Q. What is the domain of the function f(x) = 1/(x-3)?
A.
x ≠ 3
B.
x > 3
C.
x < 3
D.
All real numbers
Show solution
Solution
The function is undefined at x = 3, so the domain is x ≠ 3.
Correct Answer:
A
— x ≠ 3
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Q. What is the domain of the function f(x) = sqrt(x - 1)?
A.
x >= 1
B.
x > 1
C.
x <= 1
D.
x < 1
Show solution
Solution
The expression under the square root must be non-negative, so x - 1 >= 0, hence x >= 1.
Correct Answer:
A
— x >= 1
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Q. What is the dot product of vectors (1, 2) and (3, 4)?
Show solution
Solution
Dot product = 1*3 + 2*4 = 3 + 8 = 11
Correct Answer:
A
— 11
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Q. What is the dot product of vectors A = (2, 3, 4) and B = (1, 0, -1)?
Show solution
Solution
A . B = 2*1 + 3*0 + 4*(-1) = 2 + 0 - 4 = -2.
Correct Answer:
B
— 5
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Q. What is the eccentricity of a hyperbola defined by the equation x^2/a^2 - y^2/b^2 = 1?
A.
1
B.
√2
C.
√(1 + b^2/a^2)
D.
√(1 - b^2/a^2)
Show solution
Solution
The eccentricity e of a hyperbola is given by e = √(1 + b^2/a^2).
Correct Answer:
C
— √(1 + b^2/a^2)
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Q. What is the equation of a circle with center at (-1, 2) and radius 4?
A.
(x + 1)² + (y - 2)² = 16
B.
(x - 1)² + (y + 2)² = 16
C.
(x + 1)² + (y + 2)² = 16
D.
(x - 1)² + (y - 2)² = 16
Show solution
Solution
Using the standard form, the equation is (x + 1)² + (y - 2)² = 4² = 16.
Correct Answer:
A
— (x + 1)² + (y - 2)² = 16
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Q. What is the equation of a circle with center at (2, -3) and radius 5?
A.
(x - 2)² + (y + 3)² = 25
B.
(x + 2)² + (y - 3)² = 25
C.
(x - 2)² + (y - 3)² = 25
D.
(x + 2)² + (y + 3)² = 25
Show solution
Solution
The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Correct Answer:
A
— (x - 2)² + (y + 3)² = 25
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Q. What is the equation of a circle with center at (h, k) and radius r?
A.
(x - h)^2 + (y - k)^2 = r^2
B.
(x + h)^2 + (y + k)^2 = r^2
C.
(x - h)^2 - (y - k)^2 = r^2
D.
(x + h)^2 - (y + k)^2 = r^2
Show solution
Solution
The equation of a circle with center at (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2.
Correct Answer:
A
— (x - h)^2 + (y - k)^2 = r^2
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Q. What is the equation of an ellipse with foci at (±c, 0) and vertices at (±a, 0)?
A.
x^2/a^2 + y^2/b^2 = 1
B.
y^2/a^2 + x^2/b^2 = 1
C.
x^2/b^2 + y^2/a^2 = 1
D.
y^2/b^2 + x^2/a^2 = 1
Show solution
Solution
The standard form of the equation of an ellipse with horizontal major axis is x^2/a^2 + y^2/b^2 = 1.
Correct Answer:
A
— x^2/a^2 + y^2/b^2 = 1
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Q. What is the equation of the circle with center (2, -3) and radius 4?
A.
(x-2)² + (y+3)² = 16
B.
(x+2)² + (y-3)² = 16
C.
(x-2)² + (y-3)² = 16
D.
(x+2)² + (y+3)² = 16
Show solution
Solution
Equation of circle: (x-h)² + (y-k)² = r² => (x-2)² + (y+3)² = 4² = 16.
Correct Answer:
A
— (x-2)² + (y+3)² = 16
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Q. What is the equation of the circle with center (2, -3) and radius 5?
A.
(x-2)² + (y+3)² = 25
B.
(x+2)² + (y-3)² = 25
C.
(x-2)² + (y-3)² = 25
D.
(x+2)² + (y+3)² = 25
Show solution
Solution
Equation of circle: (x-h)² + (y-k)² = r² => (x-2)² + (y+3)² = 25.
Correct Answer:
A
— (x-2)² + (y+3)² = 25
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Q. What is the equation of the circle with center (3, -2) and radius 5?
A.
(x-3)² + (y+2)² = 25
B.
(x+3)² + (y-2)² = 25
C.
(x-3)² + (y-2)² = 25
D.
(x+3)² + (y+2)² = 25
Show solution
Solution
Equation of circle: (x-h)² + (y-k)² = r² => (x-3)² + (y+2)² = 5² = 25.
Correct Answer:
A
— (x-3)² + (y+2)² = 25
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Q. What is the equation of the directrix of the parabola x^2 = 8y?
A.
y = -2
B.
y = 2
C.
x = -4
D.
x = 4
Show solution
Solution
The directrix of the parabola x^2 = 8y is y = -2.
Correct Answer:
A
— y = -2
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Q. What is the equation of the ellipse with center at the origin, semi-major axis 5, and semi-minor axis 3?
A.
x^2/25 + y^2/9 = 1
B.
x^2/9 + y^2/25 = 1
C.
x^2/15 + y^2/5 = 1
D.
x^2/5 + y^2/15 = 1
Show solution
Solution
The equation of the ellipse is x^2/25 + y^2/9 = 1.
Correct Answer:
A
— x^2/25 + y^2/9 = 1
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Q. What is the equation of the line parallel to y = 2x + 1 that passes through the point (3, 4)?
A.
y = 2x + 2
B.
y = 2x + 1
C.
y = 2x + 3
D.
y = 2x - 2
Show solution
Solution
Parallel lines have the same slope, so y - 4 = 2(x - 3) => y = 2x - 2.
Correct Answer:
A
— y = 2x + 2
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Q. What is the equation of the line parallel to y = 2x + 3 that passes through the point (1, 1)?
A.
y = 2x - 1
B.
y = 2x + 1
C.
y = 2x + 3
D.
y = 2x - 3
Show solution
Solution
Parallel lines have the same slope: y - 1 = 2(x - 1) => y = 2x - 1.
Correct Answer:
A
— y = 2x - 1
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Q. What is the equation of the line parallel to y = 3x + 2 that passes through the point (1, 1)?
A.
y = 3x - 2
B.
y = 3x + 1
C.
y = 3x + 2
D.
y = 3x - 1
Show solution
Solution
Parallel lines have the same slope, so y - 1 = 3(x - 1) => y = 3x - 1.
Correct Answer:
D
— y = 3x - 1
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Q. What is the equation of the line parallel to y = 3x + 4 that passes through the point (0, -2)?
A.
y = 3x - 2
B.
y = -3x - 2
C.
y = 3x + 2
D.
y = -3x + 4
Show solution
Solution
Parallel lines have the same slope. The slope is 3, so using point-slope form: y + 2 = 3(x - 0) => y = 3x - 2.
Correct Answer:
A
— y = 3x - 2
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Q. What is the equation of the line parallel to y = 3x - 2 and passing through the point (2, 5)?
A.
y = 3x + 1
B.
y = 3x - 1
C.
y = 3x + 2
D.
y = 3x - 2
Show solution
Solution
The slope of the given line is 3. Using point-slope form: y - 5 = 3(x - 2) gives y = 3x + 1.
Correct Answer:
A
— y = 3x + 1
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Q. What is the equation of the line parallel to y = 3x - 2 that passes through the point (2, 5)?
A.
y = 3x + 1
B.
y = 3x - 1
C.
y = 3x + 2
D.
y = 3x - 2
Show solution
Solution
Since parallel lines have the same slope, the equation is y - 5 = 3(x - 2) which simplifies to y = 3x + 1.
Correct Answer:
A
— y = 3x + 1
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Q. What is the equation of the line parallel to y = 4x - 5 and passing through (2, 3)?
A.
y = 4x - 5
B.
y = 4x - 1
C.
y = 4x + 5
D.
y = 4x + 3
Show solution
Solution
Parallel lines have the same slope. Using point-slope form: y - 3 = 4(x - 2) => y = 4x - 5.
Correct Answer:
B
— y = 4x - 1
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Q. What is the equation of the line parallel to y = 4x - 5 that passes through the point (2, 3)?
A.
y = 4x - 5
B.
y = 4x - 1
C.
y = 4x + 5
D.
y = 4x + 3
Show solution
Solution
Parallel lines have the same slope. Using point-slope form: y - 3 = 4(x - 2) => y = 4x - 8 + 3 => y = 4x - 5.
Correct Answer:
B
— y = 4x - 1
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Q. What is the equation of the line parallel to y = 5x - 2 and passing through the point (2, 3)?
A.
y = 5x - 7
B.
y = 5x + 7
C.
y = 5x - 2
D.
y = 5x + 2
Show solution
Solution
Parallel lines have the same slope. Using point-slope form: y - 3 = 5(x - 2) gives y = 5x - 7.
Correct Answer:
A
— y = 5x - 7
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Q. What is the equation of the line passing through the points (1, 2, 3) and (4, 5, 6)?
A.
x = 1 + 3t, y = 2 + 3t, z = 3 + 3t
B.
x = 1 + t, y = 2 + t, z = 3 + t
C.
x = 1 + t, y = 2 + 2t, z = 3 + 3t
D.
x = 1 + 3t, y = 2 + 2t, z = 3 + t
Show solution
Solution
Direction ratios = (3, 3, 3), hence the line equation is x = 1 + 3t, y = 2 + 3t, z = 3 + 3t.
Correct Answer:
A
— x = 1 + 3t, y = 2 + 3t, z = 3 + 3t
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Q. What is the equation of the line that is perpendicular to y = 3x + 1 and passes through the point (2, 3)?
A.
y = -1/3x + 4
B.
y = 3x - 3
C.
y = -3x + 9
D.
y = 1/3x + 2
Show solution
Solution
The slope of the given line is 3, so the perpendicular slope is -1/3. Using point-slope form: y - 3 = -1/3(x - 2) gives y = -1/3x + 4.
Correct Answer:
A
— y = -1/3x + 4
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Q. What is the equation of the line that is perpendicular to y = 3x + 2 and passes through the point (2, 3)?
A.
y = -1/3x + 4
B.
y = 3x - 3
C.
y = -3x + 9
D.
y = 1/3x + 2
Show solution
Solution
The slope of the perpendicular line is -1/3. Using point-slope form: y - 3 = -1/3(x - 2) gives y = -1/3x + 4.
Correct Answer:
A
— y = -1/3x + 4
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Q. What is the equation of the line that is perpendicular to y = 3x + 4 and passes through the origin?
A.
y = -1/3x
B.
y = 3x
C.
y = -3x
D.
y = 1/3x
Show solution
Solution
The slope of the given line is 3. The slope of the perpendicular line is -1/3. Thus, the equation is y = -1/3x.
Correct Answer:
A
— y = -1/3x
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Q. What is the equation of the line that passes through the point (2, 3) and has a slope of -1?
A.
y = -x + 5
B.
y = -x + 3
C.
y = x + 1
D.
y = -x + 2
Show solution
Solution
Using point-slope form: y - 3 = -1(x - 2) => y = -x + 5.
Correct Answer:
A
— y = -x + 5
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Q. What is the equation of the line with slope 2 passing through the point (1, 2)?
A.
y = 2x + 1
B.
y = 2x - 2
C.
y = 2x + 2
D.
y = 2x - 1
Show solution
Solution
Using point-slope form: y - 2 = 2(x - 1) => y = 2x - 2 + 2 => y = 2x - 1.
Correct Answer:
D
— y = 2x - 1
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Q. What is the equation of the line with slope 3 passing through the point (1, 2)?
A.
y = 3x + 2
B.
y = 3x - 1
C.
y = 3x + 1
D.
y = 3x - 2
Show solution
Solution
Using point-slope form: y - 2 = 3(x - 1) => y = 3x - 1.
Correct Answer:
C
— y = 3x + 1
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Showing 2311 to 2340 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!
