NCERT Solutions for Class 12 Maths
ShareNCERT Solutions for Class 12 Maths can help you solve challenging problems during homework or while preparing for Class 12 Board exams. At Goprep, you can find solutions to all the questions for all exercises present in the NCERT textbook. Our Class 12 Maths NCERT Solutions Part1 have been solved by subject matter experts who have years of experience in teaching mathematics.
Our NCERT Solutions for Class 12 are not only easy but also provide a stepbystep procedure to solve the questions quickly. With the help of these solutions, problems from topics including, Integration, Vectors, Differentiation, Limits & Derivatives will become much simpler.
So, to give your Maths exam preparation a competitive edge, click the links given below to browse CBSE Class 12 Maths book questions and their solutions for each chapter.
NCERT Solutions for Class 12 Maths  All Chapters
 NCERT Solutions for Class 12 Maths
 NCERT Solutions for Class 12 Mathematics Part II
 NCERT Solutions for Class 12 Physics
 NCERT Solutions for Class 12 Physics Part II
 NCERT Solutions for Class 12 Chemistry
 NCERT Solutions for Class 12 Chemistry Part II
 NCERT Solutions for Class 12 Biology
 NCERT Exemplar Class 12 Physics Solutions
 NCERT Exemplar Class 12 Chemistry Solutions
 NCERT Exemplar Solutions for Class 12 Mathematics
 NCERT Exemplar Solutions for Class 12 Biology
 NCERT Solutions for Class 12th English Flamingo
 NCERT Solutions for Class 12 English Kaleidoscope
 NCERT Solutions for Class 12 English Vistas
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Developed by some of the best teachers, our NCERT Maths Solutions for Class 12 Part1 help students grasp complex Mathematical problems and concepts better and faster. NCERT solutions can help you develop a deeper understanding of the concepts. Moreover, these solutions give indepth and detailed answers to problems that are part of the Class 12th syllabus.
The Class 12th board exams play an important role in helping students secure admission in a good college. Further, these solutions have been prepared to enable students to fare well in board exams as well as JEE, BITSAT, VITEEE, and others.
While preparing for Class 12 Maths Board exam, you must practise Maths previous year question papers. Check out the links for CBSE Class 12 Maths Solved Question Papers below:
CBSE Class 12 Maths Solved Question Papers 
CBSE Class 12 Maths Question Paper 2019 
CBSE Class 12 Maths Question Paper 2018 
CBSE Class 12 Maths Previous Year Question Papers 
NCERT Solutions for Class 12 Maths (Chapterwise description)
Chapter 1: Relations and Functions
You have already studied the basic concepts of relations and functions, domain, codomain, and range previously in class 9 NCERT maths book. In class 12, we will delve even deeper into the chapter. This year, the main features of the chapter will comprise different types of relations such as empty relation, universal relation, reflexive relation, to name a few.
Further, the chapter will entail several functions such as injective (oneone), surjective (onto), and bijective (oneone and onto). Finally, you will also learn about the composition of functions. With a total of 51 examples, four exercises, and a miscellaneous exercise, you will get to solve a variety of questions.
Topics
 Types of Relations
 Types of Functions
 Composition of Functions and Invertible Function
 Binary Operations
Chapter 2: Inverse Trigonometric Functions
Having studied the inverse of a function and oneone and onto functions in chapter 1, you will have to implement these concepts in inverse trigonometric functions. These trigonometric functions will come to play in the future when you solve the questions of integration.
Finding the domains and ranges of inverse trigonometric functions will be crucial to get its principal values. Next, you will learn the properties of these functions, which will help you in simplifying the complex inverse trigonometric expressions. This chapter includes a total of 13 examples, two exercises and a miscellaneous exercise.
Topics
 Basic Concepts
 Properties of Inverse Trigonometric Functions
Important formulas of Inverse Trigonometric Functions
For suitable values of domain, we have
 y = sin^{–1} x ⇒ x = sin y
 x = sin y ⇒ y = sin^{–1} x
 sin (sin^{–1} x) = x
 sin^{–1} (sin x) = x
 sin^{–1} (1/x) = cosec^{–1} x
 cos^{–1} (x) = π – cos^{–1} x
 cos^{–1} (1/x) = sec^{–1} x
 cot^{–1} (x) = π – cot^{–1} x
 tan^{–1} (1/x) = cot^{–1} x
 sec^{–1} (x) = π – sec^{–1} x
 sin^{–1} (x) =– sin^{–1} x
 tan^{–1} (x) =– tan^{–1} x
 tan^{–1} x + cot^{–1} x = π/2
 cosec^{–1} (x) =– cosec^{–1} x
 tan^{–1} x + tan^{–1} y = tan^{–1} [(x + y)/ (1xy)]
 sin^{–1} x + cos^{–1} x = π/2
 cosec^{–1} x + sec^{–1} x = π/2
 2tan^{–1} x = sin^{–1} [(2x/ 1+x^{2})] = cos^{–1}[(1  x^{2}/ 1 + x^{2})
 2tan^{–1} x = tan^{–1} [2x/ (1x^{2})]
 tan^{–1} x + tan^{–1} y = π + tan^{–1} [(x + y)/ (1  xy)], xy>1; x, y> 0
Chapter 3: Matrices
Matrices are a powerful tool of mathematics as it can help you represent the coefficients in a system of linear equations and utility of matrices. The knowledge of matrices is necessary as it will be required in various branches of mathematics in higher classes. Also, it will play a pivotal role in helping you solve questions in chapter 4 of class 12 maths NCERT book.
You will be surprised to know that this mathematical tool has found its applications in the area of economics, genetics, industrial management, modern psychology, and sociology. In class 12, you will get acquainted with the core concepts of matrix and matrix algebra.
Topics
 Matrix
 Types of Matrices
 Operations on Matrices
 Transpose of a Matrix
 Symmetric and Skew Symmetric Matrices
 Elementary Operation (Transformation) of a Matrix
 Invertible Matrices
Important formulas of Matrices
 A = [a_{ij}]_{m × m} is a diagonal matrix if a_{ij} = 0, when i ≠ j
 A = [a_{ij}]_{n × n} is a scalar matrix if a_{ij} = 0, when i ≠ j, a_{ij} = k, (k is some constant), when i = j
 A = [a_{ij}]_{n × n} is a scalar matrix if a_{ij} = 0, when i ≠ j, a_{ij} = k, (k is some constant), when i = j
 A = [a_{ij}] = [b_{ij}] = B if (i) A and B are of the same order, (ii) a_{ij} = b_{ij} for all possible values of i and j
 kA = k[a_{ij}]_{m × n} = [k(a_{ij})]_{m × n}
 – A = (–1)A
 A + B = B + A
 A – B = A + (–1) B
 (A + B) + C = A + (B + C), where A, B and C are of the same order
 k(A + B) = kA + kB, where A and B are of the same order, k is constant
 (k + l) A = kA + lA, where k and l are constant
 If A = [a_{ij}]_{m × n }and B = [b_{jk}]_{n × p}, then AB = C = [c_{ik}]_{m × p}
Some more properties
 A(BC) = (AB)C
 A(B + C) = AB + AC
 (A + B)C = AC + BC
 (A′)′ = A
 (kA)′ = kA′
 (A + B)′ = A′ + B′
 (AB)′ = B′A′
Chapter 4: Determinants
In the previous chapter, we found that we can express the system of algebraic equations in the form of matrices. Proceeding further, we will learn about determinants having an order of 1, 2 and 3.
Later, we will delve deeper into this chapter and discuss various properties of determinants. The key learning of this chapter will include topics such as minors, cofactors, and applications of determinants. Nevertheless, determinant is one of the most scoring chapters of NCERT class 12 maths.
Topics
 Determinant
 Properties of Determinants
 Area of a Triangle
 Minors and Cofactors
 Adjoint and Inverse of a Matrix
 Applications of Determinants and Matrices
Important formulas of Determinants
1. Determinant of a matrix A = [a_{11} ]_{1× 1} is given by a_{11}  = a_{11}
2. The value of determinant of a matrix A can be obtained by adding product of elements of a row with corresponding cofactors.
A = a_{11} A_{11} + a_{12} A_{12} + a_{13} A_{13}
3. A (adj A) = (adj A) A = A I, where A is a square matrix of order n
4. A^{1} = 1 (adj A) / A
5. If a_{1} x + b_{1} y + c_{1}z = d_{1}
a_{2}x + b_{2}y + c_{2}z = d_{2},
a_{3}x + b_{3}y + c_{3}z = d_{3},
Then these equations can be written as AX = B
6. Unique solution of equation AX = B is given by X = A^{–1} B, where A ≠ 0.
Chapter 5: Continuity and Differentiability
We have already studied the differentiation of several certain functions, including polynomial and trigonometric functions. The chapter5 continuity and differentiability will introduce you to its various core concepts.
Further, you will learn to differentiate inverse trigonometric, exponential, and logarithmic functions. There are two important theorems based on experiments performed by mathematicians Rolle’s theorem and the mean value theorem. 
Topics
 Continuity
 Differentiability
 Exponential and Logarithmic Functions
 Logarithmic Differentiation
 Derivatives of Functions in Parametric Forms
 Second Order Derivative
 Mean Value Theorem
Important formulas of Continuity and Differentiability
1. Sum/ Difference of continuous functions
If f and g are two continuous functions, then
(f ± g) (x) = f(x) ± g(x) is continuous
2. Product of continuous functions
If f and g are two continuous functions, then
(f . g) (x) = f(x) . g (x) is continuous
3. Quotient of continuous functions
If f and g are two continuous functions, then
(f/ g) (x) = f (x)/ g (x), (wherever g(x) ≠ 0) is continuous
4. Standard derivatives
 d/dx (sin^{1} x) = 1/ √1  x^{2}
 d/dx (cos^{1} x) =  1/ √1  x^{2}
 d/dx (tan^{1} x) = 1/ √1 + x^{2}
 d/dx (cot^{1} x) =  1/ √1 + x^{2}
 d/dx (sec^{1} x) = 1/ x√1  x^{2}
 d/dx (cosec^{1} x) =  1/ x√1  x^{2}
 d/dx (e^{x})= ex
 d/dx (log x) = 1/x
Chapter 6: Application of Derivatives
The concept of differentiation has its applications in various disciplines, for example, in engineering, science, social science etc. Having a prior knowledge on how to find the derivative of composite, exponential, inverse trigonometric, implicit, and logarithmic functions will allow you to solve questions of this chapter easily.
In this chapter, you will learn how the derivatives can be used to determine the rate of change of quantities, to find turning points on the graph etc. Finally, you will be able to find the approximate value of certain quantities using the derivatives.
Application of Derivatives is considered one of the most challenging chapters of this book. At times, you may get stuck in a few questions, but we have you covered with our NCERT class 12 maths solutions.
Topics
 Rate of Change of Quantities
 Increasing and Decreasing Functions
 Tangents and Normals
 Approximations
 Maxima and Minima
Important formulas of Application of Derivatives
1. If two variables x and y are varying with respect to another variable t, i.e., if x = f (t) and y = g (t), then by the Chain Rule
dy/dx = (dy/ dt) / (dx/dt), if dx/ dt ≠ 0
2. A function f is said to be
a). Increasing on an interval (a,b) if
x_{1} < x_{2 }in (a, b) ⇒ f(x_{1}) < f(x_{2} ) for all x_{1} , x_{2} ∈ (a, b)
b). Decreasing on an interval (a,b) if
x_{1} < x_{2} in (a, b) ⇒ f(x_{1}) > f(x_{2} ) for all x_{1} , x_{2} ∈ (a, b)
c). Constant on an interval (a,b) if
F (x) = c for all x ∈ (a, b), where c is a constant
3. The equation of the tangent at (x_{0}, y_{0}) to the curve y = f (x) is given by
y  y_{0} = dy/dx]_{x0, y0 }(x  x_{0})
4. Equation of the normal to the curve y = f (x) at a point (x_{0}, y_{0}) is given by
y  y_{0} = 1 (x x_{0}) / (dy/ dx)] _{x0, y0}
5. Assume y = f (x), ∆x be a small increment in x and ∆y be the increment in y corresponding to the increment in x, i.e.,
∆y = f (x + ∆x)  f (x)
Then dy is given by
dy = f’ (x)dx or
dy = (dy/ dx) ∆x
Chapter 7: Integrals
One can say that chapter7 integration is centred on the concept of differentiation. Integration, also known as integral calculus, will allow you to define and calculate the area of the region bounded by the graphs of the functions.
Further, you will also learn a few standard integral formulas and formula that gives the antiderivatives. In a few situations, where the degree of one polynomial is greater than the degree of another polynomial, then you will have to find the integral using partial fractions. While in questions where two functions are given, you will have to integrate by parts.
As per the past trend, this chapter continued to have the highest weightage among all the chapters. It is recommended to solve as many questions as you can from this chapter to excel in the class 12 maths board exam.
Topics
 Integration as an Inverse Process of Differentiation
 Methods of Integration
 Integration by Partial Fractions
 Integration by Parts
 Definite Integral
 Fundamental Theorem of Calculus
 Evaluation of Definite Integrals by Substitution
 Some Properties of Definite Integrals
Important formulas of Integrals
1. Indefinite integrals
Assume d/ dx F(x) = f (x), then
∫ f (x) dx = F (x) + C
2. Properties of indefinite integrals
 ∫ [f (x) + g(x)] dx = ∫ f (x) dx + ∫ g (x) dx
 For any real number k, ∫ k f (x) dx = k ∫ f (x) dx
3. Some standard integrals
 ∫ x^{n} dx = {x^{(n +1)}/ (n + 1)} + C, n ≠ 1
 ∫ cos x dx = sin x + C
 ∫ sin x dx =  cos x + C
 ∫ sec^{2} x dx = tan x + C
 ∫ cosec^{2} x dx =  cot x + C
 ∫ sec x tan x dx = sec x + C
 ∫ cosec x cot x dx =  cosec x + C
 ∫ dx/ √1  x^{2} =  sin^{1} x + C
 ∫ dx/ √1 + x^{2} =  cot^{1} x + C
 ∫ dx/ 1 + x^{2} = tan^{1}x + C
 ∫ dx/ 1 + x^{2} =  cot^{1} x + C
 ∫ a^{x} dx = a^{x} / log a + C
 ∫ e^{x} dx = e^{x} + C
 ∫ dx/ (x √x^{2 } 1) = sec^{1} x + C
 ∫ dx/ (x √x^{2}  1) =  cosec^{1} x + C
 ∫ (1/x) dx = log x + C
4. Integration by partial fractions
 (px + q) / (x  a) (x  b) = [A/ (xa)] + [B/ (xb)], a ≠ b
 (px + q) / (x  a)^{2} = [A/ (xa)] + [B/ (xa)^{2}]
 (px^{2} + qx + r)/ (x  a) (x  b) (x  c) = [A/ (xa)] + [B/ (xb)] + [C/ (xc)]
 (px^{2} + qx + r)/ (x  a)^{2} (x  b) = [A/ (xa)] + [B/ (xa)^{2}] + [C/ (xb)]
 (px^{2} + qx + r)/ (x  a) (x^{2} + bx + c) = [A/ (xa)] + [(Bx + C)/ (x^{2} + bx + c)]
5. Integration by substitution
 ∫ tan x dx = log  sec x  + C
 ∫ cot x dx = log  sin x  + C
 ∫ sec x dx = log  sec x + tan x  + C
 ∫ cosec x dx = log  cosec x  cot x  + C
6. Integrals of some special functions
 ∫dx/ x^{2} a^{2} = (1/2a) log (x  a)/ (x + a) + C
 ∫dx/ (a^{2} x^{2}) = (1/2a) log (a + x)/ (a  x) + C
 ∫dx/ (a^{2} + x^{2}) = (1/ a) (tan^{1 }x/ a) + C
 ∫dx/ √(x^{2}  a^{2}) = log  x + √ x^{2}  a^{2} + C
 ∫dx/ (a^{2} x^{2}) = sin^{1} (x/a) + C
 ∫dx/ (a^{2} + x^{2}) = log  x + √ x^{2} + a^{2} + C
7. Integration by parts
 ∫ f_{1} (x). f_{2 }(x) dx = f_{1} (x) ∫ f_{2} (x) dx  ∫ [d/ dx (f_{1} (x). ∫ f_{2} (x) dx] dx
 ∫ e^{x} [f (x) + f’ (x)] dx = ∫ e^{x} f(x) dx + C
Chapter 8: Application of Integrals
In previous classes, you learnt to calculate areas of various geometrical figures, including circles, rectangles, triangles, and trapeziums. However, those cannot be applied to calculate the areas enclosed by curves. To find the areas of such shapes, you will need some concepts of integral calculus.
This chapter becomes automatically easier when you have already mastered the previous chapter. You can look into our NCERT class 12 maths solutions if you fail to find an accurate answer for any question of the textbook.
Topics
 Area under Simple Curves
 Area between Two Curves
Important formulas of Application of Integrals
1. The area of the region covered by the curve y = f (x), xaxis and the lines x = a and x = b (b > a) is represented by the following formula
Area = ∫_{a}^{b} ydx = ∫_{a}^{b} f (x) dx
2. The area of the region covered by the curve x = ɸ (y), yaxis and the lines y = c and y = d is represented by the following formula
Area = ∫_{c}^{d} x dy = ∫_{c}^{d }ɸ (y) dy
Chapter 9: Differential Equations
Chapter9 Differential Equations involves the combined use of formulas from differentiation and integration. Previously, you learnt to differentiate a given function and find the antiderivatives using Integral Calculus.
In this chapter, you will learn some basic concepts of differential equations, the formation of differential equations etc.
Topics
 Basic Concepts
 General and Particular Solutions of a Differential Equation
 Formation of a Differential Equation
 Methods of Solving First Order, First Degree Differential Equations
Chapter 10: Vector Algebra
In physics, we first heard of the concept called vectors. We remember that a vector quantity represents magnitude as well as the direction. Examples of vector quantities are displacement, acceleration, velocity, momentum, force, etc.
In this chapter, you will learn the concept of vector quantities from scratch. During your study, you will learn the basics of vectors, various operations on vectors, and their algebraic and geometric properties.
Topics
 Some Basic Concepts
 Types of Vectors
 Addition of Vectors
 Multiplication of a Vector by a Scalar
 Product of Two Vectors
Chapter 11: Three Dimensional Geometry
3D Geometry is to vectors what application of integrals is to integration. Having said that the concepts that you learned in the previous chapter will come to play in this chapter.
In threedimensional geometry, you will study the direction cosines and direction ratios of a line joining two points, angles between two lines, etc. Other important topics include study about a line and a plane, shortest distance between two skew lines and distance of a point from a plane.
Topics
 Direction Cosines and Direction Ratios of a Line
 Equation of a Line in Space
 Angle between Two Lines
 Shortest Distance between Two Lines
 Plane
 Coplanarity of Two Lines
 Angle between Two Planes
 Distance of a Point from a Plane
 Angle between a Line and a Plane
Important formulas of Three Dimensional Geometry
1. Direction cosines of a line joining two points P (x_{1}, y_{1}, z_{1}) and Q (x_{2}, y_{2}, z_{2}) are
(x_{2}  x_{1})/ PQ, (y_{2}  y_{1})/ PQ, (z_{2}  z_{1})/ PQ
Where PQ = √ (x_{2}  x_{1})^{2} + (y_{2}  y_{1})^{2} + (z_{2}  z_{1})^{2}
2. If a, b and c are the direction ratios and l, m and n are the direction cosines of a line then
 l = a/ √ a^{2} + b^{2} + c^{2}
 m = b/ √ a^{2} + b^{2} + c^{2}
 n = c/ √ a^{2} + b^{2} + c^{2}
3. Angle between the two lines whose direction cosines are (l_{1}, m_{1}, n_{1}) and (l_{2}, m_{2}, n_{2}) is given by
Cos θ =  (a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2}) / (√ a_{1}^{2} + b_{1}^{2} + c_{1}^{2}. √ a_{2}^{2} + b_{2}^{2} + c_{2}^{2})
4. Equation of a line through a point (x_{1}, y_{1}, z_{1}) and have direction cosines l, m and n can be represented as
(x  x_{1})/ l = (y  y_{1})/ m = (z  z_{1})/ n
5. Cartesian equation of a line passing through two points (x_{1}, y_{1}, z_{1}) and (x_{2}, y_{2}, z_{2}) can be represented as
(x  x_{1})/ (x_{2}  x_{1}) = (y  y_{1})/ (y_{2}  y_{1}) = (z  z_{1})/ (z_{2}  z_{1})
6. If equations of two lines are given as
(x  x_{1})/ l_{1} = (y  y_{1})/ m_{1} = (z  z_{1})/ n_{1} and (x  x_{1})/ l_{2} = (y  y_{2})/ m_{2} = (z  z_{2})/ n_{2} then
Acute angle between the two lines is Cos θ = l_{1} l_{2} + m_{1}m_{2} + n_{1}n_{2}
Chapter 12: Linear Programming
You should be wellversed with the systems of linear equations and their applications in daytoday problems before you start this chapter. In class 12, you will learn to apply the systems of linear inequalities to solve reallife problems. Linear programming problems has its applications in commerce, industry, management science etc.
Topics
 Linear Programming Problem and its Mathematical Formulation
 Different Types of Linear Programming Problems
Chapter 13: Probability
In earlier classes, you have learnt the fundamental concepts of probability. Also, you came to know about how to establish equivalence between the axiomatic theory and the classical theory of probability. In class 12, you will get to know the important concept of the conditional probability of an event given that another event has occurred.
Further learning of the chapter will be centred on Bayes’ theorem, multiplication rule of probability, and independence of events.
Topics
 Conditional Probability
 Multiplication Theorem on Probability
 Independent Events
 Bayes' Theorem
 Random Variables and its Probability Distributions
 Bernoulli Trials and Binomial Distribution
Important formulas of Probability
1. Theory of total probability
P(A) = P(E1 ) P (AE1 ) + P (E2 ) P (AE2 ) + ... + P (E_{n }) P(AE_{n })
2. Bayes’ theorem
P (E_{i}  A) = [P (E_{i}) P(AE_{i})] / ∑ P (E_{j}) P(AE_{j})
3. Standard deviation of the random variable X
𝛔_{x} = √ Var (X) = √ ∑ (x_{i}  𝜇)^{2} p (x_{i})
CBSE Class 12 Maths Syllabus 201920
As per the latest 12th Class Maths Syllabus, below we have provided the list of units and their chapters.
S.No. 
Name of Unit 
Name of Chapter 
1 
Relations & Functions 

2 
Algebra 

3 
Calculus 

4 
Vectors & 3D Geometry 

5 
Linear Programming 

6 
Probability 

CBSE Paper Pattern for Class 12 Maths 2020
The Central Board of Secondary Education has introduced a few major changes in the CBSE Paper Pattern for Class 12 Maths. As per the revised CBSE Syllabus, students will now face questions having analytical and reasoning perspective. This step will allow students to focus on understanding the concepts instead of rote learning.
Section 
Weightage of Question 
Number of Questions 
A 
1 (x 20) 
20 
B 
2 (x 6) 
6 
C 
4 (x 6) 
6 
D 
6 (x 4) 
4 
Total 
80 Marks 
36 
Best Reference Books for CBSE Class 12 Maths
Starting your preparation from Maths NCERT Class 12 book is a common practice for all. It can help you score over 70 marks easily without putting extra efforts. However, if you wish to score over 80 marks then we highly recommend you to practice questions from Class 12 Maths reference books. The list of best books for Class 12 Maths is tabulated below.
Best Books for Class 12 Maths 
Chapterwise Solutions 
RD Sharma Class 12 Maths 

RS Aggarwal Class 12 Maths 
CBSE Class 12 Maths Marking Scheme (Chapterwise)
Before starting the Maths exam preparation, you should go through the CBSE marking scheme for Class 12 Maths, which is tabulated below.
S No 
CBSE Class 12 Maths Topics 
Allocation of Marks 
1 
Calculus 
44 
2 
Vector & Three Dimensional Geometry 
17 
3 
Algebra 
13 
4 
Relations & Functions 
10 
5 
Probability 
10 
6 
Linear Programming 
6 
List of chapters related to Algebra in Class 12 NCERT Maths
The use of algebraic expressions and equations is prevalent in Class 12 Maths textbook. Check the list of chapters along with a brief explanation that involves the use of algebra in solving questions.
Chapters involving Algebra 
Details 
Inverse Trigonometric Functions 
The knowledge of algebra comes into use when applying certain formulas. For example 2tan1x = sin1[2x/ (1+x2)] = cos1[(1x2)/ (1 + x2) 
Matrices & Determinants 
Finding the area of the triangle, the value of a determinant requires you to solve algebraic expressions or equations. 
Continuity & Differentiability 
As this chapter involves the application of inverse trigonometric functions and laws of exponents, the use of algebra is inevitable. 
Integrals 
Some instances where you solve algebraic equations or expressions in Integrations are finding the integral by partial fractions and finding the integrals through special functions. 
Vector Algebra 
To understand this chapter, you must have a good command over algebra. The types of questions asked in this chapter include the addition of vectors, multiplication of a vector by a scalar, and product of two vectors. 
Three Dimensional Geometry 
Whether you have to find the shortest distance between two lines or coplanarity of two lines, you are going to solve all questions of this chapter algebraically. 
Benefits of CBSE Class 12 Maths NCERT Solutions
Students often panic before the Maths exam and emphasize more on reference books instead of NCERT Books. They are unaware that the most effective study resource is lying in their cupboard. Coupled with our free NCERT Solutions, you have all it takes to score high marks in CBSE Class 12 Maths exam.
Apart from it, there are various other benefits associated with Class 12 Maths NCERT Solutions that we have listed below.
 Whether a pending assignment, an upcoming unit test or CBSE Class 12 Maths Board exam, our NCERT Solutions for Class 12 Maths can help you do a quick revision.
 These solutions are explained in a stepbystep manner that makes them easier to understand.
 You can rely on Goprep’s NCERT Solutions as our experts have years of experience as subject mentors.
 Ask doubts from our experts by uploading the screenshot of the question by clicking on the ‘camera’ icon present on the homepage.
 When you read these solutions, you will end up covering all the core concepts related to a topic.
Frequently Asked Questions
 From where can I get free NCERT Solutions for Class 12 Maths?
You are currently at the same platform from where you can read Class 12 Maths NCERT Solutions for freeofcost. Goprep is an online education platform which caters to the needs of students studying in Class 6 to 12. Apart from NCERT textbook solutions, you can also access the following study material.
 How do I prepare for Class 12th Maths Board exam?
You can only achieve the desired result in Mathematics when you start practicing the subject on a daily basis from the beginning of the session. Also, you must have mastered the concepts covered in previous classes so that you can implement them while solving NCERT textbook questions.
Nevertheless, our experts have prepared a smart preparation strategy for students appearing in CBSE Class 12 Maths Board exam here.
 Prepare a pocketsize notebook and start jotting down important Maths formulae, definitions, graphs, etc.
 Practice all questions and examples of each chapter given in the NCERT Class 12 Maths book.
 Refer to Goprep’s NCERT Solutions if you are stuck in any question or do a quick revision.
 You may practice questions from reference books like RD Sharma, RS Aggarwal, etc. only after you finish practicing all questions of NCERT book.
 Finally, practice CBSE Board Class 12 question papers of the previous year to test your knowledge.
 Does CBSE Class 12 Maths Board exam contain questions from NCERT only?
The Board does not give all the questions from NCERT textbook. As per the trend of the last few years, 2030 marks questions were easy to solve which is entirely formulabased. Then come questions of 3040 marks that require a good command over the NCERT textbook. Finally, there are 2030 marks questions that are given from either NCERT Maths Exemplar or RD Sharma.
 Is Class 12 Maths NCERT book enough for CBSE Board?
If you have a good command over NCERT textbook, you may not require any additional study material to do the exam preparation. In case you complete the CBSE Class 12 Maths NCERT syllabus a few weeks before, picking a reference book will be a great idea. Alternatively, you may attempt CBSE previous year papers to boost your confidence level.
 How to score 100/100 marks in CBSE Class 12 Maths exam?
 The first and foremost, you must have a strong base in Mathematics.
 You should develop a habit of practicing questions of different level of difficulty daily.
 Solve as many extra questions as you can from NCERT Class 12 Maths Exemplar or RD Sharma, previous year Maths papers, etc.
 Take reference from our Class 12 Maths NCERT Solutions whenever you come across a doubt.
 Be consistent and do not deviate from your end goal.