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. For the hyperbola x^2/25 - y^2/16 = 1, what is the distance between the foci?
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Solution
The distance between the foci of the hyperbola is 2c, where c = √(a^2 + b^2) = √(25 + 16) = √41, so the distance is 2√41.
Correct Answer:
A
— 10
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Q. For the lines represented by the equation 2x^2 + 3xy + y^2 = 0, find the slopes of the lines.
A.
-3/2, -1
B.
1, -1/3
C.
0, -1
D.
1, 1
Show solution
Solution
The slopes can be found by solving the quadratic equation derived from the given equation.
Correct Answer:
A
— -3/2, -1
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Q. For the lines represented by the equation 2x^2 + 3xy + y^2 = 0, what is the product of the slopes?
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Solution
The product of the slopes of the lines can be found from the equation, which gives -1.
Correct Answer:
A
— -1
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Q. For the lines represented by the equation 2x^2 + 3xy + y^2 = 0, what is the sum of the slopes?
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Solution
The sum of the slopes can be found using the relationship between the coefficients of the quadratic.
Correct Answer:
A
— -3
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Q. For the lines represented by the equation 3x^2 - 2xy + y^2 = 0 to be parallel, the condition is:
A.
3 + 1 = 0
B.
3 - 1 = 0
C.
2 = 0
D.
None of the above
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Solution
The condition for parallel lines is that the determinant of the coefficients must equal zero.
Correct Answer:
A
— 3 + 1 = 0
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Q. For the lines represented by the equation 4x^2 - 12xy + 9y^2 = 0, find the slopes of the lines.
A.
1, 3
B.
2, 4
C.
3, 1
D.
0, 0
Show solution
Solution
Factoring the equation gives the slopes as m1 = 1 and m2 = 3.
Correct Answer:
A
— 1, 3
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Q. For the lines represented by the equation 4x^2 - 4xy + y^2 = 0, the angle between them is:
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
180 degrees
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Solution
The lines are at an angle of 45 degrees as the determinant of the coefficients gives a non-zero value.
Correct Answer:
B
— 45 degrees
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Q. For the lines represented by the equation 5x^2 + 6xy + 5y^2 = 0, what is the sum of the slopes?
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Solution
The sum of the slopes is given by - (coefficient of xy)/(coefficient of x^2) = -6/5.
Correct Answer:
A
— -6/5
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Q. For the lines represented by the equation 6x^2 + 5xy + y^2 = 0, what is the sum of the slopes?
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Solution
The sum of the slopes of the lines is given by -b/a, which is -5/6.
Correct Answer:
A
— -5/6
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Q. For the lines represented by the equation x^2 - 2xy + y^2 = 0, find the slopes of the lines.
A.
1, -1
B.
2, -2
C.
0, 0
D.
1, 1
Show solution
Solution
The slopes can be found by solving the quadratic equation formed by the coefficients of x^2, xy, and y^2.
Correct Answer:
A
— 1, -1
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Q. For the lines represented by the equation x^2 - 2xy + y^2 = 0, the angle between them is:
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
The angle can be calculated using the slopes derived from the equation.
Correct Answer:
B
— 45 degrees
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Q. For the matrix \( B = \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \), what is the determinant \( |B| \)?
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Solution
The determinant is 0 because the rows are linearly dependent.
Correct Answer:
A
— 0
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Q. For the parabola defined by the equation y^2 = 20x, what is the coordinates of the vertex?
A.
(0, 0)
B.
(5, 0)
C.
(0, 5)
D.
(10, 0)
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Solution
The vertex of the parabola y^2 = 4px is at (0, 0).
Correct Answer:
A
— (0, 0)
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Q. For the parabola y = x^2 - 4x + 3, find the coordinates of the vertex.
A.
(2, -1)
B.
(1, 2)
C.
(2, 1)
D.
(1, -1)
Show solution
Solution
To find the vertex, use x = -b/(2a). Here, a = 1, b = -4, so x = 2. Substitute x = 2 into the equation to find y = -1. Thus, the vertex is (2, -1).
Correct Answer:
A
— (2, -1)
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Q. For the parabola y^2 = 16x, what is the coordinates of the vertex?
A.
(0, 0)
B.
(4, 0)
C.
(0, 4)
D.
(0, -4)
Show solution
Solution
The vertex of the parabola y^2 = 4px is at (0, 0).
Correct Answer:
A
— (0, 0)
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Q. For the parabola y^2 = 20x, what is the coordinates of the vertex?
A.
(0, 0)
B.
(5, 0)
C.
(0, 5)
D.
(10, 0)
Show solution
Solution
The vertex of the parabola y^2 = 4px is at (0, 0). Here, p = 5, but the vertex remains at (0, 0).
Correct Answer:
A
— (0, 0)
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Q. For the quadratic equation 2x^2 - 4x + k = 0 to have real roots, what is the condition on k?
A.
k >= 0
B.
k <= 0
C.
k >= 2
D.
k <= 2
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Solution
The discriminant must be non-negative: (-4)^2 - 4*2*k >= 0, which simplifies to k <= 2.
Correct Answer:
C
— k >= 2
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Q. For the quadratic equation ax^2 + bx + c = 0, if a = 1, b = -3, and c = 2, what are the roots?
A.
1 and 2
B.
2 and 1
C.
3 and 0
D.
0 and 3
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Solution
The roots can be found using the quadratic formula: x = (3 ± √(9-8))/2 = 1 and 2.
Correct Answer:
A
— 1 and 2
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Q. For the quadratic equation x^2 + 2x + 1 = 0, what is the nature of the roots?
A.
Real and distinct
B.
Real and equal
C.
Complex
D.
None of the above
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Solution
The discriminant is 0, indicating that the roots are real and equal.
Correct Answer:
B
— Real and equal
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Q. For the quadratic equation x^2 + 2x + 1 = 0, what is the vertex of the parabola?
A.
(-1, 0)
B.
(-1, 1)
C.
(0, 1)
D.
(1, 1)
Show solution
Solution
The vertex can be found using the formula (-b/2a, f(-b/2a)). Here, vertex is (-1, 0).
Correct Answer:
A
— (-1, 0)
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Q. For the quadratic equation x^2 + 2x + k = 0 to have no real roots, k must be:
A.
< 0
B.
≥ 0
C.
≤ 0
D.
> 0
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Solution
The discriminant must be negative: 2^2 - 4*1*k < 0 => 4 < 4k => k > 1.
Correct Answer:
A
— < 0
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Q. For the quadratic equation x^2 + 4x + 4 = 0, what is the nature of the roots?
A.
Real and distinct
B.
Real and equal
C.
Complex
D.
None of the above
Show solution
Solution
The discriminant is 0 (b^2 - 4ac = 16 - 16 = 0), indicating real and equal roots.
Correct Answer:
B
— Real and equal
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Q. For the quadratic equation x^2 + 4x + k = 0 to have no real roots, k must be:
Show solution
Solution
The discriminant must be negative: 4^2 - 4*1*k < 0 => 16 < 4k => k > 4.
Correct Answer:
A
— 0
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Q. For the quadratic equation x^2 + 4x + k = 0 to have real roots, what is the condition on k?
A.
k >= 4
B.
k <= 4
C.
k > 0
D.
k < 0
Show solution
Solution
The discriminant must be non-negative: 4^2 - 4*1*k >= 0, which simplifies to k <= 4.
Correct Answer:
A
— k >= 4
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Q. For the quadratic equation x^2 + 6x + 8 = 0, what are the roots?
A.
-2 and -4
B.
-4 and -2
C.
2 and 4
D.
0 and 8
Show solution
Solution
Factoring gives (x+2)(x+4) = 0, hence the roots are -2 and -4.
Correct Answer:
B
— -4 and -2
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Q. For the quadratic equation x^2 + 6x + 9 = 0, what is the nature of the roots?
A.
Two distinct real roots
B.
One real root
C.
No real roots
D.
Complex roots
Show solution
Solution
The discriminant is 0, indicating one real root (a repeated root).
Correct Answer:
B
— One real root
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Q. For the quadratic equation x^2 + mx + n = 0, if the roots are 2 and 3, what is the value of n?
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Solution
The product of the roots is n = 2 * 3 = 6.
Correct Answer:
B
— 6
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Q. For the quadratic equation x^2 + px + q = 0, if the roots are 1 and -3, what is the value of p?
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Solution
The sum of the roots is 1 + (-3) = -2, hence p = -2.
Correct Answer:
A
— 2
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Q. For the quadratic equation x^2 - 10x + 25 = 0, what is the double root?
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Solution
The equation can be factored as (x-5)^2 = 0, hence the double root is x = 5.
Correct Answer:
A
— 5
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Q. For the quadratic equation x^2 - 6x + k = 0 to have equal roots, what must be the value of k?
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Solution
Setting the discriminant to zero: (-6)^2 - 4*1*k = 0 gives k = 9.
Correct Answer:
B
— 9
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