Class 11

Yes, NCERT Solutions for Class 11 Trigonometric Functions are highly useful for JEE and other competitive exams.  NCERT Textbook help students develop a clear understanding of fundamental concepts such as trigonometric identities, angle transformations, and general solutions of equations, which form the backbone of many advanced problems in exams like JEE Main and Advanced.

The step-by-step explanations in NCERT Solutions provided by Shiksha helps students in logical problem-solving techniques. Students can build the conceptual strength and formula fluency required to tackle higher-level problems found in books like Cengage or previous year question papers by practicing NCERT questions thoroughly.

According to the kinetic theory of gases class 11, the Maxwell-Boltzmann distribution law describes the gas molecules' distribution of speeds (or velocities). All molecules of gas do not move at the same speed, some move fast, some are slow and most move at an average speed. This law provides a mathematical function that helps in finding at a given temperature, how many molecules have a particular speed. The Maxwell-Boltzmann distribution law helps in defining three important types of speeds:

• Average speed: Arithmetic mean of all speeds.
• Most probable speed: Speed at which the maximum number of molecules travel.
• Root mean square (RMS) speed: Square root of the average of squares of all speeds. 

The kinetic theory talks about the molecular explanation for the classical gas laws:

Boyle's Law (P? 1/V at constant T): Gas molecules will exert more pressure when the volume of the container reduces as it has less space to move and hence it collides with the walls of the container. However, when the temperature is constant, the speed of the molecule will not change.

Charles's Law (V? T at constant P): With the increase in temperature, the speed and average kinetic energy of the molecules increase. The gas expands to maintain constant pressure and increases the volume.

The kinetic theory links the physical behaviour of gases with the molecular motion and supports the ideal gas equation.

Class 11 Maths Chapter 2 Relations and Functions explores how elements from one set can be connected or related to elements from another.  Students get to learn many concepts, can be checked below;

• Concept of the Cartesian product of sets
• Concept of Relations, and how to represent those connections using different methods like arrow diagrams or set notation.
• Idea of a function, and different types of functions such as one-one, onto, bijective, constant, and identity functions.
• Real-valued functions, like linear, quadratic, modulus, and the greatest integer function.

Students can use NCERT Solutions for Chapter 2 Relations and Functions to practice these concepts, and getting mastery in it.

The kinetic theory is based on many key assumptions, such as the following:

• The individual gas molecules volume is almost non-existing when compared to the total volume of the gas.
• A gas consists of many small, identical, hard spherical particles.
• The collisions between the gas particles and the container walls are perfectly elastic.
• Except during the collisions, there are no intermolecular forces between the atoms.
• The time spent in collisions is almost nil when compared to the time between collisions.
• The gas molecules are in random and constant motion.
• The average kinetic energy of the molecules is directly proportional to the absolute temperature.