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It changes with temperature because volume of a solution alters due to expansion and contraction of the liquid with temperature. If the density of solution is 1.
How many mL of 0. Sol: Calculation of no. An antifreeze solution is prepared from Calculate the molality of the solution. If the density of the solution is 1. A sample of drinking water was found to be severely contaminated with chloroform CHCl 3 , supposed to be a carcinogen.
The level of contamination was 15 ppm by mass. Sol: 15 ppm means 15 parts in million 10 6 by mass in the solution.
What role does the molecular interaction play in solution of alcohol in water? Sol: In case of alcohol as well as water, the molecules are interlinked by intermolecular hydrogen bonding.
However, the hydrogen bonding is also present in the molecules of alcohol and water in the solution but it is comparatively less than both alcohol and water.
This will lead to increase in vapour pressure of the solution and also decrease in its boiling point. Why do gases always tend to be less soluble in liquids as the temperature is raised?
Sol: When gases are dissolved in water, it is accompanied by a release of heat energy, i. If the bottle is opened by removing the stopper or seal, the pressure on the surface of the gas will suddenly decrease.
This will cause a decrease in the solubility of the gas in the liquid i. As a result, it will rush out of the bottle producing a hissing noise or with a fiz. In tissues, the partial pressure of oxygen is comparatively low. Therefore, oxyhaemoglobin releases oxygen in order to carry out cellular activities. The partial pressure of ethane over a solution containing 6. If the solution contains 5. So there is expansion in volume on solution formation. So weaker interactions are replaced by stronger interactions so , there is release of energy i.
What is the molecular mass of the solute? At K, the vapour pressures of the two liquid components are What will be the vapour pressure of a mixture of The vapour pressure of water is Calculate vapour pressure of 1 molal solution of a non-volatile solute in it Sol: 1 molal solution of solute means 1 mole of solute in g of the solvent. A solution containing 30g of non-volatile solute exactly in 90 g of water has a vapour pressure of 2. Further, 18g of water is then added to the solution and the new of vapour pressure becomes 2.
Calculate i molar mass of the solute. When dissolved in 20g of benzene C 6 H 6 , 1 g of AB 2 lowers the freezing point by 2. The molar depression constant for benzene is 5. Calculate atomic masses of A and B. Suggest the most important type of intermolecular attractive interaction in the following pairs: i n-hexane and n-octane ii I 2 and CCl 4.
Thus, the intermolecular interactions will be London dispersion forces. Water is a polar molecule. Thus, the intermolecular interactions will be ion-dipole interactions. Thus, intermolecular interactions will be dipole-dipole interactions. Based on solute solvent interactions, arrange the following in order of increasing solubility in n-octane and explain. Sol: n-octane C 8 H 18 is a non-polar liquid and solubility is governed by the principle that like dissolve like.
Amongst the following compounds, identify which are insoluble, partially soluble and highly soluble in water? Outside Delhi Sol:. If the solubility product of CuS is 6 x 10 , calculate the maximum molarity of CuS in aqueous solution. Nalorphene C 19 H 21 NO 3 , similar to morphine, is used to combat withdrawal symptoms in narcotic users. Dose of nalorphene generally given is 1.
Calculate the mass of 1. The depression in freezing point of water observed for the same amount of acetic acid, trichloroacetic acid and trifluoroacetic acid increases in the order given above. Explain briefly. It can be seen that a function is continuous at a point if we are able to graph it without lifting the pen. If the function is undefined, then the function is discontinuous. Summary: Continuity and differentiability, a derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions.
Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second-order derivatives. Derivative can be defined as the rate of change of one quantity with respect to another.
The concept of derivatives has been used in many ways, such as when a matter of change of temperature or rate of change of shapes and sizes. Where the derivative function is used to calculate the highest and lowest point of the curve in a graph, with the help of the graph, you can also know its turning point as well. Simple problems that illustrate basic principles and understanding of the subject as well as real-life situations.
This is used to find our many useful quantities such as areas, volumes, displacement, etc. Integrals are related to usually definite integrals.
Integration is one of the two major calculus in Mathematics. The idea of limit is used where algebra and geometry are implemented.
Integration is a step of adding or summing up the parts to find the whole, and the opposite step is known as differentiation. An integral that contains the upper and lower limits where Indefinite integrals are defined without upper and lower limits.
Summary: Integration as the inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the types given in the syllabus and problems based on them.
Definite integrals as a limit of a sum, Fundamental Theorem of Calculus without proof. Basic properties of definite integrals and evaluation of definite integrals. Applications of the Integrals is applied in various fields to the calculation of areas like Mathematics, Science, and Engineering etc. An integral is a function which is a given function is the derivative.
It is used to find the areas of the two-dimensional and volumes of three-dimensional objects. The integral is also known as anti-derivative as it is the opposite process of differentiation. And the function of Differential Equations is the rate of change of a function at a point. Basically, Differential Equations is used in physics, engineering, biology, and another field. The main study of solutions that satisfy the equations, and the properties of the solutions.
The derivatives represent a rate of change, where differential equation describes a relationship between the quantities and the speed of change.
Summary: Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. The solution of differential equations by the method of separation of variables solutions of homogeneous differential equations of the first order and first degree.
Solutions of the linear differential equation of the type given in the syllabus. There are numbers of quantities that involve magnitude as well as direction. When the quantity has magnitude and direction, then it is known as vectors. And such types of quantities are known as Vector Quantities. The main use of vectors is to describe the physical quantities having directions and magnitude associated with them.
Summary: Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors equal, unit, zero, parallel and collinear vectors , position vector of a point, negative of a vector, components Byjus Class 12 Maths Ncert Solutions Ag of a vector, the addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio.
Definition, Geometrical Interpretation, properties and application of scalar dot product of vectors, vector cross product of vectors, a scalar triple product of vectors. Dimensional Geometry is about the angle between line and plane, between two lines etc.
To understand the different types of shapes and figures, Dimensional Geometry is introduced. Summary: Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, coplanar and skew lines, the shortest distance between two lines. Cartesian and vector equation of a plane. The angle between i two lines, ii two planes, iii a line and a plane.
The distance of a point from a plane. The basic use of linear programming is to maximize or minimize the numerical value. Linear programming used in many Mathematics field and some other field such as economics, business, telecommunication, and manufacturing fields. Linear programming LP is defined as the problem of maximizing or minimizing a linear function. Summary: Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming L.
It is a number of events to occur from the total number of event that occurs. The probability formula is defined as the likelihood of an event to happen be equal to the given ratio of the number which results and the total number of outcomes.
And where Conditional Probability is the likelihood of an event or outcome occurring is defined as on the occurrence of a previous event or outcome. Repeated independent Bernoulli trials and Byjus Class 11 Maths Ncert Solutions Kit Binomial distribution. Class 12th maths plays an important role for the preparation of many undergraduate competition exams.
So well described Maths solution at Tiwari Academy help you to clear all doubts and concepts of all chapters. It is the best study material to score more marks in your class 12 board exam and competitive exams in future. There are total of 13 chapters which are given by the expert math teachers with extensive reviewed. All Maths Class 12 NCERT Solutions are provided by the experienced Math after extensive research on each and every chapter to provide correct and authentic information to the students.
These solutions for every chapter strictly adhere to the CBSE curriculum. This NCERT solutions help the students to make their concepts crystal clear once you clear the concept then you no need to read the whole stuff again and again. Theses all solutions are designed in such a way that Student can revise quickly during their Examinations.
The well-defined solution saves your revision time by providing all the necessary logics and formulae in a proper way. There will be practical or project work of 20 marks for CBSE Class 12th Mathematics subject while the written exam will be of 80 marks instead of marks.
Where Calculus carries 44 marks. It means you must do practice and focus on this unit the most. Calculus which needs a lot of logical approaches which can be mastered only with rigorous practice.
And the chapter, Vectors and Three-Dimensional Geometry which carry 17 marks which are easy units. Be sure to make diagrams while you study and practice, as it helps you to get better visualization. However, both chapters require a lot of practice to understand the application of knowledge and formulas as well.
Where Probability especially requires a logical approach and so, the basics must be clear for this unit. Relations and Functions , and Linear Programming are the relatively easy chapters. You can do well by practising these chapter. CBSE 12 Maths Solutions help you secure marks in the 12 class Board exam as efficiently as they clear your conceptual doubts. The class 12 maths NCERT solutions help students solve all the exercises given in the textbooks prescribed by the NCERT, which are easy to understand the concepts and get good marks in their board exam.
Just do practice all the exercise and learn the theorems. Also, do not skip any topic of CBSE 12th Maths syllabus and do revision times before your class 12 board exam. So these NCERT books are known for their clear explanation of each topic and a good level of practice questions. The chapters include such as Differentiation, Integration, Algebra, and others. It covers the entire CBSE syllabus. If you want to score maximum marks in 12th class board exam then you are suggested to do practice and revise thoroughly before your exam.
It is easier than the syllabus of class 11 Maths. By the practicing in perfectly you can score more marks in Class 12 Maths. The student who have cleared all concept of the early class 11 Maths syllabus, then no need to worry about the Class 12 Maths topic, they can easily understand all topics.
It can help you to clear all doubts and concept of all topics. But tiwariacademy. All solutions cover all the important theorems and formulae with detailed explanations so that student can easily clear the concept. Apart from solutions for each chapter of CBSE Class 12 Maths are the best study materials for students who are preparing for their Class 12 board exams. Students who are practising with these class 12th Maths solution for the academic year can pass the 12th class board exam.
Class 12 Maths Chapter 1 Solution in Videos. Class 12 Maths Chapter 2 Solution in Videos.
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