Q. Find the solution for the inequality: 8x - 3 > 5.
A.
x > 1
B.
x < 1
C.
x > 0.5
D.
x < 0.5
Show solution
Solution
8x - 3 > 5 => 8x > 8 => x > 1.
Correct Answer:
A
— x > 1
Learn More →
Q. Find the solution of the differential equation y' = 2y + 3.
A.
y = Ce^(2x) - 3/2
B.
y = Ce^(-2x) + 3/2
C.
y = 3/2 - Ce^(2x)
D.
y = 3/2 + Ce^(-2x)
Show solution
Solution
This is a linear first-order equation. The general solution is y = 3/2 + Ce^(-2x).
Correct Answer:
D
— y = 3/2 + Ce^(-2x)
Learn More →
Q. Find the solution of the differential equation y'' + 4y = 0.
A.
y = C1 cos(2x) + C2 sin(2x)
B.
y = C1 e^(2x) + C2 e^(-2x)
C.
y = C1 e^(x) + C2 e^(-x)
D.
y = C1 sin(2x) + C2 cos(2x)
Show solution
Solution
This is a second-order linear homogeneous differential equation. The characteristic equation has roots ±2i.
Correct Answer:
A
— y = C1 cos(2x) + C2 sin(2x)
Learn More →
Q. Find the solution of the first-order linear differential equation dy/dx + y = e^x.
A.
y = e^x + Ce^(-x)
B.
y = e^x - Ce^(-x)
C.
y = e^(-x) + Ce^x
D.
y = e^(-x) - Ce^x
Show solution
Solution
Using an integrating factor e^x, we solve to get y = e^x + Ce^(-x).
Correct Answer:
A
— y = e^x + Ce^(-x)
Learn More →
Q. Find the solution set for the inequality -2x + 3 > 1.
A.
x < 1
B.
x > 1
C.
x < 2
D.
x > 2
Show solution
Solution
Subtract 3 from both sides: -2x > -2. Then divide by -2 (reverse the inequality): x < 1.
Correct Answer:
B
— x > 1
Learn More →
Q. Find the solution set for the inequality -2x + 4 < 0.
A.
x > 2
B.
x < 2
C.
x > 4
D.
x < 4
Show solution
Solution
Subtract 4 from both sides: -2x < -4. Then divide by -2 (reverse the inequality): x > 2.
Correct Answer:
A
— x > 2
Learn More →
Q. Find the solution set for 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
Learn More →
Q. Find the solution set for the inequality -3x + 1 ≤ 4.
A.
x ≥ -1
B.
x ≤ -1
C.
x ≥ 1
D.
x ≤ 1
Show solution
Solution
-3x + 1 ≤ 4 => -3x ≤ 3 => x ≥ -1.
Correct Answer:
B
— x ≤ -1
Learn More →
Q. Find the solution set for the inequality -4x + 1 < 3.
A.
x < -0.5
B.
x > -0.5
C.
x < 0.5
D.
x > 0.5
Show solution
Solution
-4x + 1 < 3 => -4x < 2 => x > -0.5.
Correct Answer:
A
— x < -0.5
Learn More →
Q. Find the solution set for the inequality -x + 4 < 2.
A.
x > 2
B.
x < 2
C.
x > 4
D.
x < 4
Show solution
Solution
-x + 4 < 2 => -x < -2 => x > 2.
Correct Answer:
D
— x < 4
Learn More →
Q. Find the solution set for the inequality -x + 5 < 2.
A.
x > 3
B.
x < 3
C.
x ≥ 3
D.
x ≤ 3
Show solution
Solution
-x + 5 < 2 => -x < -3 => x > 3.
Correct Answer:
A
— x > 3
Learn More →
Q. Find the solution set for the inequality -x + 5 ≤ 2.
A.
x ≥ 3
B.
x ≤ 3
C.
x ≥ 5
D.
x ≤ 5
Show solution
Solution
-x + 5 ≤ 2 => -x ≤ -3 => x ≥ 3.
Correct Answer:
B
— x ≤ 3
Learn More →
Q. Find the solution set for the inequality 2(x - 1) ≥ 3.
A.
x ≥ 2.5
B.
x ≤ 2.5
C.
x ≥ 1.5
D.
x ≤ 1.5
Show solution
Solution
2(x - 1) ≥ 3 => x - 1 ≥ 1.5 => x ≥ 2.5.
Correct Answer:
A
— x ≥ 2.5
Learn More →
Q. Find the solution set for the inequality 2(x - 1) ≥ 3x + 4.
A.
x ≤ -6
B.
x ≥ -6
C.
x < -6
D.
x > -6
Show solution
Solution
2(x - 1) ≥ 3x + 4 => 2x - 2 ≥ 3x + 4 => -x ≥ 6 => x ≤ -6.
Correct Answer:
A
— x ≤ -6
Learn More →
Q. Find the solution set for the inequality 2(x - 1) ≥ 4.
A.
x < 3
B.
x > 3
C.
x ≤ 3
D.
x ≥ 3
Show solution
Solution
2(x - 1) ≥ 4 => x - 1 ≥ 2 => x ≥ 3.
Correct Answer:
D
— x ≥ 3
Learn More →
Q. Find the solution set for the inequality 2x + 1 ≤ 3x - 4.
A.
x < 5
B.
x > 5
C.
x ≤ 5
D.
x ≥ 5
Show solution
Solution
2x + 1 ≤ 3x - 4 => 1 + 4 ≤ x => x ≥ 5.
Correct Answer:
C
— x ≤ 5
Learn More →
Q. Find the solution set for the inequality 2x + 3 < 5x - 1.
A.
x < 4/3
B.
x > 4/3
C.
x < 2/3
D.
x > 2/3
Show solution
Solution
2x + 3 < 5x - 1 => 4 < 3x => x > 4/3.
Correct Answer:
B
— x > 4/3
Learn More →
Q. Find 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:
D
— x ≥ 2
Learn More →
Q. Find the solution set for the inequality 2x + 4 < 3x - 1.
A.
x < 5
B.
x > 5
C.
x ≤ 5
D.
x ≥ 5
Show solution
Solution
2x + 4 < 3x - 1 => 5 < x => x > 5.
Correct Answer:
B
— x > 5
Learn More →
Q. Find the solution set for 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:
C
— x ≥ 3
Learn More →
Q. Find the solution set for the inequality 2x + 4 ≥ 8.
A.
x < 2
B.
x > 2
C.
x ≤ 2
D.
x ≥ 2
Show solution
Solution
2x + 4 ≥ 8 => 2x ≥ 4 => x ≥ 2.
Correct Answer:
D
— x ≥ 2
Learn More →
Q. Find the solution set for the inequality 2x + 5 ≤ 3x - 1.
A.
x ≤ 6
B.
x ≥ 6
C.
x < 6
D.
x > 6
Show solution
Solution
2x + 5 ≤ 3x - 1 => 5 + 1 ≤ 3x - 2x => 6 ≤ x => x ≥ 6.
Correct Answer:
C
— x < 6
Learn More →
Q. Find the solution set for the inequality 2x - 4 > 0.
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
Learn More →
Q. Find the solution set for the inequality 2x - 7 < 3.
A.
x < 5
B.
x > 5
C.
x < 4
D.
x > 4
Show solution
Solution
Add 7 to both sides: 2x < 10. Then divide by 2: x < 5.
Correct Answer:
A
— x < 5
Learn More →
Q. Find the solution set for the inequality 3x + 1 ≤ 10.
A.
x ≤ 3
B.
x < 3
C.
x ≥ 3
D.
x > 3
Show solution
Solution
3x + 1 ≤ 10 => 3x ≤ 9 => x ≤ 3.
Correct Answer:
A
— x ≤ 3
Learn More →
Q. Find the solution set for the inequality 3x + 2 ≤ 11.
A.
x ≤ 3
B.
x < 3
C.
x ≥ 3
D.
x > 3
Show solution
Solution
3x + 2 ≤ 11 => 3x ≤ 9 => x ≤ 3.
Correct Answer:
A
— x ≤ 3
Learn More →
Q. Find the solution set for the inequality 3x + 4 ≤ 10.
A.
x ≤ 2
B.
x < 2
C.
x ≥ 2
D.
x > 2
Show solution
Solution
3x + 4 ≤ 10 => 3x ≤ 6 => x ≤ 2.
Correct Answer:
A
— x ≤ 2
Learn More →
Q. Find the solution set for the inequality 3x + 5 ≥ 2x + 8.
A.
x ≥ 3
B.
x ≤ 3
C.
x ≥ 5
D.
x ≤ 5
Show solution
Solution
3x + 5 ≥ 2x + 8 => x ≥ 3.
Correct Answer:
A
— x ≥ 3
Learn More →
Q. Find the solution set for the inequality 3x - 7 ≤ 2.
A.
x ≤ 3
B.
x ≥ 3
C.
x ≤ 1
D.
x ≥ 1
Show solution
Solution
Add 7 to both sides: 3x ≤ 9. Then divide by 3: x ≤ 3.
Correct Answer:
C
— x ≤ 1
Learn More →
Q. Find the solution set for the inequality 6 - 2x ≤ 0.
A.
x < 3
B.
x > 3
C.
x ≤ 3
D.
x ≥ 3
Show solution
Solution
6 - 2x ≤ 0 => -2x ≤ -6 => x ≥ 3.
Correct Answer:
B
— x > 3
Learn More →
Showing 661 to 690 of 2847 (95 Pages)
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!
