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. Determine the continuity of the function f(x) = { x^2, x < 1; 2x - 1, x >= 1 } at x = 1.
A.
Continuous
B.
Not continuous
C.
Depends on the limit
D.
Only left continuous
Show solution
Solution
The left limit as x approaches 1 is 1, and the right limit is also 1. Thus, f(1) = 1, making it continuous.
Correct Answer:
A
— Continuous
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Q. Determine the coordinates of the centroid of the triangle with vertices at (0, 0), (6, 0), and (3, 6).
A.
(3, 2)
B.
(3, 3)
C.
(2, 3)
D.
(0, 0)
Show solution
Solution
Centroid = ((0+6+3)/3, (0+0+6)/3) = (3, 2).
Correct Answer:
B
— (3, 3)
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Q. Determine the critical points of f(x) = x^3 - 3x + 2.
A.
-1, 1
B.
0, 2
C.
1, -2
D.
2, -1
Show solution
Solution
Setting f'(x) = 3x^2 - 3 = 0 gives x^2 = 1, so critical points are x = -1 and x = 1.
Correct Answer:
A
— -1, 1
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Q. Determine the critical points of f(x) = x^3 - 3x^2 + 4.
A.
(0, 4)
B.
(1, 2)
C.
(2, 1)
D.
(3, 0)
Show solution
Solution
f'(x) = 3x^2 - 6x. Setting f'(x) = 0 gives x = 0 and x = 2. Critical points are (0, 4) and (2, 1).
Correct Answer:
B
— (1, 2)
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Q. Determine the critical points of f(x) = x^3 - 6x^2 + 9x.
A.
x = 0, 3
B.
x = 1, 2
C.
x = 2, 3
D.
x = 1, 3
Show solution
Solution
Setting f'(x) = 0 gives critical points at x = 0 and x = 3.
Correct Answer:
A
— x = 0, 3
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Q. Determine the critical points of f(x) = x^4 - 4x^3 + 6.
A.
x = 0, 3
B.
x = 1, 2
C.
x = 2, 3
D.
x = 1, 3
Show solution
Solution
Setting f'(x) = 0 gives critical points at x = 1 and x = 2.
Correct Answer:
B
— x = 1, 2
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Q. Determine the critical points of f(x) = x^4 - 8x^2 + 16.
A.
x = 0, ±2
B.
x = ±4
C.
x = ±1
D.
x = 2
Show solution
Solution
Setting f'(x) = 0 gives critical points at x = 0, ±2.
Correct Answer:
A
— x = 0, ±2
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Q. Determine the critical points of f(x) = x^4 - 8x^2.
A.
x = 0, ±2
B.
x = ±4
C.
x = ±1
D.
x = 2
Show solution
Solution
f'(x) = 4x^3 - 16x = 4x(x^2 - 4). Critical points are x = 0, ±2.
Correct Answer:
A
— x = 0, ±2
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Q. Determine the critical points of the function f(x) = x^3 - 6x^2 + 9x.
A.
(0, 0)
B.
(1, 4)
C.
(2, 0)
D.
(3, 0)
Show solution
Solution
f'(x) = 3x^2 - 12x + 9. Setting f'(x) = 0 gives (x - 1)(x - 3) = 0, so critical points are x = 1 and x = 3.
Correct Answer:
D
— (3, 0)
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Q. Determine the derivative of f(x) = 1/x.
A.
-1/x^2
B.
1/x^2
C.
1/x
D.
-1/x
Show solution
Solution
Using the power rule, f'(x) = -1/x^2.
Correct Answer:
A
— -1/x^2
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Q. Determine the derivative of f(x) = ln(x^2 + 1).
A.
2x/(x^2 + 1)
B.
1/(x^2 + 1)
C.
2/(x^2 + 1)
D.
x/(x^2 + 1)
Show solution
Solution
Using the chain rule, f'(x) = (1/(x^2 + 1)) * (2x) = 2x/(x^2 + 1).
Correct Answer:
A
— 2x/(x^2 + 1)
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Q. Determine the derivative of f(x) = x^2 * e^x.
A.
e^x * (x^2 + 2x)
B.
e^x * (2x + 1)
C.
2x * e^x
D.
x^2 * e^x
Show solution
Solution
Using the product rule, f'(x) = d/dx(x^2 * e^x) = e^x * (x^2 + 2x).
Correct Answer:
A
— e^x * (x^2 + 2x)
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Q. Determine 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 = 5² = 25.
Correct Answer:
A
— (x - 2)² + (y + 3)² = 25
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Q. Determine the equation of the line that passes through the points (0, 0) and (3, 9).
A.
y = 3x
B.
y = 2x
C.
y = 3x + 1
D.
y = x + 1
Show solution
Solution
The slope m = (9 - 0) / (3 - 0) = 3. The equation is y = 3x.
Correct Answer:
A
— y = 3x
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Q. Determine 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 + 3
D.
y = x + 3
Show solution
Solution
f'(x) = 2x + 2. At x = 1, f'(1) = 4. The point is (1, 4). The tangent line is y - 4 = 4(x - 1) => y = 4x - 4 + 4 => y = 4x - 2.
Correct Answer:
A
— y = 3x - 2
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Q. Determine the family of curves represented by the equation x^2 - y^2 = c, where c is a constant.
A.
Circles
B.
Ellipses
C.
Hyperbolas
D.
Parabolas
Show solution
Solution
The equation x^2 - y^2 = c represents a family of hyperbolas with varying values of c.
Correct Answer:
C
— Hyperbolas
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Q. Determine the family of curves represented by the equation x^2/a^2 + y^2/b^2 = 1.
A.
Circles
B.
Ellipses with varying axes
C.
Hyperbolas
D.
Parabolas
Show solution
Solution
The equation x^2/a^2 + y^2/b^2 = 1 represents a family of ellipses with varying semi-major and semi-minor axes.
Correct Answer:
B
— Ellipses with varying axes
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Q. Determine the family of curves represented by the equation y = ax^2 + bx + c.
A.
Parabolas
B.
Circles
C.
Ellipses
D.
Straight lines
Show solution
Solution
The equation y = ax^2 + bx + c represents a family of parabolas with varying coefficients a, b, and c.
Correct Answer:
A
— Parabolas
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Q. Determine the family of curves represented by the equation y = ax^3 + bx.
A.
Cubic functions
B.
Quadratic functions
C.
Linear functions
D.
Exponential functions
Show solution
Solution
The equation y = ax^3 + bx represents a family of cubic functions where a and b are constants.
Correct Answer:
A
— Cubic functions
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Q. Determine the family of curves represented by the equation y = ax^3 + bx^2 + cx + d.
A.
Cubic functions
B.
Quadratic functions
C.
Linear functions
D.
Exponential functions
Show solution
Solution
The equation y = ax^3 + bx^2 + cx + d represents a family of cubic functions.
Correct Answer:
A
— Cubic functions
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Q. Determine the family of curves represented by the equation y = e^(kx) for varying k.
A.
Exponential curves
B.
Linear functions
C.
Quadratic functions
D.
Logarithmic functions
Show solution
Solution
The equation y = e^(kx) represents a family of exponential curves with varying growth rates determined by k.
Correct Answer:
A
— Exponential curves
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Q. Determine the family of curves represented by the equation y = k/x, where k is a constant.
A.
Hyperbolas
B.
Circles
C.
Ellipses
D.
Parabolas
Show solution
Solution
The equation y = k/x represents a family of hyperbolas with varying values of 'k'.
Correct Answer:
A
— Hyperbolas
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Q. Determine the family of curves represented by the equation y = kx^2, where k is a constant.
A.
Circles
B.
Ellipses
C.
Parabolas
D.
Hyperbolas
Show solution
Solution
The equation y = kx^2 represents a family of parabolas that open upwards or downwards depending on the sign of k.
Correct Answer:
C
— Parabolas
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Q. Determine the focus of the parabola defined by the equation x^2 = 12y.
A.
(0, 3)
B.
(0, -3)
C.
(3, 0)
D.
(-3, 0)
Show solution
Solution
The equation x^2 = 4py gives 4p = 12, hence p = 3. The focus is at (0, p) = (0, 3).
Correct Answer:
A
— (0, 3)
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Q. Determine the focus of the parabola given by the equation x^2 = 8y.
A.
(0, 2)
B.
(0, 4)
C.
(2, 0)
D.
(4, 0)
Show solution
Solution
The standard form of the parabola is x^2 = 4py. Here, 4p = 8, so p = 2. The focus is at (0, p) = (0, 2).
Correct Answer:
B
— (0, 4)
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Q. Determine the hybridization of the central atom in BF3.
A.
sp
B.
sp2
C.
sp3
D.
dsp3
Show solution
Solution
Boron in BF3 is sp2 hybridized, forming three equivalent sp2 hybrid orbitals.
Correct Answer:
B
— sp2
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Q. Determine the hybridization of the central atom in O3.
A.
sp
B.
sp2
C.
sp3
D.
dsp3
Show solution
Solution
The central atom in ozone (O3) is sp2 hybridized, forming a resonance structure.
Correct Answer:
B
— sp2
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Q. Determine the hybridization of the central atom in PCl5.
A.
sp
B.
sp2
C.
sp3
D.
dsp3
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Solution
Phosphorus in PCl5 is dsp3 hybridized, allowing it to form five bonds.
Correct Answer:
D
— dsp3
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Q. Determine the intervals where the function f(x) = x^3 - 3x is increasing.
A.
(-∞, -1)
B.
(-1, 1)
C.
(1, ∞)
D.
(-∞, 1)
Show solution
Solution
f'(x) = 3x^2 - 3. Setting f'(x) = 0 gives x = ±1. f'(x) > 0 for x > 1, so f(x) is increasing on (1, ∞).
Correct Answer:
C
— (1, ∞)
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Q. Determine the intervals where the function f(x) = x^4 - 4x^3 has increasing behavior.
A.
(-∞, 0) U (2, ∞)
B.
(0, 2)
C.
(0, ∞)
D.
(2, ∞)
Show solution
Solution
f'(x) = 4x^3 - 12x^2 = 4x^2(x - 3). The function is increasing where f'(x) > 0, which is in the intervals (-∞, 0) and (3, ∞).
Correct Answer:
A
— (-∞, 0) U (2, ∞)
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