Q. What is the value of the limit: lim (x -> ∞) (1/x)?
A.
0
B.
1
C.
Infinity
D.
Undefined
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Solution
As x approaches infinity, 1/x approaches 0.
Correct Answer:
A
— 0
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Q. What is the value of the series 1 + 1/2 + 1/3 + ... + 1/n as n approaches infinity?
A.
0
B.
1
C.
∞
D.
undefined
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Solution
The series diverges to infinity as n approaches infinity.
Correct Answer:
C
— ∞
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Q. What is the value of x if 2x + 3 = 11?
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Solution
Subtract 3 from both sides: 2x = 8. Then divide by 2: x = 4.
Correct Answer:
C
— 4
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Q. What is the value of x if 3x - 5 = 16?
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Solution
Solving for x: 3x = 21 => x = 7.
Correct Answer:
A
— 7
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Q. What is the value of x in the equation 2x^2 - 8x + 6 = 0?
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Solution
Using the quadratic formula, x = [8 ± sqrt(64 - 48)] / 4 = [8 ± 4] / 4, giving x = 3 or x = 1.
Correct Answer:
C
— 3
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Q. What is the value of x in the equation 3x - 5 = 7?
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Solution
Solving for x: 3x = 12, thus x = 4.
Correct Answer:
A
— 4
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Q. What is the value of x in the equation 5(x - 2) = 3x + 4?
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Solution
Expanding gives 5x - 10 = 3x + 4. Rearranging gives 2x = 14, thus x = 7.
Correct Answer:
A
— -1
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Q. What is the value of x in the equation 5x - 3 = 2x + 12?
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Solution
Rearranging gives 5x - 2x = 12 + 3 => 3x = 15 => x = 5.
Correct Answer:
B
— 4
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Q. What is the value of x in the equation 5x - 3 = 2x + 6?
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Solution
Rearranging gives 5x - 2x = 6 + 3 => 3x = 9 => x = 3.
Correct Answer:
B
— 2
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Q. What is the value of z if z^2 = -1?
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Solution
The solutions to z^2 = -1 are z = i and z = -i.
Correct Answer:
A
— i
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Q. What is the value of \( \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{vmatrix} \)?
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Solution
The determinant is 0 because the first column is repeated.
Correct Answer:
A
— 0
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Q. What is the value of \( \tan(\tan^{-1}(3)) \)?
A.
0
B.
1
C.
3
D.
undefined
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Solution
By definition, \( \tan(\tan^{-1}(x)) = x \). Therefore, \( \tan(\tan^{-1}(3)) = 3 \).
Correct Answer:
C
— 3
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Q. What is the value of |z| if z = -3 + 4i?
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Solution
|z| = √((-3)^2 + (4)^2) = √(9 + 16) = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the value of |z| if z = 4 - 3i?
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Solution
|z| = √(4^2 + (-3)^2) = √(16 + 9) = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the value of |z| if z = 4e^(iπ/3)?
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Solution
The modulus |z| = 4, as it is the coefficient in the polar form.
Correct Answer:
A
— 4
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Q. What is the value of |z|^2 if z = 4 - 3i?
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Solution
|z|^2 = 4^2 + (-3)^2 = 16 + 9 = 25.
Correct Answer:
A
— 25
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Q. What is the variance of the data set {4, 8, 6, 5, 3}?
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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 = 2.56.
Correct Answer:
A
— 2.5
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Q. What is the variance of the data set: 1, 2, 3, 4, 5?
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Solution
Mean = 3. Variance = [(1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²] / 5 = 2.
Correct Answer:
B
— 1.5
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Q. What is the variance of the data set: 2, 4, 4, 4, 5, 5, 7, 9?
A.
2.5
B.
3.5
C.
4.5
D.
5.5
Show solution
Solution
Mean = 5.0; Variance = [(2-5)^2 + (4-5)^2 + (4-5)^2 + (4-5)^2 + (5-5)^2 + (5-5)^2 + (7-5)^2 + (9-5)^2] / 8 = 2.5.
Correct Answer:
A
— 2.5
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Q. What is the variance of the following data set: {5, 7, 8, 9, 10}?
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Solution
Mean = 7.8, Variance = [(5-7.8)² + (7-7.8)² + (8-7.8)² + (9-7.8)² + (10-7.8)²] / 5 = 3.
Correct Answer:
B
— 3
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Q. What is the vertex of the parabola defined by the equation y = -2(x - 1)^2 + 4?
A.
(1, 4)
B.
(1, -4)
C.
(4, 1)
D.
(-1, 4)
Show solution
Solution
The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).
Correct Answer:
A
— (1, 4)
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Q. What is the vertex of the parabola given by the equation y = -2(x - 1)^2 + 4?
A.
(1, 4)
B.
(1, -4)
C.
(4, 1)
D.
(-1, 4)
Show solution
Solution
The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).
Correct Answer:
A
— (1, 4)
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Q. What is the vertex of the parabola represented by the equation y = -2(x - 1)^2 + 4?
A.
(1, 4)
B.
(1, -4)
C.
(-1, 4)
D.
(-1, -4)
Show solution
Solution
The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).
Correct Answer:
A
— (1, 4)
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Q. What is the vertex of the parabola represented by the equation y = 2x^2 - 8x + 5?
A.
(2, -3)
B.
(2, -7)
C.
(4, -3)
D.
(4, -7)
Show solution
Solution
The vertex can be found using x = -b/(2a) = 4. Substituting x = 4 into the equation gives y = -3.
Correct Answer:
A
— (2, -3)
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Q. What is the weighted mean of the scores 70, 80, 90 with weights 1, 2, 3 respectively?
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Solution
Weighted mean = (70*1 + 80*2 + 90*3) / (1 + 2 + 3) = 85.
Correct Answer:
B
— 85
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Q. What is the weighted mean of the scores 70, 80, and 90 with weights 1, 2, and 3 respectively?
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Solution
Weighted mean = (70*1 + 80*2 + 90*3) / (1 + 2 + 3) = 85.
Correct Answer:
B
— 85
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Q. What is the weighted mean of the scores 80, 90, and 70 with weights 1, 2, and 1 respectively?
Show solution
Solution
Weighted mean = (80*1 + 90*2 + 70*1) / (1 + 2 + 1) = 85.
Correct Answer:
B
— 85
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Q. What is the x-intercept of the line 3x + 4y - 12 = 0?
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Solution
To find the x-intercept, set y = 0. Thus, 3x - 12 = 0 gives x = 4.
Correct Answer:
B
— 3
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Q. What is the y-intercept of the line 5x + 2y - 10 = 0?
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Solution
Setting x = 0 in the equation gives 2y - 10 = 0, thus y = 5.
Correct Answer:
C
— 2
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Q. What is the y-intercept of the line represented by the equation 5x + 2y = 10?
Show solution
Solution
Set x = 0: 2y = 10 => y = 5. The y-intercept is (0, 5).
Correct Answer:
B
— 2
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Showing 2731 to 2760 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!
