 6 - 3x ≤ 0.
A.
x ≥ 2
B.
x < 2
C.
x > 2
D.
x ≤ 2
Show solution
Solution
Subtract 6 from both sides: -3x ≤ -6. Then divide by -3 (reverse the inequality): x ≥ 2.
Correct Answer:
A
— x ≥ 2
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Q. Solve the inequality 6 - 3x ≥ 0. What is the solution?
A.
x ≤ 2
B.
x ≥ 2
C.
x < 2
D.
x > 2
Show solution
Solution
6 - 3x ≥ 0 => -3x ≥ -6 => x ≤ 2.
Correct Answer:
B
— x ≥ 2
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Q. Solve the inequality 6x + 2 < 14.
A.
x < 2
B.
x < 3
C.
x > 2
D.
x > 3
Show solution
Solution
6x + 2 < 14 => 6x < 12 => x < 2.
Correct Answer:
B
— x < 3
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Q. Solve the inequality 7 - 3x > 1.
A.
x < 2
B.
x > 2
C.
x < 3
D.
x > 3
Show solution
Solution
7 - 3x > 1 => -3x > -6 => x < 2.
Correct Answer:
B
— x > 2
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Q. Solve the inequality 7 - 3x > 1. What is the solution?
A.
x < 2
B.
x > 2
C.
x ≤ 2
D.
x ≥ 2
Show solution
Solution
7 - 3x > 1 => -3x > -6 => x > 2.
Correct Answer:
B
— x > 2
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Q. Solve the inequality 7 - 3x < 1. What is the solution?
A.
x < 2
B.
x > 2
C.
x < 3
D.
x > 3
Show solution
Solution
7 - 3x < 1 => -3x < -6 => x > 2.
Correct Answer:
B
— x > 2
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Q. Solve the inequality 7 - x < 2.
A.
x > 5
B.
x < 5
C.
x > 7
D.
x < 7
Show solution
Solution
7 - x < 2 => -x < -5 => x > 5.
Correct Answer:
A
— x > 5
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Q. Solve the inequality 7x + 2 < 3x + 10.
A.
x < 2
B.
x > 2
C.
x ≤ 2
D.
x ≥ 2
Show solution
Solution
7x + 2 < 3x + 10 => 4x < 8 => x < 2.
Correct Answer:
B
— x > 2
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Q. Solve the inequality 7x - 4 < 2x + 11. What is the solution?
A.
x < 3
B.
x > 3
C.
x ≤ 3
D.
x ≥ 3
Show solution
Solution
7x - 4 < 2x + 11 => 5x < 15 => x < 3.
Correct Answer:
B
— x > 3
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Q. Solve the inequality 7x - 5 < 2x + 10. What is the solution?
A.
x < 1
B.
x > 1
C.
x < 2
D.
x > 2
Show solution
Solution
7x - 5 < 2x + 10 => 5x < 15 => x < 3.
Correct Answer:
B
— x > 1
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Q. Solve the inequality 8 - x > 3.
A.
x < 5
B.
x > 5
C.
x < 3
D.
x > 3
Show solution
Solution
8 - x > 3 => -x > -5 => x < 5.
Correct Answer:
A
— x < 5
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Q. Solve the inequality x/3 + 2 > 1. What is the solution?
A.
x > -3
B.
x < -3
C.
x > 3
D.
x < 3
Show solution
Solution
x/3 + 2 > 1 => x/3 > -1 => x > -3.
Correct Answer:
C
— x > 3
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Q. Solve the inequality x/3 - 2 > 1. What is the solution set?
A.
x < 9
B.
x > 9
C.
x < 3
D.
x > 3
Show solution
Solution
x/3 - 2 > 1 => x/3 > 3 => x > 9.
Correct Answer:
B
— x > 9
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Q. Solve the inequality x/3 - 2 ≤ 1. What is the solution?
A.
x ≤ 9
B.
x ≥ 9
C.
x ≤ 3
D.
x ≥ 3
Show solution
Solution
x/3 - 2 ≤ 1 => x/3 ≤ 3 => x ≤ 9.
Correct Answer:
A
— x ≤ 9
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Q. Solve the inequality x/4 - 1 < 0.
A.
x < 4
B.
x > 4
C.
x ≤ 4
D.
x ≥ 4
Show solution
Solution
x/4 - 1 < 0 => x/4 < 1 => x < 4.
Correct Answer:
A
— x < 4
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Q. Solve the inequality: 4x + 1 ≥ 3.
A.
x ≥ 0.5
B.
x ≤ 0.5
C.
x ≥ 1
D.
x ≤ 1
Show solution
Solution
4x + 1 ≥ 3 => 4x ≥ 2 => x ≥ 0.5.
Correct Answer:
A
— x ≥ 0.5
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Q. Solve 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:
B
— x ≤ 4
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Q. The angle between the lines represented by the equation 2x^2 + 3xy + y^2 = 0 is:
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
60 degrees
Show solution
Solution
Using the angle formula, we find the angle between the lines is 60 degrees.
Correct Answer:
D
— 60 degrees
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Q. The angle between the lines represented by the equation 3x^2 - 4xy + 2y^2 = 0 is:
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
90 degrees
Show solution
Solution
Using the formula tan(θ) = |(m1 - m2) / (1 + m1*m2)|, we find that the angle is 60 degrees.
Correct Answer:
C
— 60 degrees
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Q. The area of a rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5, 4) is:
Show solution
Solution
Length = 5 - 1 = 4, Width = 4 - 1 = 3. Area = Length * Width = 4 * 3 = 12.
Correct Answer:
B
— 16
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Q. The area of triangle ABC is 24 cm², and the base BC = 8 cm. What is the height from A to BC?
A.
6 cm
B.
8 cm
C.
4 cm
D.
3 cm
Show solution
Solution
Area = 1/2 * base * height => 24 = 1/2 * 8 * height => height = 6 cm.
Correct Answer:
A
— 6 cm
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Q. The area of triangle ABC is 30 square units, and the base BC is 10 units. What is the height from A to BC?
A.
3 units
B.
6 units
C.
5 units
D.
4 units
Show solution
Solution
Area = 1/2 * base * height => 30 = 1/2 * 10 * height => height = 6 units.
Correct Answer:
B
— 6 units
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Q. The argument of the complex number z = -1 - i is?
A.
-3π/4
B.
3π/4
C.
π/4
D.
-π/4
Show solution
Solution
The argument of z = -1 - i is θ = tan^(-1)(-1/-1) = -3π/4.
Correct Answer:
A
— -3π/4
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Q. The average of five numbers is 18. If one number is excluded, the average becomes 16. What is the excluded number?
Show solution
Solution
Total sum = 5 * 18 = 90. New sum = 4 * 16 = 64. Excluded number = 90 - 64 = 26.
Correct Answer:
C
— 24
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Q. The average of five numbers is 18. If one number is removed, the average becomes 16. What was the removed number?
Show solution
Solution
Total of five numbers = 5 * 18 = 90. Total of four numbers = 4 * 16 = 64. Removed number = 90 - 64 = 26.
Correct Answer:
C
— 24
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Q. The condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be parallel is:
A.
h^2 = ab
B.
h^2 > ab
C.
h^2 < ab
D.
a + b = 0
Show solution
Solution
The lines are parallel if h^2 = ab.
Correct Answer:
A
— h^2 = ab
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Q. The condition for the lines represented by the equation x^2 + 2xy + y^2 = 0 to be coincident is:
A.
Discriminant > 0
B.
Discriminant = 0
C.
Discriminant < 0
D.
None of the above
Show solution
Solution
For the lines to be coincident, the discriminant must be equal to zero.
Correct Answer:
B
— Discriminant = 0
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Q. The condition for the lines represented by the equation x^2 + y^2 + 2xy = 0 to be coincident is:
A.
Discriminant = 0
B.
Discriminant > 0
C.
Discriminant < 0
D.
None of the above
Show solution
Solution
For the lines to be coincident, the discriminant of the quadratic must be zero.
Correct Answer:
A
— Discriminant = 0
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Q. The condition for the lines represented by the equation x^2 + y^2 - 4x - 6y + 9 = 0 to be coincident is:
A.
Discriminant = 0
B.
Discriminant > 0
C.
Discriminant < 0
D.
None of the above
Show solution
Solution
For the lines to be coincident, the discriminant of the quadratic must equal zero.
Correct Answer:
A
— Discriminant = 0
Learn More →
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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!
