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. If the roots of the equation x^2 + 3x + k = 0 are real and distinct, what is the range of k?
A.
k < 9
B.
k > 9
C.
k < 0
D.
k > 0
Show solution
Solution
For real and distinct roots, the discriminant must be positive: 3^2 - 4*1*k > 0 => 9 - 4k > 0 => k < 9.
Correct Answer:
A
— k < 9
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Q. If the roots of the equation x^2 + 4x + k = 0 are real and distinct, what is the condition on k?
A.
k < 16
B.
k > 16
C.
k = 16
D.
k <= 16
Show solution
Solution
The discriminant must be greater than zero: 4^2 - 4*1*k > 0 => 16 - 4k > 0 => k < 4.
Correct Answer:
A
— k < 16
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Q. If the roots of the equation x^2 + 4x + k = 0 are real and equal, what is the minimum value of k?
Show solution
Solution
For real and equal roots, the discriminant must be zero: 16 - 4k = 0, thus k = 4.
Correct Answer:
B
— -4
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Q. If the roots of the equation x^2 + 5x + 6 = 0 are a and b, what is the value of a + b?
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Solution
Using Vieta's formulas, the sum of the roots is -b/a = -5/1 = -5.
Correct Answer:
A
— 5
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Q. If the roots of the equation x^2 + 5x + k = 0 are -2 and -3, find k.
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Solution
Using Vieta's formulas, k = (-2)(-3) = 6.
Correct Answer:
B
— 6
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Q. If the roots of the equation x^2 + 6x + k = 0 are -2 and -4, what is the value of k?
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Solution
Using the sum and product of roots: -2 + -4 = -6 and -2*-4 = k => k = 8.
Correct Answer:
C
— 10
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Q. If the roots of the equation x^2 + mx + n = 0 are -2 and -3, what is the value of m + n?
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Solution
The sum of the roots is -(-2 - 3) = 5, so m = 5. The product of the roots is (-2)(-3) = 6, so n = 6. Thus, m + n = 5 + 6 = 11.
Correct Answer:
C
— -7
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Q. If the roots of the equation x^2 + px + q = 0 are -2 and -3, what is the value of p + q?
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Solution
Using Vieta's formulas, p = -(-2 - 3) = 5 and q = (-2)(-3) = 6. Therefore, p + q = 5 + 6 = 11.
Correct Answer:
C
— -7
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Q. If the roots of the equation x^2 + px + q = 0 are -2 and -3, what is the value of p?
Show solution
Solution
Using Vieta's formulas, p = -(-2 - 3) = 5.
Correct Answer:
A
— 5
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Q. If the roots of the equation x^2 + px + q = 0 are 1 and -1, what is the value of p?
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Solution
The sum of the roots is 0, hence p = -sum = 0.
Correct Answer:
A
— 0
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Q. If the roots of the equation x^2 + px + q = 0 are equal, what is the relationship between p and q?
A.
p^2 = 4q
B.
p^2 > 4q
C.
p^2 < 4q
D.
p + q = 0
Show solution
Solution
For equal roots, the discriminant must be zero: p^2 - 4q = 0, hence p^2 = 4q.
Correct Answer:
A
— p^2 = 4q
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Q. If the roots of the equation x^2 - 5x + k = 0 are equal, what is the value of k?
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Solution
For the roots to be equal, the discriminant must be zero. Thus, b^2 - 4ac = 0 => 25 - 4k = 0 => k = 25.
Correct Answer:
C
— 6
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Q. If the roots of the equation x^2 - 5x + k = 0 are real and equal, what is the minimum value of k?
Show solution
Solution
The minimum value of k is 6, as the discriminant must be zero.
Correct Answer:
C
— 6
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Q. If the roots of the equation x^2 - 5x + k = 0 are real and equal, what is the value of k?
Show solution
Solution
For real and equal roots, the discriminant must be zero: 25 - 4k = 0, thus k = 6.
Correct Answer:
C
— 6
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Q. If the roots of the equation x^2 - 6x + k = 0 are 2 and 4, find the value of k.
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Solution
Using Vieta's formulas, k = 2 * 4 = 8.
Correct Answer:
B
— 10
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Q. If the roots of the equation x^2 - 7x + p = 0 are 3 and 4, what is the value of p?
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Solution
Using Vieta's formulas, the sum of the roots is 7 and the product is p. Thus, 3 * 4 = p, so p = 12.
Correct Answer:
C
— 16
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Q. If the roots of the equation x^2 - 7x + p = 0 are in the ratio 3:4, what is the value of p?
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Solution
Let the roots be 3k and 4k. Then, 3k + 4k = 7 => 7k = 7 => k = 1. The product of the roots is 3k * 4k = 12k^2 = p => p = 12.
Correct Answer:
C
— 20
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Q. If the roots of the equation x^2 - kx + 8 = 0 are equal, what is the value of k?
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Solution
For equal roots, the discriminant must be zero: k^2 - 4*1*8 = 0, solving gives k = 4.
Correct Answer:
A
— 4
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Q. If the roots of the quadratic equation ax^2 + bx + c = 0 are 3 and -2, what is the value of c if a = 1 and b = -1?
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Solution
Using the product of the roots, c = 3 * (-2) = -6.
Correct Answer:
A
— -6
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Q. If the roots of the quadratic equation ax^2 + bx + c = 0 are equal, what is the condition on a, b, and c?
A.
b^2 - 4ac > 0
B.
b^2 - 4ac = 0
C.
b^2 - 4ac < 0
D.
a + b + c = 0
Show solution
Solution
The condition for equal roots is given by the discriminant b^2 - 4ac = 0.
Correct Answer:
B
— b^2 - 4ac = 0
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Q. If the roots of the quadratic equation x^2 + mx + n = 0 are 3 and 4, what is the value of m?
Show solution
Solution
The sum of the roots is 3 + 4 = 7, hence m = -7.
Correct Answer:
A
— 7
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Q. If the roots of the quadratic equation x^2 + px + q = 0 are equal, what is the relationship between p and q?
A.
p^2 = 4q
B.
p^2 > 4q
C.
p^2 < 4q
D.
p + q = 0
Show solution
Solution
For equal roots, the discriminant must be zero: p^2 - 4q = 0, hence p^2 = 4q.
Correct Answer:
A
— p^2 = 4q
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Q. If the roots of the quadratic equation x^2 - 3x + p = 0 are 1 and 2, what is the value of p?
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Solution
Using Vieta's formulas, sum of roots = 1 + 2 = 3 and product of roots = 1*2 = 2. Thus, p = 2.
Correct Answer:
D
— 6
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Q. If the scalar product of two vectors A and B is 0, what can be said about the vectors?
A.
They are parallel
B.
They are orthogonal
C.
They are equal
D.
They are collinear
Show solution
Solution
If A · B = 0, then the vectors are orthogonal.
Correct Answer:
B
— They are orthogonal
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Q. If the scalar product of vectors A = (x, y, z) and B = (2, -1, 3) is 10, what is the equation?
A.
2x - y + 3z = 10
B.
2x + y + 3z = 10
C.
2x - y - 3z = 10
D.
2x + y - 3z = 10
Show solution
Solution
A · B = 2x - y + 3z = 10.
Correct Answer:
A
— 2x - y + 3z = 10
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Q. If the scores of 10 students are: 50, 60, 70, 80, 90, 100, 50, 60, 70, 80, what is the mode?
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Solution
Mode is the value that appears most frequently. Here, 50, 60, 70, and 80 all appear twice, but 50 is the smallest.
Correct Answer:
A
— 50
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Q. If the scores of 5 students are 10, 20, 30, 40, and x, and the mean is 30, what is the value of x?
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Solution
Mean = (10 + 20 + 30 + 40 + x) / 5 = 30. Solving gives x = 50.
Correct Answer:
C
— 50
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Q. If the scores of 7 students are 50, 60, 70, 80, 90, 100, and 110, what is the median score?
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Solution
Arranging the scores: 50, 60, 70, 80, 90, 100, 110. Median = 80 (4th value).
Correct Answer:
B
— 80
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Q. If the scores of a student are 50, 60, 70, 80, and 90, what is the mode?
A.
50
B.
60
C.
70
D.
No mode
Show solution
Solution
All scores occur only once, so there is no mode.
Correct Answer:
D
— No mode
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Q. If the scores of a student in five subjects are 60, 70, 80, 90, and 100, what is the median score?
Show solution
Solution
Arranging the scores: 60, 70, 80, 90, 100. Median = 80 (middle value).
Correct Answer:
B
— 80
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