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. The equation of a line passing through the points (1, 2) and (3, 6) is:
A.
y = 2x
B.
y = 3x - 1
C.
y = x + 1
D.
y = 4x - 2
Show solution
Solution
Slope = (6-2)/(3-1) = 2. Using point-slope form: y - 2 = 2(x - 1) => y = 2x.
Correct Answer:
A
— y = 2x
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Q. The equation of a parabola is given by x^2 = 16y. What is the length of the latus rectum?
Show solution
Solution
The length of the latus rectum for the parabola x^2 = 4py is given by 4p. Here, 4p = 16, so p = 4. Thus, the length of the latus rectum is 4p = 16.
Correct Answer:
B
— 8
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Q. The equation of an ellipse is given by 4x^2 + 9y^2 = 36. What is the eccentricity of the ellipse?
A.
0.5
B.
0.6
C.
0.7
D.
0.8
Show solution
Solution
Rewriting gives x^2/9 + y^2/4 = 1. Here, a^2 = 9, b^2 = 4, c = √(a^2 - b^2) = √(9 - 4) = √5. Eccentricity e = c/a = √5/3 ≈ 0.6.
Correct Answer:
B
— 0.6
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Q. The equation of an ellipse with foci at (0, ±c) and major axis along the y-axis is given by?
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 equation of an ellipse with foci at (0, ±c) and major axis along the y-axis is y^2/a^2 + x^2/b^2 = 1.
Correct Answer:
B
— y^2/a^2 + x^2/b^2 = 1
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Q. The equation of motion for a simple harmonic oscillator is given by x(t) = A cos(ωt + φ). What does A represent?
A.
Angular frequency
B.
Phase constant
C.
Amplitude
D.
Displacement
Show solution
Solution
A represents the amplitude of the oscillation, which is the maximum displacement from the mean position.
Correct Answer:
C
— Amplitude
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Q. The equation of motion for a simple harmonic oscillator is given by x(t) = A cos(ωt + φ). What does φ represent?
A.
Amplitude
B.
Phase constant
C.
Angular frequency
D.
Time period
Show solution
Solution
In the equation of motion for simple harmonic motion, φ is the phase constant, which determines the initial position of the oscillator.
Correct Answer:
B
— Phase constant
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Q. The equation of the directrix of the parabola y^2 = 8x is?
A.
x = -2
B.
x = 2
C.
y = -4
D.
y = 4
Show solution
Solution
The directrix of the parabola y^2 = 8x is given by x = -2.
Correct Answer:
A
— x = -2
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Q. The equation of the line passing through (1, 2) and (3, 6) is:
A.
y = 2x
B.
y = 3x - 1
C.
y = x + 1
D.
y = 4x - 2
Show solution
Solution
Slope = (6-2)/(3-1) = 2. Using point-slope form: y - 2 = 2(x - 1) => y = 2x.
Correct Answer:
A
— y = 2x
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Q. The equation of the line passing through the points (1, 2) and (3, 6) is:
A.
y = 2x
B.
y = 3x - 1
C.
y = 4x - 2
D.
y = x + 1
Show solution
Solution
Slope = (6-2)/(3-1) = 2. Using point-slope form: y - 2 = 2(x - 1) => y = 2x.
Correct Answer:
A
— y = 2x
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Q. The equation of the pair of lines through the origin is given by y = mx. If m1 and m2 are the slopes, what is the condition for them to be perpendicular?
A.
m1 + m2 = 0
B.
m1 * m2 = 1
C.
m1 - m2 = 0
D.
m1 * m2 = -1
Show solution
Solution
For two lines to be perpendicular, the product of their slopes must equal -1.
Correct Answer:
D
— m1 * m2 = -1
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Q. The equation of the pair of lines through the origin with slopes m1 and m2 is given by:
A.
y = mx
B.
y^2 = mx
C.
x^2 + y^2 = 0
D.
x^2 - 2mxy + y^2 = 0
Show solution
Solution
The correct form of the equation representing the lines through the origin is x^2 - 2mxy + y^2 = 0.
Correct Answer:
D
— x^2 - 2mxy + y^2 = 0
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Q. The equation of the pair of lines through the origin with slopes m1 and m2 is:
A.
y = m1x + m2x
B.
y = (m1 + m2)x
C.
y = m1x - m2x
D.
y = m1x * m2x
Show solution
Solution
The equation of the lines can be expressed as y = (m1 + m2)x, representing the sum of the slopes.
Correct Answer:
B
— y = (m1 + m2)x
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Q. The equation of the tangent line to the curve y = x^2 at the point (2, 4) is:
A.
y = 2x
B.
y = 4x - 4
C.
y = 4x - 8
D.
y = x + 2
Show solution
Solution
The slope of the tangent at x = 2 is f'(x) = 2x, so f'(2) = 4. The equation of the tangent line is y - 4 = 4(x - 2), which simplifies to y = 4x - 8.
Correct Answer:
C
— y = 4x - 8
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Q. The equation of the tangent to the curve y = x^2 at the point (2, 4) is:
A.
y = 2x - 4
B.
y = 2x
C.
y = x + 2
D.
y = x^2 - 2
Show solution
Solution
The derivative f'(x) = 2x. At x = 2, f'(2) = 4. The equation of the tangent line is y - 4 = 4(x - 2), which simplifies to y = 2x - 4.
Correct Answer:
A
— y = 2x - 4
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Q. The equation x^2 + 2x + 1 = 0 can be factored as:
A.
(x + 1)(x + 1)
B.
(x - 1)(x - 1)
C.
(x + 2)(x + 1)
D.
(x - 2)(x - 1)
Show solution
Solution
This is a perfect square: (x + 1)^2 = 0.
Correct Answer:
A
— (x + 1)(x + 1)
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Q. The equation x^2 + 4x + 4 = 0 has:
A.
Two distinct roots
B.
One repeated root
C.
No real roots
D.
None of these
Show solution
Solution
The discriminant is 0, indicating one repeated root.
Correct Answer:
B
— One repeated root
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Q. The equation x^2 - 2x + 1 = 0 has:
A.
Two distinct roots
B.
One repeated root
C.
No real roots
D.
Infinitely many roots
Show solution
Solution
The discriminant is 0, indicating one repeated root.
Correct Answer:
B
— One repeated root
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Q. The equation x^2 - 6x + k = 0 has roots that are both positive. What is the range of k?
A.
k < 0
B.
k > 0
C.
k > 9
D.
k < 9
Show solution
Solution
For both roots to be positive, k must be greater than the square of half the coefficient of x: k > (6/2)^2 = 9.
Correct Answer:
C
— k > 9
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Q. The expression 4^(x+1) can be rewritten as?
A.
2^(2x+2)
B.
2^(x+1)
C.
2^(x+2)
D.
4^x
Show solution
Solution
4^(x+1) = (2^2)^(x+1) = 2^(2(x+1)) = 2^(2x+2).
Correct Answer:
A
— 2^(2x+2)
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Q. The family of curves defined by the equation x^2 + y^2 = r^2 represents:
A.
Ellipses
B.
Hyperbolas
C.
Circles
D.
Parabolas
Show solution
Solution
The equation x^2 + y^2 = r^2 represents a circle with radius r.
Correct Answer:
C
— Circles
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Q. The family of curves defined by the equation y = a(x - h)^2 + k represents which type of function?
A.
Linear
B.
Quadratic
C.
Cubic
D.
Rational
Show solution
Solution
The equation y = a(x - h)^2 + k represents a quadratic function in vertex form.
Correct Answer:
B
— Quadratic
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Q. The family of curves defined by the equation y = a(x - h)^2 + k represents:
A.
Parabolas
B.
Circles
C.
Ellipses
D.
Hyperbolas
Show solution
Solution
The equation y = a(x - h)^2 + k represents a family of parabolas with vertex (h, k).
Correct Answer:
A
— Parabolas
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Q. The family of curves defined by the equation y = ax^2 + bx + c is known as:
A.
Linear functions
B.
Quadratic functions
C.
Polynomial functions
D.
Rational functions
Show solution
Solution
The equation y = ax^2 + bx + c represents a quadratic function.
Correct Answer:
B
— Quadratic functions
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Q. The family of curves defined by the equation y = e^(kx) is classified as:
A.
Linear
B.
Exponential
C.
Logarithmic
D.
Polynomial
Show solution
Solution
The equation y = e^(kx) represents a family of exponential curves.
Correct Answer:
B
— Exponential
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Q. The family of curves defined by the equation y = k/x represents which type of function?
A.
Linear
B.
Quadratic
C.
Rational
D.
Exponential
Show solution
Solution
The equation y = k/x represents a rational function.
Correct Answer:
C
— Rational
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Q. The family of curves defined by the equation y = k/x represents:
A.
Linear functions
B.
Hyperbolas
C.
Parabolas
D.
Circles
Show solution
Solution
The equation y = k/x represents a family of hyperbolas.
Correct Answer:
B
— Hyperbolas
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Q. The family of curves defined by y = kx^3 represents:
A.
Linear curves
B.
Cubic curves
C.
Quadratic curves
D.
Exponential curves
Show solution
Solution
The equation y = kx^3 represents a family of cubic curves.
Correct Answer:
B
— Cubic curves
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Q. The family of curves given by the equation y = a sin(bx + c) is known as:
A.
Linear functions
B.
Trigonometric functions
C.
Exponential functions
D.
Polynomial functions
Show solution
Solution
The equation y = a sin(bx + c) represents a family of trigonometric functions.
Correct Answer:
B
— Trigonometric functions
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Q. The family of curves given by the equation y = kx + b is characterized by:
A.
Different slopes
B.
Different intercepts
C.
Both a and b
D.
None of the above
Show solution
Solution
The equation y = kx + b represents a family of straight lines with different slopes (k) and intercepts (b).
Correct Answer:
C
— Both a and b
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Q. The family of curves given by y = a sin(bx) is characterized by:
A.
Linear behavior
B.
Periodic behavior
C.
Exponential growth
D.
Quadratic growth
Show solution
Solution
The equation y = a sin(bx) represents a family of periodic curves.
Correct Answer:
B
— Periodic behavior
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