JEE Important Questions

Here are some important questions commonly asked in the Joint Entrance Examination (JEE), covering key topics across Physics, Chemistry, and Mathematics. These questions are representative of the types of problems students should be prepared to solve:

Physics

Electrostatics

Question: Two charges q1q1​ and q2q2​ are placed at a distance rr apart in a vacuum. Calculate the force between them using Coulomb's Law. How does the force change if a dielectric medium is introduced between them?
Concepts Tested: Coulomb's law, dielectric constant, and electric forces.

Mechanics (Projectile Motion)

Question: A projectile is launched with an initial velocity v0v0​ at an angle θθ with the horizontal. Derive the time of flight, maximum height, and range of the projectile.
Concepts Tested: Kinematic equations, vector decomposition, and trigonometry.

Thermodynamics

Question: Explain the first law of thermodynamics. Calculate the work done by an ideal gas during an isothermal expansion from volume V1V1​ to V2V2​.
 Concepts Tested: First law of thermodynamics, work done in thermodynamic processes, and properties of ideal gases.

Optics (Wave Optics)

Question: In a double-slit experiment, light of wavelength λλ produces an interference pattern on a screen placed at a distance DD from the slits. Derive the expression for the fringe width and explain the conditions for constructive and destructive interference.
Concepts Tested: Interference, Young's double-slit experiment, and wave properties of light.

Magnetism and Electromagnetic Induction

Question: A circular loop of radius rr and resistance RR is placed in a magnetic field BB that varies with time as B=B0sin⁡(ωt)B=B0​sin(ωt). Calculate the induced EMF and current in the loop.
Concepts Tested: Faraday’s Law, Lenz’s Law, and electromagnetic induction.

Chemistry

Organic Chemistry (Reactions of Alkenes)

 Question: Describe the mechanism of the Markovnikov addition of HBr to propene. What product would be formed if peroxide is present during the reaction?
 Concepts Tested: Reaction mechanisms, Markovnikov's rule, and the anti-Markovnikov effect.

Physical Chemistry (Chemical Kinetics)

Question: Derive the integrated rate equation for a first-order reaction. If the half-life of a first-order reaction is 20 minutes, calculate the rate constant.
Concepts Tested: Rate laws, half-life, and first-order reactions.

Inorganic Chemistry (Coordination Compounds)

Question: Explain the crystal field splitting in an octahedral complex. How does the strength of the ligand affect the splitting energy and the color of the complex?
Concepts Tested: Crystal field theory, ligand field strength, and electronic transitions.

Thermodynamics (Entropy and Gibbs Free Energy)

Question: For the reaction 2A+B→3C+D2A+B→3C+D, the enthalpy change ΔHΔH is -100 kJ/mol, and the entropy change ΔSΔS is -200 J/K·mol. Calculate the Gibbs free energy   change at 298 K and predict whether the reaction is spontaneous.
Concepts Tested: Gibbs free energy, spontaneity of reactions, and entropy.

Electrochemistry

Question: A galvanic cell is made up of zinc and copper electrodes with solutions of their respective sulfates. Write the cell notation, calculate the cell potential using the    standard electrode potentials, and explain the working principle of the cell.
Concepts Tested: Electrochemical cells, Nernst equation, and standard electrode potential.

Mathematics

Calculus (Differentiation)

Question: Find the derivative of the function f(x)=x3ln⁡(x)f(x)=x3ln(x). Also, determine the critical points and identify the local maxima and minima.
Concepts Tested: Differentiation, product rule, and critical points analysis.

Coordinate Geometry (Conic Sections)

Question: Derive the equation of an ellipse with foci at (c,0)(c,0) and (−c,0)(−c,0), and explain the relationship between the semi-major axis, semi-minor axis, and the distance between the foci.
Concepts Tested: Standard form of conic sections, properties of ellipses, and geometric interpretation.

Probability and Statistics

Question: A box contains 10 white and 5 black balls. Two balls are drawn at random without replacement. What is the probability that both balls drawn are black?
Concepts Tested: Basic probability, combinations, and conditional probability.

Vector Algebra

Question: Find the vector equation of the plane passing through the point (1,2,3)(1,2,3) and perpendicular to the vector n=2i−3j+kn=2i−3j+k.
Concepts Tested: Vector equations of planes, normal vectors, and dot products.

Complex Numbers

Question: Solve the equation z4+1=0z4+1=0 in the complex plane. Represent the solutions graphically.
Concepts Tested: Roots of complex numbers, polar form, and geometric representation.

These questions are designed to test fundamental concepts and problem-solving skills in key areas of the JEE syllabus. Practicing similar questions can help students gain confidence and improve their performance in the actual exam.