Q. What is the solution to 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:
B
— x ≤ 1
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Q. What is the solution to the inequality 6 - 3x ≥ 0?
A.
x < 2
B.
x > 2
C.
x ≤ 2
D.
x ≥ 2
Show solution
Solution
6 - 3x ≥ 0 => -3x ≥ -6 => x ≤ 2.
Correct Answer:
C
— x ≤ 2
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Q. What is the solution to the inequality 6x + 2 < 14?
A.
x < 2
B.
x > 2
C.
x < 3
D.
x > 3
Show solution
Solution
6x + 2 < 14 => 6x < 12 => x < 2.
Correct Answer:
A
— x < 2
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Q. What is the solution to the inequality 6x + 2 ≤ 14?
A.
x ≤ 2
B.
x < 2
C.
x ≥ 2
D.
x > 2
Show solution
Solution
6x + 2 ≤ 14 => 6x ≤ 12 => x ≤ 2.
Correct Answer:
A
— x ≤ 2
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Q. What is the solution to the inequality 6x + 4 < 2x + 20?
A.
x < 4
B.
x > 4
C.
x ≤ 4
D.
x ≥ 4
Show solution
Solution
6x + 4 < 2x + 20 => 4x < 16 => x < 4.
Correct Answer:
A
— x < 4
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Q. What is the solution to the inequality 6x + 4 ≤ 2x + 16?
A.
x ≤ 3
B.
x ≥ 3
C.
x ≤ 4
D.
x ≥ 4
Show solution
Solution
6x + 4 ≤ 2x + 16 => 4x ≤ 12 => x ≤ 3.
Correct Answer:
B
— x ≥ 3
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Q. What is the solution to 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:
A
— x < 2
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Q. What is the solution to 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. What is the solution to the inequality 7x + 2 > 5?
A.
x > 0.5
B.
x < 0.5
C.
x ≥ 0.5
D.
x ≤ 0.5
Show solution
Solution
7x + 2 > 5 => 7x > 3 => x > 0.5.
Correct Answer:
A
— x > 0.5
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Q. What is the solution to the inequality 7x + 2 > 5x + 6?
A.
x < 2
B.
x > 2
C.
x ≤ 2
D.
x ≥ 2
Show solution
Solution
7x + 2 > 5x + 6 => 2x > 4 => x > 2.
Correct Answer:
B
— x > 2
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Q. What is the solution to the inequality 7x + 2 < 5?
A.
x < -1
B.
x > -1
C.
x < 1
D.
x > 1
Show solution
Solution
7x + 2 < 5 => 7x < 3 => x < -1.
Correct Answer:
A
— x < -1
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Q. What is the solution to the inequality 7x + 3 > 24?
A.
x < 3
B.
x > 3
C.
x ≤ 3
D.
x ≥ 3
Show solution
Solution
7x + 3 > 24 => 7x > 21 => x > 3.
Correct Answer:
B
— x > 3
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Q. What is the solution to the inequality 7x + 5 < 2x + 20?
A.
x < 3
B.
x > 3
C.
x < 4
D.
x > 4
Show solution
Solution
7x + 5 < 2x + 20 => 5x < 15 => x < 3.
Correct Answer:
A
— x < 3
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Q. What is the solution to the inequality 7x - 4 < 3x + 8?
A.
x < 3
B.
x > 3
C.
x < 2
D.
x > 2
Show solution
Solution
7x - 4 < 3x + 8 => 4x < 12 => x < 3.
Correct Answer:
B
— x > 3
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Q. What is the solution to the inequality 8 - 2x > 0?
A.
x < 4
B.
x > 4
C.
x < 2
D.
x > 2
Show solution
Solution
8 - 2x > 0 => -2x > -8 => x < 4.
Correct Answer:
B
— x > 4
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Q. What is the solution to the inequality x/2 - 1 ≤ 3?
A.
x ≤ 8
B.
x ≥ 8
C.
x ≤ 6
D.
x ≥ 6
Show solution
Solution
x/2 - 1 ≤ 3 => x/2 ≤ 4 => x ≤ 8.
Correct Answer:
A
— x ≤ 8
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Q. What is the solution to the inequality x/3 - 2 ≤ 1?
A.
x ≤ 9
B.
x ≥ 9
C.
x < 9
D.
x > 9
Show solution
Solution
x/3 - 2 ≤ 1 => x/3 ≤ 3 => x ≤ 9.
Correct Answer:
A
— x ≤ 9
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Q. What is the standard deviation of the data set {10, 12, 23, 23, 16, 23, 21, 16}?
Show solution
Solution
Mean = 19.5, Variance = 25, Standard Deviation = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the standard deviation of the data set {10, 12, 23, 23, 16, 23, 21}?
A.
5.5
B.
4.5
C.
6.5
D.
3.5
Show solution
Solution
Mean = 19.14, Variance = 20.25, Standard Deviation = √20.25 = 4.5.
Correct Answer:
B
— 4.5
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Q. What is the standard deviation of the data set {4, 8, 6, 5, 3}?
A.
1.58
B.
2.58
C.
3.58
D.
4.58
Show solution
Solution
Mean = 5.2. Variance = [(4-5.2)² + (8-5.2)² + (6-5.2)² + (5-5.2)² + (3-5.2)²]/5 = 6.56. Standard Deviation = √6.56 ≈ 2.56.
Correct Answer:
B
— 2.58
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Q. What is the standard deviation of the data set: 1, 2, 3, 4, 5?
Show solution
Solution
Mean = 3. Standard Deviation = sqrt[((1-3)^2 + (2-3)^2 + (3-3)^2 + (4-3)^2 + (5-3)^2)/5] = sqrt[2] = 1.414.
Correct Answer:
A
— 1
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Q. What is the standard form of the equation of a parabola that opens upwards with vertex at the origin?
A.
y^2 = 4ax
B.
x^2 = 4ay
C.
y^2 = -4ax
D.
x^2 = -4ay
Show solution
Solution
The standard form of a parabola that opens upwards is given by x^2 = 4ay.
Correct Answer:
B
— x^2 = 4ay
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Q. What is the sum of the coefficients in the expansion of (2 + 3x)^4?
A.
81
B.
64
C.
100
D.
125
Show solution
Solution
The sum of the coefficients is found by substituting x = 1: (2 + 3*1)^4 = 5^4 = 625.
Correct Answer:
A
— 81
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Q. What is the sum of the coefficients in the expansion of (x + 1)^5?
Show solution
Solution
The sum of the coefficients is found by substituting x = 1, so (1 + 1)^5 = 2^5 = 32.
Correct Answer:
D
— 32
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Q. What is the sum of the coefficients in the expansion of (x + 1)^7?
Show solution
Solution
The sum of the coefficients is found by substituting x = 1, giving (1 + 1)^7 = 2^7 = 128.
Correct Answer:
A
— 128
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Q. What is the sum of the complex numbers 2 + 3i and 4 - 5i?
A.
6 - 2i
B.
6 + 2i
C.
2 - 2i
D.
2 + 2i
Show solution
Solution
The sum is (2 + 4) + (3 - 5)i = 6 - 2i.
Correct Answer:
A
— 6 - 2i
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Q. What is the sum of the first 5 natural numbers?
Show solution
Solution
Sum = 1 + 2 + 3 + 4 + 5 = 15.
Correct Answer:
B
— 15
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Q. What is the sum of the first 5 terms of the series 1, 1/2, 1/4, ...?
Show solution
Solution
S_5 = 1 + 1/2 + 1/4 + 1/8 + 1/16 = 1.5.
Correct Answer:
A
— 1.5
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Q. What is the sum of the first 6 terms of the arithmetic series 10, 15, 20, ...?
A.
90
B.
100
C.
110
D.
120
Show solution
Solution
The sum S_n = n/2 * (2a + (n-1)d) = 6/2 * (2*10 + 5*5) = 3 * (20 + 25) = 135.
Correct Answer:
A
— 90
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Q. What is the sum of the first n terms of the arithmetic series 2, 5, 8, ...?
A.
n/2 * (2 + (n-1) * 3)
B.
n * (2 + 3n)/2
C.
3n^2/2 + n/2
D.
n * (n + 1)
Show solution
Solution
The first term a = 2, common difference d = 3. The sum of the first n terms S_n = n/2 * (2a + (n-1)d) = n/2 * (2 + (n-1) * 3).
Correct Answer:
A
— n/2 * (2 + (n-1) * 3)
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Showing 2581 to 2610 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!
