NCERT

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.

An inverse of a function does just opposite work as the original function does in other words it essentially "undoes" what the original function does. If a function f maps an input x to an output y (written as f (x) = y),

 then its inverse function is denoted as  f? ¹ (y) and  f? ¹ (y) = x

However, Students must be aware that not all functions have inverses. For an inverse function, the function must be one-one (injective) and onto (surjective): So that every possible output value is covered.

Together, these two properties make the function bijective, and only bijective functions have well-defined inverses. If a function isn't one-one (like f (x) = x²), it can't have a true inverse unless its domain is restricted.

A relation deals with, how elements from any set  (A) are related to elements of another set (B). there are various form of relations, such as Reflexive, Symatric, Transitive and Equivalance. On the other hand, Functions are special case of Relations where every element in Set A is related to exactly one element in Set B. Functions works like mathematics formulas, for a given set of input the out put will always remain the same. Students will be abel to check the type of relations, and application in class 11 Math Relation and Function chapter. We have provided Class 11 Math Relations and Functions NCERT Solutions on shiskha 

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.