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. A ball is thrown vertically upwards with a speed of 30 m/s. How high will it rise before coming to rest momentarily?
A.
45 m
B.
30 m
C.
60 m
D.
75 m
Solution
Using the equation v² = u² + 2as, where v = 0, u = 30 m/s, and a = -9.8 m/s² (acceleration due to gravity), we have 0 = (30)² + 2*(-9.8)*s. Solving gives s = 45.92 m, approximately 45 m.
Q. A ball is thrown vertically upwards with a speed of 30 m/s. What is the maximum height it reaches? (g = 9.8 m/s²)
A.
45.9 m
B.
46.0 m
C.
46.1 m
D.
46.2 m
Solution
Using conservation of energy, initial kinetic energy = potential energy at maximum height. 0.5mv² = mgh. Solving gives h = v²/(2g) = (30)²/(2 * 9.8) = 45.9 m.
Q. A ball is tied to a string and swung in a vertical circle. At the highest point of the circle, what is the condition for the ball to remain in circular motion?
A.
Tension must be zero
B.
Tension must be maximum
C.
Weight must be zero
D.
Centripetal force must be zero
Solution
At the highest point, the tension can be zero if the centripetal force is provided entirely by the weight.
Q. A ball is tied to a string and swung in a vertical circle. At the highest point of the circle, what is the condition for the ball to just maintain circular motion?
A.
Tension = 0
B.
Tension = mg
C.
Tension > mg
D.
Tension < mg
Solution
At the highest point, the centripetal force is provided by the weight, so T + mg = mv²/r, T = 0.
Q. A ball is tied to a string and swung in a vertical circle. At the highest point, the tension in the string is 2 N and the weight of the ball is 3 N. What is the speed of the ball at the highest point if the radius of the circle is 1 m?
A.
1 m/s
B.
2 m/s
C.
3 m/s
D.
4 m/s
Solution
At the highest point, T + mg = mv²/r. 2 N + 3 N = mv²/1. v² = 5, v = √5 ≈ 2.24 m/s.
Q. A ball rolls down a ramp and reaches a speed of 10 m/s at the bottom. If the ramp is 5 m high, what is the ball's moment of inertia if it is a solid sphere?
A.
(2/5)m(10^2)
B.
(1/2)m(10^2)
C.
(1/3)m(10^2)
D.
(5/2)m(10^2)
Solution
Using conservation of energy, mgh = (1/2)mv^2 + (1/2)(2/5)mv^2. Solving gives the moment of inertia I = (2/5)m(10^2).
Q. A ball rolls down a ramp. If it starts from rest and rolls without slipping, what is the relationship between its linear speed and angular speed at the bottom?
A.
v = Rω
B.
v = 2Rω
C.
v = R/2ω
D.
v = 3Rω
Solution
The relationship is given by v = Rω, where v is the linear speed, R is the radius, and ω is the angular speed.
Q. A ball rolls without slipping on a flat surface. If the ball's radius is doubled while keeping its mass constant, how does its moment of inertia change?
A.
Increases by a factor of 2
B.
Increases by a factor of 4
C.
Increases by a factor of 8
D.
Remains the same
Solution
The moment of inertia of a solid sphere is (2/5)MR^2. If the radius is doubled, the moment of inertia increases by a factor of 4.
Q. A beam of light enters a prism with an angle of 60 degrees. If the refractive index of the prism is 1.5, what is the angle of refraction inside the prism?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
90 degrees
Solution
Using Snell's law, sin(θ2) = sin(60)/1.5, we find θ2 = 30 degrees.
Q. A beam of light enters a prism with an angle of incidence of 45 degrees. If the refractive index of the prism is 1.5, what is the angle of refraction inside the prism?
Q. A beam of light in glass (n=1.5) strikes the glass-air interface at an angle of 60°. Will total internal reflection occur?
A.
Yes
B.
No
C.
Only if the angle is increased
D.
Only if the angle is decreased
Solution
To determine if total internal reflection occurs, we first find the critical angle using sin(θc) = 1/n = 1/1.5, which gives θc ≈ 41.8°. Since 60° > 41.8°, total internal reflection will not occur.
Q. A beam of light passes through a prism with a refractive index of 1.5. If the angle of the prism is 60 degrees, what is the angle of minimum deviation?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
Solution
For a prism, the angle of minimum deviation D is given by D = A(n - 1), where A is the angle of the prism. Here, D = 60(1.5 - 1) = 30 degrees.
Q. A beam of light passes through a thin convex lens with a focal length of 15 cm. If the object is placed 30 cm from the lens, what is the image distance?
A.
10 cm
B.
15 cm
C.
20 cm
D.
30 cm
Solution
Using the lens formula, 1/f = 1/v - 1/u; here, f = 15 cm and u = -30 cm. Thus, 1/v = 1/15 + 1/30 = 1/10, giving v = 10 cm.
