combination formula

In the previous post we have discussed about Differentials Calculus and In today's session we are going to discuss about combination formula. Combination is a technique we use for the purpose of counting the number of ways we can have probable arrangements for the given events. In probability also we would find the use of combination a lot. The combination formula is written as follows:
If we have N events and we wish to select b possible events from N, then we would write it as:
^NC _b = N! / b! (N – b)!
To solve the formula for combination we must have knowledge of how to expand a factorial of any number. Let us consider an example of combination as follows:
Example: In how many ways we can select 2 black and 4 red balls from a container which contains 10 black and 10 red balls.
Solution: It is been given that the container contains 20 balls in total out of which 10 are black and the rest 10 are red. To select 2 black balls from the container we must use the combination formula for 10 black balls. So, the number of ways we can choose two black balls out of 10 is equal to ¹⁰ C ₂. Similarly, the number of ways to choose 4 red balls from the 10 red balls is equal to ¹⁰ C ₄. So, finally we get the total number of ways of selecting 2 black and 4 red balls from the container of 10 black and 10 red balls as:
¹⁰C ₂ + ¹⁰ C ₄ = 10! / 2! (8)! + 10! / 4! (6)! = 10 x 9 /2 + 10 x 9 x 8 x 7 /24 = 45 + 210 = 255 ways.
Next we discuss the concept of how to calculate density. Density can be calculated by using a simple formula: Density = Mass /Volume. These concepts are important from the perspective of icse syllabus for class 8.

Differentials Calculus

Differentials Calculus in mathematics is a part of calculus which has many important uses and can be used to derive quantities like change of rate, slope of a tangent at any point on the curve, maximum and minimum values of function etc. For instance, suppose we are given a continuous function whose slope, critical point and max or min values are to be calculated, we use application of differentiation. The first differential is used for the purpose of finding the rate change and the critical points whereas on differentiating the 1st differential again we get the max & min values.

Let us consider an example of differential calculus as follows: Suppose we have a function h (x) = 5 x⁵, then its first derivative would give us h’ (x) = 25 x⁴. Substituting h’ (x) = 0 we get x = 0. Thus the critical point is obtained at x = 0. In case the h’ (x) would have resulted in a fixed value; we say that there exist no min or max values for the function. In our example we are not getting any fixed value. Next we differentiate the 1st derivative again to get the maximum or minimum values. If the h’’ (x) comes – ve, then it is maximum value and for h’’ (x) + ve we get minimum value. In case h’’ (x) = 0 the value resembles an inflection point, and can be mistreated. In our example we would get h’’ (x) = 100 x3. Next we find out the maximum or the minimum value for the function.

Next we study how to add fractions with unlike denominators: It is a very simple concept and for solving such problems we take the LCM of the denominators. For instance: 12 /13 + 11 /10 = (120 + 143)/130 = 263/130. These concepts are important and are discussed in the icse sample papers in  detail. In the next session we will discuss about combination formula. 

Identity matrix

Matrix can be considered as an array where elements are stored in the form of rows and columns. Here elements in matrix can be considered as any type like algebraic expression, symbols or numbers. Matrix can be treated as a useful way for representing the linear transformation in a simple manner. Values in a matrix can be represented as shown below.

Suppose we have some values like 1, 2, 3, 4, 5, 6, 7, 8 and 9.

We have a matrix of 3 * 3 size then it can be represent above given values in form of matrix as:

 1  2  3

 4  5  6

 7  8  9

Now we will discuss about one of the types of matrix which is known as identity matrix. According to the definition of Identity matrix we can say that it is a kind of matrix where I A = A and A I = A. If we want to simplify the definition of identity matrix then we can say that it is square matrix which has a value 1 in diagonal position of matrix from top left to down right and all remaining position carry value zero into it. Sometimes this matrix is also known as unit matrix. How a identity matrix looks like is given below:

                             1  0  0

Identity Matrix =          0  1  0

                             0  0  1

Some properties of identity matrix are described below:

A ) When unit matrix includes the product of two square matrix then it can be said that it generates the inverse of one another.

B ) When unit matrix is multiply by itself then it generates the same output.

C ) This kind of unit matrix has a positive definite square root value.

In mathematics, the concept of Math Order of Operations defines a priority level of any operation that describes which operation should be performed first when any mathematical expression carry multiple operations.

Free download cbse books are available on various websites. In the next session we will discuss about Differentials Calculus.

Mathematical Induction

Mathematical induction is a process which can be applied to set of general statements for sets of positive integers or their connected sequences.

In this we find either a given statement is true for entire natural numbers or not. As we discussed that in the case of natural numbers we will include only positive numbers. This should not be interpreted as a form of inductive reasoning. The easiest form of induction characterizes that either a statement that includes a natural number 'n' holds for all values of 'n' is true or not.

It can be understood with help of an example:

Example: Show that sum of first 'n' odd integers is n²?

It can be written as 1 + 3 + 5 + 7 + ... + (2n - 1) = n² for all positive integers.

Let’s have a proof of above expression: First find the value of A (n). It is equals to A (n): 1 + 3 + 5 + 7 + ... + (2n - 1) = n², then in basic step we have to show A (1) is true. So it can be written as: Trivial: 1 = 1².

In Inductive step we need to show that A (n) is true for all 'n' therefore A (n + 1) is also true for all 'n'. Let A (n) is true so 1 + 3 + 5 + 7 + ... + (2n - 1) = n²,

Also write it as A (n + 1): 1 + 3 + 5 + 7 + ... + (2n - 1) + (2n + 1) = (n + 1)² follows:

 1 + 3 + 5 + 7 + ... + (2n - 1) + (2n + 1) = (n + 1)²,

It can also be written as:

n² + (2n + 1) = (n + 1)², this is the proof of mathematical induction.

Precipitation Reaction is used in formation of solid in a solution or inside another solid.

Cbse syllabus for class 11 is available online..

 

Slope

In the previous post we have discussed about Proof of bay s theorem and In today's session we are going to discuss about,Slope of a line can be defined as ratio of change in vertical axis to change in horizontal among two points on a line. If the slope of line is undefined or not defined then it is known as vertical line and if the slope of line is given as 0, then it is known as horizontal line. Formula to find the slope equation is given as:

                   y = mx + c,

Here value of ‘m’ stands for slope of line and y- intercept is given by ‘c’. It is also described by using the formula given below:

m = k₁ – k₂ / l₁ – l₂,

Here ‘m’ stands for slope of line and a₁, a₂ are the points defined on y- axis and b₁, b₂ are the points defined on x- axis. Above equation can also be written as:

     m = k₂– k₁ / l₂ – l₁,

In this gradient of a line is also defined which is denoted by the given formula:

         m = tan θ,

Let’s take an example. It will be clear with help of an example:

Example 1: - Calculate slope of the line segment that join the points (4, -7) and (-7, 4)?

Solution: - As we see above that it is a line segment that join the points (4, -7) and (-7, 4). As we know that formula to find the slope is given as:

m = k₂ – k₁ / l₂ – l₁, here value of k₁ = 4, l₁ = -7 and k₂ = -7, l₂ = 4

Now put given values in formula to find its value. On putting value in formula to get result.

m = -7 – 4 / 4 – (-7), on further solving we get:

m = - 11 / 11,

So here we get the value of 'm' is -1. In this way we can find out the value of 'm'.

Mann Whitney Test can be used to see either two independent samples of observations are drawn from same distributions.

To prepare for 10 th board exams focus on cbse sample papers for class 10.

Proof of bay s theorem

In mathematics, we will study different theorem. Here we will understand the concept of bay s theorem. Bay’s theorem can have two distinct interpretations. It is an important concept of Bayesian statistics and has different properties in the field of science and engineering. Formula that is used to solve the probability, that name was given after the 18 th – century by the great scientist British mathematician Thomas bayes. Now we talk about the formula used in Bay’s theorem which is given below :
K (I / J) = K (I ∩ J) / K (J) = K (I) * K (J | I) / K (J)
Now we will understand the proof of bay’s theorem: Suppose we have X and Y_j be two sets. Then the conditional probability requires that:
P (X ∩ Y_j) = P (X) P (Y_j | P), here the symbol ‘∩’ represented as intersection (‘and’) and also said :
P (X ∩ Y_j) = P (Y_j ∩ X) = P (Y_j) P (X | Y_j), therefore it can be written as:
P (Y_j ∩ X) = P (Y_j) P (X | Y_j) / P (X), now assume Z = ∪_{i = 1}ⁿX_i, so X_i is an event in Z and X_i ∩ X_j = ⱷ for i ≠ j, then we can write it as:
X = X ∩ Z = X ∩ (∪_{i = 1}ⁿX_i) = ∪_{i = 1}ⁿ(X ∩ X_i),
P (X) = P (∪_{i = 1}ⁿ(X ∩ X_i)) = ∑_{i = 1}^N P (X ∩ X_i), it can also be written as:
P (X) = ∑_{i = 1}^N P (X_i) P (X | X_i),
P (X_i | X) = P (X_i) P (X | X_i) / ∑_{i = 1}^N P (X_i) P (X | X_i) this is the proof of bay’s theorem.
Paper Chromatography is technique that is used for separating and identifying mixtures that can be colored, especially pigments. Before entering in the board exam please prefer cbse sample papers. It is helpful for examination point of view.

definition of a function

In the previous post we have discussed about How to Find the Domain of a Function and In today's session we are going to discuss about definition of a function. In this blog we will discuss the definition of a function. Function is used to show relationship among set of inputs and set of outputs in which every value of input is related to exactly one value of output. In other words a relation defined from I to J such that a sub set of I * J is called as function from I to J. Let's us understand the concept of function and its types. There are different types of function which are given as:

One – one function

Many one function

Onto function

Now we will have small introduction about all its types.

One – one function (it is also called as injection function): - A function f: I → J is said to be one – one function if every input value of element 'I' has different image in 'J'. So it can be written as:

f : I → J is one – one if value of 'i' not equal to 'j'. (i ≠ j) → f (i) ≠ f (j) for all ij Ԑ I.

Many one function: - A function f :I → J is said to be many one function if two or more elements of set 'I' have same images in 'J'. In mathematical form it can be written as:

f: I → J is a many one function if there exist a, b Ԑ I such that a ≠ b but f (a) = f (b).

Onto function: - A function f: I → J is said to be onto function or it is also said to be 'surjection' if every value of element 'J' is image of some element of 'I' that is if f (I) = J, and range of 'f' is co – domain of function 'f' or in other words elements of 'J' has no pre – image in element 'I'. This is all about types of functions.

We will study Primary Structure of a Protein in chemistry. Primary structure is join together by covalent or peptide bonds. cbse sample paper for class x is important for class 10 th student.

How to Find the Domain of a Function

Hello friends, in mathematics we will study about the range and domain of function. Here we will discuss how to find the domain of a function. Function can be defined as a tool used to demonstrate the relationship between values. Now we will see how to find the domain of a function. Generally, functions are defined as f (p) where ‘p’ is the value you assign it. Like, f (p) = p / 2 ('f' of 'p' is divided by 2) is a function, because for every value of 'p' you get another value 'p / 2. If we put different values of function 'p'. First of all if we put value of 'p' as 2 then we get:

⇒f (2) = 1,
⇒f (4) = 2.
To find domain of function it is necessary to learn what the domain of a function is. When we select the entire x - coordinates values in the given function, then these x- coordinates values are known as domain of a function. In same way, the possible ‘y’ coordinate values are said to be the range of a function. Suppose we have some values (6, -5), (-9, 4), (11, -9), (-15, 1), then domain of function can be found as:

The domain of a given function = 6, -9, 11, -15.

Range is all ‘y’ coordinate values, (know more about Domain of a function, here)

Range = -5, 4, -9, 1. Now we will discuss how to find domain of a function in details. We need to follow some steps to find domain of a function:

Step 1: First of all we have to assume a function that contains ‘x’ and ‘y’ coordinates.

Step 2: As we know the domain of a function is all ‘x’ coordinates values.

So, we can say that in a function if values of ‘x’ and ‘y’ coordinates are known then we can easily find the domain and range of a function. This is all about the domain of a function.

The Specific Heat Capacity of Water is 1 calorie/gram °C = 4.186 joule/gram °C that is higher than any other common substance. If we solve cbse sample papers for class 10 then we will achieve good marks in the 10^th board exam.

tangent line approximation

In the previous post we have discussed about Newtons Law of Cooling Differential equation and In today's session we are going to discuss about tangent line approximation. The tangent line approximation in mathematics may be defined as approximating the value of any function that is hard to calculate with the help of the value of another function that is nearest to it.

To have more precise understanding of the tangent line approximation, let us take a very simple example. Consider a square root function f (x) that is f (x) = √x.

Now if we take x equal to 9 then f (9) = √9 which comes out as 3 and is very easily calculated. However if we consider x = 8.9 then f (8.9) = √8.9 and this cannot be calculated easily. Thus for f (8.9) = √(9 – 0.1), the value can be approximated with the help of the value which we got from f (9) = √9 = 3 ( since 0.1 is very small ).

Thus we can say that if the value of f (b + h) is hard to find whereas f ( b ) can be very easily calculated where | h | is very small (here the mod is taken as we need positive value of h) then the value of f (b+h) can be approximated with the help of the value of f (b). (know more about tangent line approximation, here)

Since in the example given above the value of h is equal to -0.1 thus the value of the function f can be approximated at the point (b+h) with the help of the tangent line to the graph of function f at the point b when | h | is very small.

In order to get more help on topics: tangent line approximation, Transcription and Translation and cbse paper for class 9, you can visit our next article.

Newtons Law of Cooling Differential equation

In the previous post we have discussed about Derivative of secx and In today's session we are going to discuss about Newton's Law of Cooling Differential equation. Hello friends I hope you have well underst0ood all the previous topic , today we are going to discuss a new topic Newton s Law Of Cooling Differential Equation. As we all know that Newton’s law of motion are very popular to all of us, but very few people are aware of Newton’s law of cooling, according to this law , if we put any body in air then its temperature decreases or increases with its surroundings. As we all know that the cooling rate of any body depend on its surroundings, on this same fact Newton’s law was given. As this law is a very old law, so people are not having any knowledge of heat, so people have to accept this law without knowing that weather Newton done this law practically or not. In the same time when Newton law was introduced, one more law was there called as Stefan’s law, according to this law the energy radiated by a body in atmosphere is directly proportional to the fourth power of its temperature. There is a condition called as condition of thermal equilibrium in which Newton Law and Stefan’s law are same, there is one difference between Newton Law and Stefan Law is Newton Law always Deals with the internal temperature while Stefan law deal with temperature of body. (know more about Differential equation, here)

We can get the Newton’s Law Of Cooling Equation by some simple calculation but before we need to have knowledge of some terms like Heat Conductivity, area of martial and thickness of wall.

We will denote heat conductivity by K, thickness by t and area by A, so required equation for cooling law is,

dQ / dt = KA(θ – θo) / t.

Here θ is the temperature of outer surface and θo is the temperature of inner surface.

If you have 10th Cbse Sample Paper. Go through Transition Metal topic, it is a important topic in mathematics.

Derivative of secx

In the previous post we have discussed about cosine law and In today's session we are going to discuss about Derivative of secx. Trigonometric can be defined as the relationship between the angles and sides of a triangle. In the trigonometric there are different types of function and derivative of functions. Here we will study the different types of derivatives. Derivatives of trigonometric  function are mention below:

d / da sin (a) = cos (a)	d / da cos (a) = - sin (a)
d / da tan (a) = sec2 (a)	d / da csc (a) = - csc (a) cot (a)
d / da sec (a) = sec (a) tan (a)	d / da cot (a) = - csc2 (a)

(know more about Derivative, here). These above mention are the different types of derivatives of trigonometric functions. Now we will find the Derivative of secx. We are earlier studies the derivative of sec x is sec (x) tan (x). Now see the prove of Derivative Of Secx. To find the derivative of sec x first we write the sec x in the derivative form:

Prove = d / dx sec = sec x tan x;

We know that sec x = 1 / cos x;

We can also write in place of sec x as:

= d / dx [1 / cos x]

We can solve it by u / v methods:

u / v = u d / dx (v) – v d / dx u / u2

So we can write the above expression as:

= [cos x d / dx (1) – 1 d / dx cos x] / cos2 x;

If we find the derivative of 1 and cos x we get:

= [cos x (0) – 1 (- sin x)] / cos2x;

If we solve we get:

= [0 + sin x] / cos2 x;

On further solving we get:

= Sec x tan x.

So the proof of sec x is sec x tan x.

This is how we can solve the derivative value. Centripetal Acceleration Formula is used to find the speed along to a given circular path and its radius is directed along to the center. icse sample papers 2013 is very helpful for exam point of view.

cosine law

Hello friends, In the previous post we have discussed about Derivative of cot and today we are going to discuss a very important topic cosine law, as we are now familiar with trigonometric parameters. All the parameters have their specific role in trigonometry and we use all the parameters according to our need. As we well know that the six parameters are sin, cos, tan, sec, cot and cosec. As we well know that we can apply all these law to a triangle and we also know that any triangle consists of three angle and three sides, now if we talk about cosine law then  if we are having the value of  two sides of a triangle and we are also having the value of the angle opposite to the side of triangle which we want to measure, suppose if a triangle consists of three sides as a ,b and c and if the value of  b and c are given and we are asked to find side a by cosine law then we must have the value of angle A.  We can write cosine law as,

a2 = b2 + c2 – 2bccosA

Here a, b and c are sides of the triangle and A is the angle between them.

Now we will see an example, in which we will apply cosine law

Example:  A triangle is having sides as b= 2 cm and c = 3cm and angle A = 60 degree find the side a by cosine law?

Solution: as we know by cosine law,

a2 = b2 + c2 – 2bccosA

Now we will put our values in this,

a2 = 4 + 6 – 2 *2*3 *1/2

a2 = 10 -6

a2 = 4

a = 2

This is the required solution of the given problem by cosine law.

 If you are having cbse class 10 sample papers then go through First Derivative Test, it is an important topic in mathematics.

Derivative of cot

A branch of mathematics, which represents the relationship among the angles and sides of a triangle, is said to be trigonometry. Different types of function are explained in the trigonometry; here we will discuss the different types of derivatives. Derivatives of trigonometric function are as follows:

⇨ d / da sin (a) = cos (a);

⇨ d / da cos (a) = - sin (a);

⇨ d / da tan (a) = sec2 (a);

⇨ d / ds csc (a) = - csc (a) cot (a);

⇨ d / da sec (a) = sec (a) tan (a);

⇨ d / da cot (a) = - csc2 (a);

These are all different types of derivatives of trigonometric functions. Here we will see the Derivative of cot a. Let’s discuss the prove of derivative of Cot a. First we write the cot a in the derivative form:

Proof = d / da cot a = - csc2 a; we can also write the cot a as:

⇨ Cot a = 1 / tan a;

We can also write in place of cot a as:

= d / da [1 / tan a]

We can solve it by u / v methods:

u / v = [u d / dx (v) – v d] / dx u / u2;                         

Put the expression in this method so that we can easily find the solution.

Now, we can write the above expression as:

= [tan a d / da (1) – 1 d / da tan a] / tan2 a;

 If we find the derivative of 1 and tan a, we get:

= [tan a (0) – 1 (sec2 a)] / tan2 a;

If we solve we get:

= [0 – sec2 a] / tan2 a;

On further solving we get:

= - csc2 a.

There are different types of methods to Solving Multistep Equations. To get more information about the multistep equation then prefer icse board syllabus and In the next session we will discuss about cosine law.

Ellipse Equation

An ellipse can be defined as a closed curve on a plane which can be obtained from intersection of a cone onto a plane. In the standard definition we can say that an ellipse is a curved line that creates closed shape in which summation of distances from two focus points to all other points on the line are constant. We can describe the circle as an example of ellipse, in the case when it is squashed into an oval. In the simple mean we can define the ellipse by the distance of two focus point. In the case select any on ellipse then sum of the distance to the focus point is constant.
Ellipse is a part of geometrical mathematics which also has the properties like other geometrical shape. Like ellipse has center, major and minor axis, focus point, circumference, area, chord, tangent and secant property. Here we are going to discussing about the ellipse equation.
Ellipse equation means to say to represent the concept of ellipse in the form of equation. In the form of equation ellipse can be define as a 2-demensional closed curve which can be represented as:
                                   (p – r)² / a² + ( q – s)² / b² = 1
In the above given ellipse notation r, s, a and b can be consider as a real numbers, in which a and b are the category of positive numbers.  (know more about Ellipse, here)
In the general form an ellipse equation can be represented as below given format:
  Pa² + Qb² + Ra + Sb + e = 0
There are some of the terms are describe below  which is related to an ellipse equation:
focus :  sometime this can be refer as foci point which ha sthe nature of fix points that shows the distances to any point of an ellipse that are represented in linear relation.
Area:  It can be consider as a mathematical term which express a particular measurement or region which is associated to a surface.
Directrix:  In the concpet of Ellipse equation the term directrix can be define as a fixed line that demonstrates a curve or surface.

The Box Plot is a concept of descriptive mathematics that performs the task of representing the data in the graphical form. CBSE Board Syllabus is design and issued by the Central Board Of Secondary Education to guide the teachers and students for board examination preparation. 

How to Solve Definite Integral Problems

In the previous post we have discussed about How to Solve Antiderivative  and In this blog we are going to discuss about the topic definite integral which is an important topic of calculus. In mathematics calculus is very useful to define the quantities that are not solved with the help of simple algebraic functions and rules. Integration is the process of finding the value that are in the limits defined in the integration function. It also define in therms of area on the xy plane of the graph where limits defines the axis of the graph it is easily explained by an expression as if there is a function f (n) and it will be integrated in the limits p and q that is written as F = ʃ _p ^q f (n) d n and here function F define the area on the plane XY that is bounded with in the x axis and y axis where x = define the area above the x axis and x = q define the area below the x axis.
Whenever a integration process is done within the closed interval that is come into the category of definite integral that is explain as if there is a function p (s) that is integrated with in the interval a and b is expressed as
ʃ_a ^b p (s) d s = lim _{n→ infinity} ∑ n _u = 1 p (s _u) d s
here ∑ n _u = 1 p (s _u) d s define the sum of the values that are come into the interval a to for the function g (s).
 Harmonic Mean is one of the method for finding the measure of central tendency that is used for calculation of quantitative data. ISEET stands for Indian science engineering Eligibility test and Syllabus of ISEET have all the related topics of physics that are categorized according to the section define in the syllabus.

How to Solve Antiderivative

In this blog we are going to discuss about the topic Antiderivative . In calculus antiderivative is define as the function that is opposite to the derivative function. It define as the function f which gives the derivative F that means f ' = F. It is calculate by doing the opposite functioning of differntiation.

Antiderivative is also define as the integration function that is also known as the indefinite integration. It is defined by a simple example as if we take a function f = sin (a) then the derivative of function f is define as the f' = cos (a) and when we find he antiderivative of f' that is equal to f that means antiderivative of function f' = f that means antiderivative of cos (a) is define as

ʃ cos (a) d a = sin (a) + c.

As we know that differentiation and integration are opposite process and differentiation is another name of anti derivation . It follows all the rules of integration as If there is define the limit of the function Êƒp q f (a) d a = f (q) – f (P) . there are also some properties of antiderivative that are as follows:
ʃ a n d a = a n+1 / (n +1) + c. here c is the constant value .

There is one thing have to know before finding the antiderivative that there is several integrals of a function that are different to each other on the basis of their constant term that is generated at the time of integration.

Topic on Cumulative Frequency defines all the related problems of cumulative frequency define into the calculus in a very simple way. ISEET Chemistry syllabus define all the topics of chemistry that helps the student to secure good marks in the chemistry and In the next session we will discuss about How to Solve Antiderivative. 

Define Laplace Transform

Laplace transform is a type of integral transform that are popularly used in the field of physics and engineering. In mathematical notation the concept of Laplace transform can be represented as L f(a). The above given notation can be consider as a linear operator for a function f (a). Here the value ‘a’ can be considered as a real argument, which should be greater than equal to zero. When the Laplace transform are performed on the above given function then it transform them into f(a) → f(b). Here f(b) can be consider as function with complex argument ‘b’.

Normally the concept of Laplace transform is related to the Fourier transform. But there is big difference between them. Laplace transform resolves a function into moments whereas in same aspect Fourier transform perform the task of representing a function in a series of modes. The concept of Laplace transform is formed by Great mathematician Mr. Pierre Laplace at the time when he performing his experiment on Probability theory. In the below we show you how a Laplace transforms works:

Suppose there F(a) is a function defined as [0, ∞]. Now laplace transform for F(a) can be defiend  as new function :

L(f(b)) = ⌠0∞ e-ba f(a)da = lim α→∞ ⌠0α e ba f(a)da

the basic meaning of above given mathematical notation is that there is a function f(a) on which Laplace transform are performed that gives the new function f(b) with a complex number b. The scope of integral depends on types of function of interest. The basic reason behind the use of Laplace transform is that to reduce a differential equation to an algebra problem. In mathematics, Laplace transform works well when forcing function in differentiation equation gets more complicated. The Statistical Inference is a mathematical process that perform the task of drawing conclusion from data. karnataka education board came into existence into real world in the year of 1966. The main work of karnataka education board is conducting SSLC examinations and In the next session we will discuss about How to Solve Antiderivative.