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# NCERT Solutions for Class 12 2024 – Physics, Chemistry, Maths, Biology

NCERT Solutions for Class 12 2023-24: The NCERT Solutions for Class 12 are meant to help students understand what the subject holds. These solutions are designed as per the latest syllabus and guidelines that will make it easier for students to prepare for the exam. By referring to these NCERT Solutions, they can clearly understand the paper pattern. As a result, they will be able to solve the questions thoroughly.

This article deals with the NCERT Solutions for Class 12 for Maths, Physics, Chemistry and Biology. Students can access these NCERT Solutions from Embibe. They can also get numerous questions and mock tests related to these that will help students solve the questions properly and answer them. Continue reading to find more information on NCERT Solutions for Class 12.

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## NCERT Solutions for Class 12 2023-24

NCERT Solutions for Class 12 are the perfect study material for students preparing for their final exams. These solutions provide in-depth explanations for all the questions in the NCERT textbook, making it easier for students to understand and retain the concepts for a longer time.

Embibe’s practice questions, NCERT books, and mock tests complement NCERT Solutions perfectly and provide a comprehensive study plan for students. The practice questions cover all the important topics and give students a better understanding of the subjects. Mock tests, on the other hand, help students in testing their preparation level and provide a real-time exam-like experience.

#### NCERT Class 12 Maths Chapters

Chapter No. Chapter Name
1 Relations and Functions
2 Inverse Trigonometric Functions
3 Matrices
4 Determinants
5 Continuity and Differentiability
6 Application of Derivatives
7 Integrals
8 Application of Integrals
9 Differential Equations
10 Vector Algebra
11 Three-Dimensional Geometry
12 Linear Programming
13 Probability

#### NCERT Class 12 Chemistry Chapters

Students can refer to the following chapters for Class 12 Chemistry NCERT solutions 2023-24:

#### NCERT Class 12 Biology Chapters

Students can check out the subsequent NCERT Biology Class 11 chapters to have a sound preparation for their Class 12 board exams.

### NCERT Solutions for Class 12: Points to Remember

The NCERT solutions for Class 12 provide a clear understanding of the concepts, helping students to grasp the subject matter and retain it for a longer time. With step-by-step explanations for all the questions present in the NCERT textbook on Embibe, students can easily grasp the complex topics and feel confident about their preparation. Learn some of the important points mentioned below:

NCERT Class 12 Maths

• Matrices
• A set of numbers (real or imaginary) or symbols or expressions arranged in the form of a rectangular array of m rows and n columns is called an m × n matrix.
• A matrix having only one row is called a row matrix.
• A matrix having only one column is called a column matrix.
• A matrix in which the number of rows is equal to the number of columns say n, is called a square matrix of order n.
• Application of Derivatives
• A function f(x) is said to be monotonic on (a, b) if it is either strictly increasing or strictly decreasing on (a,b).
• A function f(x) is said to be a strictly increasing function on (a, b) if x1 < x2 ⇒ f(x1) < f(x2) for all x1 , x2 ∈ (a, b).
• The necessary and sufficient condition for a differentiable function defined on (a, b) to be strictly increasing on (a, b) is that f'(x) > 0 for all x ∈ (a, b).
• The necessary and sufficient condition for a differentiable function defined on (a,b) to be strictly decreasing on (a, b) is that f'(x) < 0 for all x ∈ (a, b).
• Vector Algebra
• Any two non-zero, non-collinear vectors are linearly independent.
• Any two collinear vectors are linearly dependent.
• Any three non-coplanar vectors are linearly independent.
• Any three coplanar vectors are linearly dependent.

NCERT Class 12 Physics

• Electric Charges and Fields
• An electric field line is a curve drawn in such a way that the tangent at each point on the curve gives the direction of the electric field at that point.
• Field lines are continuous curves without any breaks.
• Two field lines cannot cross each other.
• Electrostatic field lines start at positive charges and end at negative charges.
• Magnetism and Matter
• It has been known since ancient times that magnets tend to point in the north-south direction.
• There are two poles; the North Pole and the South Pole. Like magnetic poles repel and unlike ones attract.
• Magnetic monopoles do not exist. If you slice a magnet in half, you get two smaller magnets.
• Atoms
• Atoms, as a whole, are electrically neutral and therefore contain equal amounts of positive and negative charges.
• In Thomson’s model, an atom is a spherical cloud of positive charges with electrons embedded in it.
• In Rutherford’s model, most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus (typically one by ten thousand the size of an atom), and the electrons revolve around it.
• Rutherford’s model predicts that atoms are unstable because the accelerated electrons revolving around the nucleus must spiral into the nucleus. This contradicts the stability of matter.
• It cannot explain the characteristic line spectra of atoms of different elements.
• Semiconductor Electronics
• Metals have low resistivity (10−2 to 10−8 Ωm)
• Insulators have very high resistivity (1011 Ωm−1 to 1019 Ωm−1)
• Semiconductors have intermediate values of resistivity. (10−5 Ω m−1 to 106 Ωm−1)
• Semiconductors are elemental (Si,Ge) as well as compound (GaAs,CdS, etc.).
• Pure semiconductors are called intrinsic semiconductors. ne = nh for intrinsic semiconductors.

NCERT Class 12 Chemistry

• Solid State
• Solid is the form of matter which possesses a definite shape and a definite volume.
• If intermolecular forces > thermal energy, the substance exists as a solid.
• Classification of Solid: Crystalline (Regular arrangement of particles, anisotropic), Amorphous (No regular arrangement of particles, isotropic).
• Classification of crystalline solids: Ionic, Molecular, Covalent/Network, Metallic
• Chemical Kinetics
• Chemical Kinetics is the branch of chemistry which deals with the study of reaction rates and their mechanism.
• Rate of Reaction: It is the rate of change of concentration of any of the reactants or products with time at any particular moment of time.
• Average Rate: The rate of reaction measured over a long time interval is called average rate. It is given as Δx/Δt.
• The p-Block Elements
• Elements: N, P, As, Sb & Bi
• Electronic configuration: ns2np3
• Oxidation state: +3 and +5. +3 oxidation state is favoured by heavier elements due to the ‘inert pair effect’.
• Nitrogen differs from other elements of group 15 due to its small size, formation of pπ–pπ multiple bonds with itself and with highly electronegative atoms like O or C and non-availability of d orbitals to expand its valence shell.
• Alcohols, Phenols and Ethers
• Alcohols are versatile compounds. They react both as nucleophiles and electrophiles.
• Electron withdrawing groups in phenol increase its acidic strength and electron releasing groups decrease it.
• Alcohols undergo nucleophilic substitution with hydrogen halides to yield alkyl halides.
• Dehydration of alcohol gives alkenes.
• Primary alcohols on oxidation yield aldehydes with mild oxidising agents and carboxylic acids with strong oxidising agents while secondary alcohols yield ketones.

NCERT Class 12 Biology

• Reproduction in Organisms
• Reproduction is the biological process by which new individual organisms’ offspring are produced from their parents.
• It enables a species to live generation after generation.
• There are two major types of reproduction in the biological world; asexual and sexual.
• Asexual reproduction is without the formation or union of gametes or sex cells.
• It is common in organisms that have a relatively simple organisation such as Monerans, Fungi, Algae, Protozoa, and lower invertebrates such as sponges, jellyfishes, flatworms and many annelids.
• The offspring formed by asexual reproduction are morphologically and genetically identical and are referred to as clones.
• Evolution
• According to the Big Bang theory, the expansion of the observable universe began with a large-scale and violent explosion of a small, primaeval “super-atom.”
• Most widely accepted view of the origin of our solar system is the nebular hypothesis proposed by Kant (1753 A.D.).
• Earth began to form over 4.6 billion years ago.
• Theory of spontaneous generation of life was articulated by Francesco Redi (1668), A.L. Spallanzani (1767) and Louis Pasteur (1867).
• Louis Pasteur demonstrated the theory of biogenesis and finally disproved the theory of spontaneous generation in 1861 by his experiments with the “swan neck” flask.
• Microbes in Human Welfare
• Microbes are the major components of biological systems on this Earth.
• All microbes are not pathogenic, many microbes play an important role in the welfare of human society.
• Microbes and microbially derived products are used almost every day.
• Biotechnology
• Biotechnology has provided many useful products by using microbes, plants and animals and their metabolic systems.
• Recombinant DNA (rDNA) technology modifies microbes, plants and animals by manipulating genes in them.
• Genetically Modified (GM) crops and animals are of immense value and have been developed by using methods to transfer one or more genes from one organism to another by using rDNA technology.
• GM plants were developed to provide resistance against stresses such as drought, heat, cold, salt, etc.

Students can visit Embibe to get access to all the important points for NCERT Class 12 Maths, Physics, Chemistry and Biology.

### NCERT Solutions for Class 12: All Subjects

Students can download the NCERT Solutions for Class 12 for Maths, Physics, Chemistry and Biology from the following:

### FAQs on NCERT Solutions for Class 12 2023-24

Some frequently asked questions related to NCERT Solutions for Class 12 are provided below:

Q: How do NCERT Solutions for Class 12 help in exam preparation?

Ans: NCERT Solutions for Class 12 provide a clear understanding of all the concepts, making it easier for students to grasp the subject matter. The solutions also help students identify their strengths and weaknesses, thereby allowing them to focus on their weaker areas and improve their overall performance.

Q: Will these NCERT 12th Solutions help in competitive exams like JEE and AIPMT/NEET?

Ans: NCERT books have been termed as the Bible for many top competitive examinations. These 12th NCERT solutions will help build the conceptual knowledge to solve complex questions.

Q: Are NCERT Solutions for Class 12 available online?

Ans: Yes, NCERT Solutions for Class 12 are available online, and students can easily access them from Embibe.

Q: Where do I find NCERT Solutions for Class 12 Biology?

Ans: On Embibe, students will find NCERT Solutions for Class 12 Biology for all 16 Chapters.

Q: How important are mock tests for Class 12 students?

Ans: Mock tests are an important aspect of exam preparation for Class 12 students. These tests provide a real-time exam-like experience, helping students to understand their strengths and weaknesses and improve their performance. Embibe provides comprehensive mock tests for Class 12 students to help them in their exam preparation.

We hope this detailed article on NCERT Solutions for Class 12 helps you achieve good results in your Class 12 exams. For more updates on NCERT Solutions for Class 12, stay tuned to Embibe.