JEE Main MCQ & Objective Questions
The JEE Main exam is a crucial step for students aspiring to enter prestigious engineering colleges in India. It tests not only knowledge but also the ability to apply concepts effectively. Practicing MCQs and objective questions is essential for scoring better, as it helps in familiarizing students with the exam pattern and enhances their problem-solving skills. Engaging with practice questions allows students to identify important questions and strengthen their exam preparation.
What You Will Practise Here
Fundamental concepts of Physics, Chemistry, and Mathematics
Key formulas and their applications in problem-solving
Important definitions and theories relevant to JEE Main
Diagrams and graphical representations for better understanding
Numerical problems and their step-by-step solutions
Previous years' JEE Main questions for real exam experience
Time management strategies while solving MCQs
Exam Relevance
The topics covered in JEE Main are not only significant for the JEE exam but also appear in various CBSE and State Board examinations. Many concepts are shared with the NEET syllabus, making them relevant across multiple competitive exams. Common question patterns include conceptual applications, numerical problems, and theoretical questions that assess a student's understanding of core subjects.
Common Mistakes Students Make
Misinterpreting the question stem, leading to incorrect answers
Neglecting units in numerical problems, which can change the outcome
Overlooking negative marking and not managing time effectively
Relying too heavily on rote memorization instead of understanding concepts
Failing to review and analyze mistakes from practice tests
FAQs
Question: How can I improve my speed in solving JEE Main MCQ questions?Answer: Regular practice with timed quizzes and focusing on shortcuts can significantly enhance your speed.
Question: Are the JEE Main objective questions similar to previous years' papers?Answer: Yes, many questions are based on previous years' patterns, so practicing them can be beneficial.
Question: What is the best way to approach JEE Main practice questions?Answer: Start with understanding the concepts, then attempt practice questions, and finally review your answers to learn from mistakes.
Now is the time to take charge of your preparation! Dive into solving JEE Main MCQs and practice questions to test your understanding and boost your confidence for the exam.
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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Q. What is the equation of the line with slope 3 that passes through the point (1, 2)?
A.
y = 3x + 2
B.
y = 3x - 1
C.
y - 2 = 3(x - 1)
D.
y = 2x + 1
Show solution
Solution
Using point-slope form: y - y1 = m(x - x1) => y - 2 = 3(x - 1).
Correct Answer:
C
— y - 2 = 3(x - 1)
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Q. What is the equation of the line with slope 5 that passes through the point (1, 2)?
A.
y = 5x - 3
B.
y = 5x + 2
C.
y = 5x + 1
D.
y = 5x - 2
Show solution
Solution
Using point-slope form: y - 2 = 5(x - 1) gives y = 5x - 3.
Correct Answer:
C
— y = 5x + 1
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Q. What is the equation of the parabola that opens upwards with vertex at the origin and passes through the point (2, 8)?
A.
y = 2x^2
B.
y = x^2
C.
y = 4x^2
D.
y = 8x^2
Show solution
Solution
The vertex form of a parabola is y = ax^2. Since it passes through (2, 8), we have 8 = a(2^2) => 8 = 4a => a = 2. Thus, the equation is y = 4x^2.
Correct Answer:
C
— y = 4x^2
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Q. What is the equation of the parabola with focus at (0, 2) and directrix y = -2?
A.
x^2 = 8y
B.
x^2 = -8y
C.
y^2 = 8x
D.
y^2 = -8x
Show solution
Solution
The distance from the focus to the directrix is 4, so the equation is y = (1/4)(x - 0)^2 + 0, which simplifies to x^2 = 8y.
Correct Answer:
A
— x^2 = 8y
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Q. What is the equation of the parabola with focus at (0, 3) and directrix y = -3?
A.
x^2 = 12y
B.
y^2 = 12x
C.
y = 3x^2
D.
x = 3y^2
Show solution
Solution
The distance from the focus to the directrix is 6, so p = 3. The equation is y^2 = 4px = 12y.
Correct Answer:
A
— x^2 = 12y
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Q. What is the equation of the tangent line to the curve y = x^2 + 2x at the point where x = 1?
A.
y = 3x - 2
B.
y = 2x + 1
C.
y = 2x + 2
D.
y = x + 3
Show solution
Solution
f'(x) = 2x + 2. At x = 1, f'(1) = 4. The point is (1, 3). The tangent line is y - 3 = 4(x - 1) => y = 4x - 1.
Correct Answer:
A
— y = 3x - 2
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Q. What is the equation of the tangent line to the curve y = x^2 + 2x at the point (1, 3)?
A.
y = 2x + 1
B.
y = 2x + 2
C.
y = 3x
D.
y = x + 2
Show solution
Solution
f'(x) = 2x + 2. At x = 1, f'(1) = 4. The tangent line is y - 3 = 4(x - 1) => y = 4x - 1.
Correct Answer:
A
— y = 2x + 1
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Q. What is the equilibrium constant expression for the reaction N2(g) + 3H2(g) ⇌ 2NH3(g)?
A.
Kc = [NH3]^2 / ([N2][H2]^3)
B.
Kc = [N2][H2]^3 / [NH3]^2
C.
Kc = [NH3]^2 / [N2][H2]
D.
Kc = [N2][H2] / [NH3]^2
Show solution
Solution
The equilibrium constant Kc is given by the ratio of the concentration of products to reactants, raised to the power of their coefficients.
Correct Answer:
A
— Kc = [NH3]^2 / ([N2][H2]^3)
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Q. What is the equilibrium constant expression for the reaction: 2A + B ⇌ C?
A.
[C]/([A]^2[B])
B.
[A]^2[B]/[C]
C.
[C]/[A][B]
D.
[A][B]/[C]
Show solution
Solution
The equilibrium constant K is given by the expression K = [C]/([A]^2[B]) for the reaction 2A + B ⇌ C.
Correct Answer:
A
— [C]/([A]^2[B])
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