Class 11

Doppler Effect in class 11 chapter 14 waves refers to the variation in the wavelength or frequency of a wave in relation to an observer moving relative to the wave source. When the wave source moves toward the observer, the frequency increases, and waves are compressed. If the source moves away, the frequency reduces and the waves are stretched. The Doppler Effect can be observed with the sound of a passing train or ambulance. This concept is also used in medical imaging technologies like Doppler ultrasound, radar, and astronomy to find whether galaxies or stars are moving away or towards the Earth.

The Binomial Theorem is taught as chapter 7 in Class 11 Maths as per the latest CBSE syllabus. The Binomial Theorem is a method of expanding expressions raised to a power, such as $(a + b)^n$, where n is a natural number. There are several other topics which are essential part of Binomial Theorem such as mid term, nth term, and numerical constant of nth term, which are important to understand Binomial Theorem. Binomial Theorem helps simplify complex algebraic expansions using binomial coefficients and Pascal's Triangle.

The NCERT Solutions for Permutations and Combinations include step-by-step solutions of all the exercises of the chapter. However, NCERT Solved examples are not included in the NCERT Solutions. Students can read the NCERT textbooks for the solved examples of the chapter and NCERT Solutions for the exercises. We have provided Permutations and Combination Solutions which are useful in getting clarity of concepts, learning problem-solving.

Shiksha has prepared NCERT Textbooks solutions for all the chapters of 10+2 Science stream subjects. These NCERT Solutions for Chapter 6 Permutations and Combinations  offer detailed, step-by-step explanations for all the exercises in the Permutations and Combinations.

NCERT Solutions can be used as a good mathematical guide and tool for students preparing for scholl level or competitve exams such as JEE, NDA and others. These Solutions help students understand the logic behind arrangement and selection, making complex concepts simpler and easier to grasp.

Class 11 Mathematics exam will be based on the CBSE exam format aligned with CBSE syllabus. NCERT textbooks are best resources to understand, practice and apply concepts to perform well in the annual or other school level exams. So NCERT Solutions are best mathematics guide available to understand the NCERT textbook questions in detail with explainations. For class 11 Maths preparations, NCERT Solutions for permutations and combinations are enough and those who are preparing fopr competitive exams must use some additional reference books.

NCERT Textbooks includes the question which requires solution to be represented in coordinate plane. Our NCERT Solutions include clear, visual explanations of how to graph linear inequalities on the Cartesian plane. Students can learn how to shade the correct half-plane based on the inequality sign and how to determine whether the boundary line should be solid or dotted. Students can take help of our well designed NCERT Solutions provided on our pages to get ahead in the race of competition.

The chapter Linear Inequalities is an important part of the Class 11 CBSE Maths syllabus. Linear Inequalities carry a weightage of approximately 6–8 marks in the CBSE annual exam. Students must know that this is a high-scoring chapter because the questions are usually straightforward and concept-based.

Linear Inequalities helps students solve inequalities algebraically and represent them graphically, which is essential for understanding real-world problems with constraints. It also builds the foundation for Linear Programming in Class 12, a major application topic for class 12 boards.

Linear Inequality is indexed as chapter 5 in the CBSE class 11 mathematics. A linear inequality is an expression that shows the relationship between two algebraic expressions using inequality symbols like <, >? , or? , instead of an equal sign. For example,

$2x + 3 < 7 \quad \text {or} \quad 3x - 4 \geq 5$

The highest power of the variable in linear inequalities, is 1, and they graph as straight lines on the coordinate plane (with shaded regions showing the inequality). Linear inequalities are used in many ways such as to find many range of possible values, solve optimization problems, and computer science.

When two waves of the same amplitude, frequency and speed travel in opposite directions and collide with each other, then a standing wave is formed. It is usually seen in the bounded medium, like a string fixed at both ends. It is different from the travelling waves and does not appear to move along the medium. At fixed locations, it forms specific points called nodes (with zero displacement) and antinodes (with maximum displacement). It is an important concept in understanding musical instruments, resonance and wave behaviour in closed and open pipes. The standing waves help in visualizing how energy can be stored in waveforms.