Q. Solve the equation 2sin(x) + √3 = 0 for x in the interval [0, 2π].
A.
5π/3
B.
π/3
C.
2π/3
D.
4π/3
Show solution
Solution
Rearranging gives sin(x) = -√3/2, so x = 4π/3 and x = 5π/3.
Correct Answer:
A
— 5π/3
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Q. Solve the equation 2sin(x) - 1 = 0 for x in the interval [0, 2π].
A.
π/6
B.
5π/6
C.
π/2
D.
7π/6
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Solution
The solution is x = π/2.
Correct Answer:
C
— π/2
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Q. Solve the equation 3cos^2(x) - 1 = 0.
A.
x = π/3, 2π/3
B.
x = π/4, 3π/4
C.
x = 0, π
D.
x = π/6, 5π/6
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Solution
Rearranging gives cos^2(x) = 1/3, so x = π/3 and 2π/3.
Correct Answer:
A
— x = π/3, 2π/3
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Q. Solve the equation 3sin(x) - 4 = 0 for x in the interval [0, 2π].
A.
π/6
B.
π/3
C.
2π/3
D.
5π/6
Show solution
Solution
The solution is x = π/3.
Correct Answer:
B
— π/3
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Q. Solve the equation cos(x) + sin(x) = 1 for x in the interval [0, 2π].
A.
π/4
B.
π/2
C.
3π/4
D.
0
Show solution
Solution
The only solution is x = π/2.
Correct Answer:
B
— π/2
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Q. Solve the equation cos(x) = -1/2 for x in the interval [0, 2π].
A.
2π/3, 4π/3
B.
π/3, 5π/3
C.
π/2, 3π/2
D.
0, π
Show solution
Solution
The solutions are x = 2π/3 and x = 4π/3 in the interval [0, 2π].
Correct Answer:
A
— 2π/3, 4π/3
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Q. Solve the equation dy/dx = y^2 - x.
A.
y = sqrt(x + C)
B.
y = x + C
C.
y = 1/(C - x)
D.
y = x - C
Show solution
Solution
This is a separable equation. Separating variables and integrating gives y = 1/(C - x).
Correct Answer:
C
— y = 1/(C - x)
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Q. Solve the equation sin(2x) = 0 for x in the interval [0, 2π].
A.
0, π, 2π
B.
π/2, 3π/2
C.
π/4, 3π/4
D.
π/6, 5π/6
Show solution
Solution
The solutions are x = 0, π, 2π.
Correct Answer:
A
— 0, π, 2π
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Q. Solve the equation sin(2x) = 1 for x in the interval [0, 2π].
A.
π/4
B.
3π/4
C.
π/2
D.
5π/4
Show solution
Solution
The equation sin(2x) = 1 gives 2x = π/2 + 2nπ, hence x = π/4 + nπ/2. In [0, 2π], the solutions are π/4 and 5π/4.
Correct Answer:
C
— π/2
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Q. Solve the equation sin(2x) = √3/2 for x in the interval [0, 2π].
A.
π/12
B.
5π/12
C.
7π/12
D.
11π/12
Show solution
Solution
The solutions are x = π/12, 5π/12, 7π/12, and 11π/12.
Correct Answer:
A
— π/12
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Q. Solve the equation sin(3x) = 0 for x in the interval [0, 2π].
A.
0, π, 2π
B.
0, π/3, 2π/3
C.
0, π/2, π
D.
0, π/4, π/2
Show solution
Solution
The solutions are x = 0, π, 2π, and x = nπ/3 for n = 0, 1, 2, 3, 4, 5.
Correct Answer:
A
— 0, π, 2π
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Q. Solve the equation sin(x) = 0.5 for x in the interval [0, 2π].
A.
π/6
B.
5π/6
C.
7π/6
D.
11π/6
Show solution
Solution
The solutions are x = π/6 and x = 5π/6 in the interval [0, 2π].
Correct Answer:
A
— π/6
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Q. Solve the equation tan(x) = √3 for x in the interval [0, 2π].
A.
π/3
B.
2π/3
C.
4π/3
D.
5π/3
Show solution
Solution
The solutions are x = π/3 and x = 4π/3 in the interval [0, 2π].
Correct Answer:
A
— π/3
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Q. Solve the equation tan^2(x) = 3 for x in the interval [0, 2π].
A.
π/3
B.
2π/3
C.
4π/3
D.
5π/3
Show solution
Solution
The solutions are x = π/3 and x = 4π/3.
Correct Answer:
A
— π/3
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Q. Solve the equation tan^2(x) = 3.
A.
x = π/3
B.
x = 2π/3
C.
x = 4π/3
D.
x = 5π/3
Show solution
Solution
The solutions are x = π/3 and x = 4π/3.
Correct Answer:
A
— x = π/3
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Q. Solve the equation y' = y(1 - y).
A.
y = 1/(C - x)
B.
y = 1/(C + x)
C.
y = C/(1 + x)
D.
y = C/(1 - x)
Show solution
Solution
Separating variables and integrating gives y = 1/(C - x).
Correct Answer:
A
— y = 1/(C - x)
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Q. Solve the first-order linear differential equation dy/dx + y/x = x.
A.
y = x^2 + C/x
B.
y = Cx^2 + x
C.
y = C/x + x^2
D.
y = x^2 + C
Show solution
Solution
Using the integrating factor e^(∫(1/x)dx) = x, we can solve the equation.
Correct Answer:
A
— y = x^2 + C/x
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Q. Solve the inequality -2x + 4 > 0. What is the solution?
A.
x < 2
B.
x > 2
C.
x < -2
D.
x > -2
Show solution
Solution
-2x + 4 > 0 => -2x > -4 => x < 2
Correct Answer:
B
— x > 2
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Q. Solve the inequality -2x + 4 < 0.
A.
x > 2
B.
x < 2
C.
x > 4
D.
x < 4
Show solution
Solution
-2x + 4 < 0 => -2x < -4 => x > 2.
Correct Answer:
A
— x > 2
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Q. Solve the inequality -2x + 5 > 1.
A.
x < 2
B.
x > 2
C.
x < 3
D.
x > 3
Show solution
Solution
-2x + 5 > 1 => -2x > -4 => x < 2.
Correct Answer:
B
— x > 2
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Q. Solve the inequality -3x + 2 ≤ 5. What is the solution?
A.
x ≤ -1
B.
x ≥ -1
C.
x < -1
D.
x > -1
Show solution
Solution
-3x + 2 ≤ 5 => -3x ≤ 3 => x ≥ -1.
Correct Answer:
B
— x ≥ -1
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Q. Solve the inequality -4x + 1 > 9.
A.
x < -2
B.
x > -2
C.
x < 2
D.
x > 2
Show solution
Solution
Subtract 1 from both sides: -4x > 8. Then divide by -4 (reverse the inequality): x < -2.
Correct Answer:
B
— x > -2
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Q. Solve the inequality -4x + 8 > 0.
A.
x < 2
B.
x > 2
C.
x < 4
D.
x > 4
Show solution
Solution
-4x + 8 > 0 => -4x > -8 => x < 2.
Correct Answer:
B
— x > 2
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Q. Solve the inequality -4x + 8 ≤ 0. What is the solution?
A.
x < 2
B.
x > 2
C.
x ≤ 2
D.
x ≥ 2
Show solution
Solution
-4x + 8 ≤ 0 => -4x ≤ -8 => x ≥ 2.
Correct Answer:
C
— x ≤ 2
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Q. Solve the inequality -5x + 3 < 2. What is the solution?
A.
x > 1
B.
x < 1
C.
x ≤ 1
D.
x ≥ 1
Show solution
Solution
-5x + 3 < 2 => -5x < -1 => x > 1.
Correct Answer:
B
— x < 1
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Q. Solve the inequality -x/2 + 4 > 0. What is the solution set?
A.
x < 8
B.
x > 8
C.
x ≤ 8
D.
x ≥ 8
Show solution
Solution
-x/2 + 4 > 0 => -x/2 > -4 => x < 8.
Correct Answer:
B
— x > 8
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Q. Solve the inequality -x/2 + 4 > 0. What is the solution?
A.
x < 8
B.
x > 8
C.
x < -8
D.
x > -8
Show solution
Solution
-x/2 + 4 > 0 => -x/2 > -4 => x < 8.
Correct Answer:
A
— x < 8
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Q. Solve the inequality 2(x - 1) > 3. What is the solution?
A.
x > 5/2
B.
x < 5/2
C.
x > 1/2
D.
x < 1/2
Show solution
Solution
2(x - 1) > 3 => x - 1 > 3/2 => x > 5/2.
Correct Answer:
A
— x > 5/2
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Q. Solve the inequality 2(x - 1) > 3x + 4. What is the solution?
A.
x < -1
B.
x > -1
C.
x < 1
D.
x > 1
Show solution
Solution
2(x - 1) > 3x + 4 => 2x - 2 > 3x + 4 => -x > 6 => x < -6.
Correct Answer:
A
— x < -1
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Q. Solve the inequality 2x + 4 ≤ 10.
A.
x ≤ 3
B.
x < 3
C.
x ≥ 3
D.
x > 3
Show solution
Solution
2x + 4 ≤ 10 => 2x ≤ 6 => x ≤ 3.
Correct Answer:
A
— 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!
