JEE Main Preparation Resources for Competitive Exams

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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.

Chemistry Syllabus (JEE Main) Mathematics Syllabus (JEE Main) Physics Syllabus (JEE Main)

Q. If A = {1, 2, 3} and B = {3, 4, 5}, what is A Δ B (symmetric difference)?

A. {1, 2}
B. {4, 5}
C. {1, 2, 4, 5}
D. {3}

Solution

The symmetric difference A Δ B includes elements in either A or B but not in both, which are {1, 2, 4, 5}.

Correct Answer: C — {1, 2, 4, 5}

Q. If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ (A ∩ B)?

A. {1, 2, 3}
B. {3, 4, 5}
C. {1, 2, 3, 4, 5}
D. {1, 2, 5}

Solution

First, A ∩ B = {3}. Then, A ∪ {3} = {1, 2, 3}.

Correct Answer: A — {1, 2, 3}

Q. If A = {1, 2, 3} and B = {3, 4}, what is the Cartesian product A × B?

A. {(1, 3), (2, 4)}
B. {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}
C. {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4), (1, 1), (2, 2), (3, 3)}
D. {}

Solution

The Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B, which is {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}.

Correct Answer: B — {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}

Q. If A = {1, 2, 3}, how many subsets does A have?

A. 2
B. 3
C. 4
D. 8

Solution

The number of subsets of a set with n elements is 2^n. Here, n = 3, so 2^3 = 8.

Correct Answer: D — 8

Q. If A = {1, 2, 3}, what is the power set of A?

A. {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
B. {∅, {1, 2, 3}}
C. {1, 2, 3}
D. {1, 2, 3, ∅}

Solution

The power set of a set with n elements has 2^n subsets. Here, n=3, so the power set has 2^3 = 8 subsets.

Correct Answer: A — {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Q. If A = {1, 2} and B = {x | x is an odd integer}, what is A × B?

A. {(1, 1), (2, 1)}
B. {(1, 3), (2, 3)}
C. {(1, 1), (1, 3), (2, 1), (2, 3)}
D. {(1, 2), (2, 2)}

Solution

The Cartesian product A × B consists of all ordered pairs (a, b) where a ∈ A and b ∈ B. Thus, A × B = {(1, x), (2, x)} for all odd integers x.

Correct Answer: C — {(1, 1), (1, 3), (2, 1), (2, 3)}

Q. If A = {x | x is a letter in the word 'MATH'} and B = {x | x is a letter in the word 'SET'}, what is A ∩ B?

A. {M, A, T}
B. {A, T}
C. {T}
D. {}

Solution

The intersection A ∩ B consists of common letters, which is {T}.

Correct Answer: C — {T}

Q. If A = {x | x is a letter in the word 'MATH'} and B = {x | x is a letter in the word 'SCIENCE'}, what is A ∩ B?

A. {A}
B. {M, A, T}
C. {A, C, E}
D. {A, T}

Solution

The intersection A ∩ B includes letters that are common in both words. The only common letter is 'A', so A ∩ B = {A}.

Correct Answer: A — {A}

Q. If A = {x | x is a multiple of 3} and B = {x | x is a multiple of 5}, what is A ∩ B?

A. {15}
B. {3, 5}
C. {0}
D. {}

Solution

The intersection A ∩ B consists of common multiples, which is {0}.

Correct Answer: C — {0}

Q. If A = {x | x is a natural number and x < 5} and B = {x | x is a natural number and x > 2}, what is A ∩ B?

A. {1, 2}
B. {3, 4}
C. {2, 3, 4}
D. {1, 2, 3, 4}

Solution

Set A = {1, 2, 3, 4} and set B = {3, 4, 5, ...}. The intersection A ∩ B = {3, 4}.

Correct Answer: B — {3, 4}

Q. If A = {x | x is a natural number less than 10} and B = {x | x is a prime number}, what is A ∩ B?

A. {2, 3, 5, 7}
B. {1, 2, 3, 4}
C. {2, 4, 6, 8}
D. {}

Solution

The intersection A ∩ B includes all prime numbers less than 10, which are {2, 3, 5, 7}.

Correct Answer: A — {2, 3, 5, 7}

Q. If A = {x | x is a natural number less than 5} and B = {x | x is a natural number less than 3}, what is A - B?

A. {1, 2}
B. {3, 4}
C. {1, 2, 3, 4}
D. {2, 3, 4}

Solution

Set A = {1, 2, 3, 4} and set B = {1, 2}. Thus, A - B = {3, 4}.

Correct Answer: B — {3, 4}

Q. If A = {x | x is a natural number less than 5} and B = {x | x is a prime number}, what is A ∩ B?

A. {1, 2, 3, 4}
B. {2, 3}
C. {3, 5}
D. {}

Solution

The natural numbers less than 5 are {1, 2, 3, 4} and the prime numbers are {2, 3}. Their intersection is {2, 3}.

Correct Answer: B — {2, 3}

Q. If A = {x | x is a natural number less than 5} and B = {x | x is an odd natural number}, what is A ∩ B?

A. {1, 2, 3, 4}
B. {1, 3}
C. {2, 4}
D. {1, 2, 3}

Solution

The intersection A ∩ B includes elements that are in both A and B. Here, A = {1, 2, 3, 4} and B = {1, 3}, so A ∩ B = {1, 3}.

Correct Answer: B — {1, 3}

Q. If A = {x | x is a prime number less than 10} and B = {2, 3, 5, 7}, what is A = B?

A. True
B. False
C. Cannot be determined
D. None of the above

Solution

Both sets A and B contain the same elements: {2, 3, 5, 7}. Therefore, A = B is True.

Correct Answer: A — True

Q. If A = {x | x is a prime number less than 10} and B = {2, 3, 5, 7}, what is A?

A. {2, 3, 5, 7}
B. {1, 2, 3, 4, 5, 6, 7, 8, 9}
C. {2, 3, 5, 7, 11}
D. {2, 3, 5, 7, 9}

Solution

The set A consists of all prime numbers less than 10, which are {2, 3, 5, 7}.

Correct Answer: A — {2, 3, 5, 7}

Q. If A = {x | x is a vowel} and B = {x | x is a consonant}, what is A ∩ B?

A. {a, e, i, o, u}
B. {}
C. {a, b, c}
D. {a, e, i}

Solution

The intersection A ∩ B is empty because no letter can be both a vowel and a consonant.

Correct Answer: B — {}

Q. If A = {x | x is an even integer} and B = {x | x is a multiple of 3}, what is A ∪ B?

A. {0, 2, 4, 6, ...}
B. {0, 3, 6, 9, ...}
C. {0, 2, 3, 4, 6, 9, ...}
D. {0, 2, 3, 4, 6, 8, 9, ...}

Solution

The union of sets A and B, A ∪ B, includes all even integers and all multiples of 3. Thus, A ∪ B = {0, 2, 3, 4, 6, 9, ...}.

Correct Answer: C — {0, 2, 3, 4, 6, 9, ...}

Q. If A = {x | x is an even integer} and B = {x | x is a multiple of 4}, what is A ⊆ B?

A. True
B. False
C. Depends on x
D. None of the above

Solution

A is the set of all even integers, while B is the set of multiples of 4. Not all even integers are multiples of 4 (e.g., 2 is even but not a multiple of 4), hence A is not a subset of B.

Correct Answer: B — False

Q. If A = {x | x is an even integer} and B = {x | x is a prime number}, what is A ∩ B?

A. {2}
B. {2, 3}
C. {2, 4}
D. {}

Solution

The only even prime number is 2, so A ∩ B = {2}.

Correct Answer: A — {2}

Q. If A = {x | x is an even number} and B = {x | x is a prime number}, what is A ∩ B?

A. {2}
B. {2, 3}
C. {2, 4}
D. {}

Solution

A ∩ B = {2} as 2 is the only even prime number.

Correct Answer: A — {2}

Q. If A = | 1 2 | | 3 4 |, find det(A).

A. -2
B. 2
C. 0
D. 4

Solution

det(A) = (1)(4) - (2)(3) = 4 - 6 = -2.

Correct Answer: B — 2

Q. If A = | 1 2 | | 3 4 |, what is det(A)?

A. -2
B. 2
C. 0
D. 4

Solution

det(A) = (1*4) - (2*3) = 4 - 6 = -2.

Correct Answer: B — 2

Q. If A = | 1 2 | | 3 5 |, what is det(2A)?

A. -10
B. 10
C. 20
D. 40

Solution

det(2A) = 2^2 * det(A) = 4 * (1*5 - 2*3) = 4 * (-1) = -4.

Correct Answer: C — 20

Q. If a battery provides a voltage of 9 V and is connected to a circuit with a total resistance of 3 ohms, what is the power consumed by the circuit?

A. 27 W
B. 18 W
C. 9 W
D. 3 W

Solution

Power P = V^2 / R. Here, P = 9^2 / 3 = 81 / 3 = 27 W.

Correct Answer: B — 18 W

Q. If a beam is supported at both ends and a load is applied at the center, what is the reaction force at each support?

A. Equal to the load
B. Half the load
C. Double the load
D. Zero

Solution

In this case, the reaction force at each support is half the load applied at the center.

Correct Answer: B — Half the load

Q. If a beam of light passes through a prism with an angle of 60 degrees and the refractive index of the prism is √3, what is the angle of minimum deviation?

A. 30 degrees
B. 60 degrees
C. 45 degrees
D. 15 degrees

Solution

Using the formula for minimum deviation, D = (n - 1)A. Here, n = √3 and A = 60 degrees. Thus, D = (√3 - 1) * 60 degrees, which approximates to 30 degrees.

Correct Answer: A — 30 degrees

Q. If a block is on a horizontal surface and a force is applied at an angle, how does this affect the normal force acting on the block?

A. Increases normal force
B. Decreases normal force
C. No effect on normal force
D. Depends on the angle

Solution

Applying a force at an angle reduces the normal force because part of the applied force acts vertically upward, counteracting the weight of the block.

Correct Answer: B — Decreases normal force

Q. If a boat can travel 20 km upstream in 4 hours, what is the speed of the current if the speed of the boat in still water is 10 km/h?

A. 2 km/h
B. 3 km/h
C. 4 km/h
D. 5 km/h

Solution

Speed upstream = distance/time = 20/4 = 5 km/h. Speed of current = speed of boat - speed upstream = 10 - 5 = 5 km/h.

Correct Answer: A — 2 km/h

Q. If a boat can travel at 15 km/h in still water and the current is 5 km/h, what is the speed of the boat upstream?

A. 10 km/h
B. 15 km/h
C. 20 km/h
D. 25 km/h

Solution

Speed upstream = speed of boat - speed of current = 15 - 5 = 10 km/h.

Correct Answer: A — 10 km/h

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