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NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables are discussed here. Class 10 Maths chapter 3 is an important chapter of Algebra and this chapter are created by expert team at careers360 keeping in mind of latest CBSE syllabus 2023. In Class 10 Maths chapter 3 solutions, students will learn to solve the linear equation with two variables. Class 10 Maths chapter 3 NCERT solutions contain the answers of all exercise NCERT questions.
NCERT Class 10 Maths chapter 3 solutions are helpful to know the answers to the questions asked in NCERT class 10 maths book. Apart from this, by going through NCERT solutions for class 10 maths chapter 3, they will come to know about various methods of solving questions. NCERT solutions for class 10 are also available for other subjects.
Also read,
Types of Linear Equations:
S. No. | Types of Linear Equation | General form | Description | Solutions |
1. | Linear Equation in one Variable | ax + b = 0 | Where a ≠ 0 and a & b are real numbers | One Solution |
2. | Linear Equation in Two Variables | ax + by + c = 0 | Where a ≠ 0 & b ≠ 0 and a, b & c are real numbers | Infinite Solutions possible |
3. | Linear Equation in Three Variables | ax + by + cz + d = 0 | Where a ≠ 0, b ≠ 0, c ≠ 0 and a, b, c, d are real numbers | Infinite Solutions possible |
Simultaneous System of Linear Equations: A pair of equations in the format:
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
This arrangement is visually depicted through the use of two straight lines on the Cartesian plane, as explained in the following context:
When there is a unique solution then
x/(b1c2 - b2c1) = y/(c1a2 - c2a1) = 1/(a1b2 - a2b2)
This formula can be remembered as the diagram given below
Free download NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables PDF for CBSE Exam.
Class 10 Maths Chapter 3 solutions Pair of Linear Equations in two variables Excercise: 3.1
Answer: Let x be the age of Aftab and y be the age of his daughter
Now, According to the question,
Also,
Now, let's represent both equations graphically,
From (1), we get
So, Putting different values of x we get corresponding values of y
X | 0 | 7 | -7 |
Y | 6 | 7 | 5 |
And From (2) we get,
So, Putting different values of x we get corresponding values of y
X | 0 | 3 | 6 |
Y | -2 | -1 | 0 |
GRAPH:
Answer:
Let the price of one Bat be x and the price of one ball be y,
Now, According to the question,
From(1) we have
By putting different values of x, we get different corresponding values of y.So
X | 100 | 300 | -100 |
Y | 600 | 500 | 700 |
Now, From (2), we have,
By putting different values of x, we get different corresponding values of y.So
X | 100 | 400 | -200 |
Y | 400 | 300 | 500 |
GRAPH:
Answer:
Let, x be the cost of 1kg apple and y be the cost of 1kg grapes.
Now, According to the question,
On a day:
After One Month:
Now, From (1) we have
Putting different values of x we get corresponding values of y, so,'
X | 80 | 60 | 50 |
Y | 0 | 40 | 60 |
And From (2) we have,
Putting different values of x we get corresponding values of y, so,
X | 50 | 60 | 70 |
Y | 50 | 30 | 10 |
Graph:
Class 10 Maths Chapter 3 solutions Pair of Linear Equations in Two Variables Excercise: 3.2
Q1 Form the pair of linear equations in the following problems and find their solutions graphically.
Answer:
Let the number of boys is x and the number of girls is y.
Now, According to the question,
Total number of students in the class = 10, i.e.
And
the number of girls is 4 more than the number of boys,i.e.
Different points (x, y) for equation (1)
X | 5 | 6 | 4 |
Y | 5 | 4 | 6 |
Different points (x,y) satisfying (2)
X | 5 | 6 | 7 |
y | 1 | 2 | 3 |
Graph,
As we can see from the graph, both lines intersect at the point (7,3). that is x= 7 and y = 3 which means the number of boys in the class is 7 and the number of girls in the class is 3.
Q1 Form the pair of linear equations in the following problems and find their solutions graphically.
Answer:
Let x be the price of 1 pencil and y be the price of 1 pen,
Now, According to the question
And
Now, the points (x,y), that satisfies the equation (1) are
X | 3 | -4 | 10 |
Y | 5 | 10 | 0 |
And, the points(x,y) that satisfies the equation (2) are
X | 3 | 8 | -2 |
Y | 5 | -2 | 12 |
The Graph,
As we can see from the Graph, both line intersects at point (3,5) that is, x = 3 and y = 5 which means cost of 1 pencil is 3 and the cost of 1 pen is 5.
Answer:
Give, Equations,
Comparing these equations with , we get
As we can see
It means that both lines intersect at exactly one point.
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means that both lines are coincident.
Q2 On comparing the ratios , and , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident: (iii)
Answer:
Give, Equations,
Comparing these equations with , we get
As we can see
It means that both lines are parallel to each other.
Answer:
Give, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have exactly one solution and thus pair of linear equations is consistent.
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have no solution and thus pair of linear equations is inconsistent.
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have exactly one solution and thus pair of linear equations is consistent.
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have an infinite number of solutions and thus pair of linear equations is consistent.
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have an infinite number of solutions and thus pair of linear equations is consistent.
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have an infinite number of solutions and thus pair of linear equations is consistent.
The points (x,y) which satisfies in both equations are
X | 1 | 3 | 5 |
Y | 4 | 2 | 0 |
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have no solution and thus pair of linear equations is inconsistent.
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have exactly one solution and thus pair of linear equations is consistent.
Now The points(x, y) satisfying the equation are,
X | 0 | 2 | 3 |
Y | 6 | 2 | 0 |
And The points(x,y) satisfying the equation are,
X | 0 | 1 | 2 |
Y | -2 | 0 | 2 |
GRAPH:
As we can see both lines intersects at point (2,2) and hence the solution of both equations is x = 2 and y = 2.
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have no solution and thus pair of linear equations is inconsistent.
Answer:
Let be the length of the rectangular garden and be the width.
Now, According to the question, the length is 4 m more than its width.i.e.
Also Given Half Parameter of the rectangle = 36 i.e.
Now, as we have two equations, on adding both equations, we get,
Putting this in equation (1),
Hence Length and width of the rectangle are 20m and 16 respectively.
Given the equation,
As we know that the condition for the intersection of lines , is ,
So Any line with this condition can be
Here,
As
the line satisfies the given condition.
Given the equation,
As we know that the condition for the lines , for being parallel is,
So Any line with this condition can be
Here,
As
the line satisfies the given condition.
Given the equation,
As we know that the condition for the coincidence of the lines , is,
So any line with this condition can be
Here,
As
the line satisfies the given condition.
Given, two equations,
And
The points (x,y) satisfying (1) are
X | 0 | 3 | 6 |
Y | 1 | 4 | 7 |
And The points(x,y) satisfying (2) are,
X | 0 | 2 | 4 |
Y | 6 | 3 | 0 |
GRAPH:
As we can see from the graph that both lines intersect at the point (2,3), And the vertices of the Triangle are ( -1,0), (2,3) and (4,0). The area of the triangle is shaded with a green color.
Pair of linear equations in two variables class 10 solutions Excercise: 3.3
Q1 Solve the following pair of linear equations by the substitution method. (i)
Answer:
Given, two equations,
Now, from (1), we have
Substituting this in (2), we get
Substituting this value of x in (3)
Hence, Solution of the given equations is x = 9 and y = 5.
Q1 Solve the following pair of linear equations by the substitution method (ii)
Answer:
Given, two equations,
Now, from (1), we have
Substituting this in (2), we get
Substituting this value of t in (3)
Hence, Solution of the given equations is s = 9 and t = 6.
Q1 Solve the following pair of linear equations by the substitution method. (iii)
Answer:
Given, two equations,
Now, from (1), we have
Substituting this in (2), we get
This is always true, and hence this pair of the equation has infinite solutions.
As we have
,
One of many possible solutions is .
Q1 Solve the following pair of linear equations by the substitution method. (iv)
Answer:
Given, two equations,
Now, from (1), we have
Substituting this in (2), we get
Substituting this value of x in (3)
Hence, Solution of the given equations is,
.
Q1 Solve the following pair of linear equations by the substitution method. (v)
Answer:
Given, two equations,
Now, from (1), we have
Substituting this in (2), we get
Substituting this value of x in (3)
Hence, Solution of the given equations is,
.
Q1 Solve the following pair of linear equations by the substitution method. (vi)
Answer:
Given,
From (1) we have,
Putting this in (2) we get,
putting this value in (3) we get,
Hence
Q2 Solve and and hence find the value of ‘ ’ for which .
Answer:
Given, two equations,
Now, from (1), we have
Substituting this in (2), we get
Substituting this value of x in (3)
Hence, Solution of the given equations is,
Now,
As it satisfies ,
Hence Value of m is -1.
(i) The difference between the two numbers is 26 and one number is three times the other. Find them.
Answer:
Let two numbers be x and y and let the bigger number is y.
Now, According to the question,
And
Now, the substituting value of y from (2) in (1) we get,
Substituting this in (2)
Hence the two numbers are 13 and 39.
Answer:
Let the larger angle be x and smaller angle be y
Now, As we know the sum of supplementary angles is 180. so,
Also given in the question,
Now, From (2) we have,
Substituting this value in (1)
Now, Substituting this value of x in (3), we get
Hence the two supplementary angles are
Answer:
Let the cost of 1 bat is x and the cost of 1 ball is y.
Now, According to the question,
Now, From (1) we have
Substituting this value of y in (2)
Now, Substituting this value of x in (3)
Hence, The cost of one bat is 500 Rs and the cost of one ball 50 Rs.
Answer:
Let the fixed charge is x and the per km charge is y.
Now According to the question
And
Now, From (1) we have,
Substituting this value of x in (2), we have
Now, Substituting this value in (3)
Hence, the fixed charge is 5 Rs and the per km charge is 10 Rs.
Now, Fair For 25 km :
Hence fair for 25km is 255 Rs.
Answer:
Let the numerator of the fraction be x and denominator of the fraction is y
Now According to the question,
Also,
Now, From (1) we have
Substituting this value of y in (2)
Substituting this value of x in (3)
Hence the required fraction is
Answer:
Let x be the age of Jacob and y be the age of Jacob's son,
Now, According to the question
Also,
Now,
From (1) we have,
Substituting this value of x in (2)
Substituting this value of y in (3),
Hence, Present age of Jacob is 40 years and the present age of Jacob's son is 10 years.
Pair of linear equations in two variables class 10 solutions Excercise: 3.4
Q1 Solve the following pair of linear equations by the elimination method and the substitution method :
(i)
Answer:
Elimination Method:
Given, equations
Now, multiplying (1) by 3 we, get
Now, Adding (2) and (3), we get
Substituting this value in (1) we, get
Hence,
Substitution method :
Given, equations
Now, from (1) we have,
substituting this value in (2)
Substituting this value of x in (3)
Hence,
Q1 Solve the following pair of linear equations by the elimination method and the substitution method :
(ii)
Answer:
Elimination Method:
Given, equations
Now, multiplying (2) by 2 we, get
Now, Adding (1) and (3), we get
Putting this value in (2) we, get
Hence,
Substitution method :
Given, equations
Now, from (2) we have,
substituting this value in (1)
Substituting this value of x in (3)
Hence,
Answer:
Elimination Method:
Given, equations
Now, multiplying (1) by 3 we, get
Now, Subtracting (3) from (2), we get
Putting this value in (1) we, get
Hence,
Substitution method :
Given, equations
Now, from (2) we have,
substituting this value in (1)
Substituting this value of x in (3)
Hence,
Answer:
Elimination Method:
Given, equations
Now, multiplying (2) by 2 we, get
Now, Adding (1) and (3), we get
Putting this value in (2) we, get
Hence,
Substitution method :
Given, equations
Now, from (2) we have,
substituting this value in (1)
Substituting this value of x in (3)
Hence,
Answer:
Let the numerator of the fraction be x and denominator is y,
Now, According to the question,
Also,
Now, Subtracting (1) from (2) we get
Putting this value in (1)
Hence
And the fraction is
Answer:
Let the age of Nuri be x and age of Sonu be y.
Now, According to the question
Also,
Now, Subtracting (1) from (2), we get
putting this value in (2)
Hence the age of Nuri is 50 and the age of Nuri is 20.
Answer:
Let the unit digit of the number be x and 10's digit be y.
Now, According to the question,
24323
Also
Now adding (1) and (2) we get,
now putting this value in (1)
Hence the number is 18.
Answer:
Let the number of Rs 50 notes be x and the number of Rs 100 notes be y.
Now, According to the question,
And
Now, Subtracting(1) from (2), we get
Putting this value in (1).
Hence Meena received 10 50 Rs notes and 15 100 Rs notes.
Answer:
Let fixed charge be x and per day charge is y.
Now, According to the question,
And
Now, Subtracting (2) from (1). we get,
Putting this in (1)
Hence the fixed charge is 15 Rs and per day charge is 3 Rs.
Pair of linear equations in two variables class 10 solutions Excercise: 3.5
Given, two equations,
Comparing these equations with , we get
As we can see,
Hence, the pair of equations has no solution.
Given, two equations,
Comparing these equations with , we get
As we can see,
Hence, the pair of equations has exactly one solution.
By Cross multiplication method,
Comparing these equations with , we get
As we can see,
Hence, the pair of equations has infinitely many solutions.
Given the equations,
Comparing these equations with , we get
As we can see,
Hence, the pair of equations has exactly one solution.
By Cross multiplication method,
Given equations,
As we know, the condition for equations to have an infinite solution is
So, Comparing these equations with, , we get
From here we get,
Also,
Now, Subtracting (2) from (1) we get
Substituting this value in (1)
Hence, .
Q2 (ii) For which value of k will the following pair of linear equations have no solution?
Given, the equations,
As we know, the condition for equations to have no solution is
So, Comparing these equations with, , we get
From here we get,
Hence, the value of K is 2.
Q3 Solve the following pair of linear equations by the substitution and cross-multiplication methods :
Given the equations
By Substitution Method,
From (1) we have
Substituting this in (2),
Substituting this in (3)
Hence .
By Cross Multiplication Method
Let the fixed charge be x and the cost of food per day is y,
Now, According to the question
Also
Now subtracting (1) from (2),
Putting this value in (1)
Hence, the Fixed charge is Rs 400 and the cost of food per day is Rs 30.
Let numerator of a fraction be x and the denominator is y.
Now, According to the question,
Also,
Now, Subtracting (1) from (2) we get,
Putting this value in (2) we get,
Hence, the fraction is
.
Let the number of right answer and wrong answer be x and y respectively
Now, According to the question,
And
Now, subtracting (2) from (1) we get,
Putting this value in (1)
Hence the total number of question is
Let the speed of the first car is x and the speed of the second car is y.
Let's solve this problem by using relative motion concept,
the relative speed when they are going in the same direction= x - y
the relative speed when they are going in the opposite direction= x + y
The given relative distance between them = 100 km.
Now, As we know,
Relative distance = Relative speed * time .
So, According to the question,
Also,
Now Adding (1) and (2) we get
putting this in (1)
Hence the speeds of the cars are 40 km/hour and 60 km/hour.
Let be the length of the rectangle and be the width,
Now, According to the question,
Also,
By Cross multiplication method,
Hence the length and width of the rectangle are 17 units and 9 units respectively.
NCERT Solutions for class 10 math chapter 3 Pair of Linear Equations in Two Variables Excercise: 3.6
Q1 Solve the following pairs of equations by reducing them to a pair of linear equations:
Given Equations,
Let,
Now, our equation becomes
And
By Cross Multiplication method,
And Hence,
Q1 Solve the following pairs of equations by reducing them to a pair of linear equations:
Given Equations,
Let,
Now, our equation becomes
And
By Cross Multiplication method,
So,
.
And hence
Q1 Solve the following pairs of equations by reducing them to a pair of linear equations:
Given Equations,
Let,
Now, our equation becomes
And
By Cross Multiplication method,
And Hence,
Q1 Solve the following pairs of equations by reducing them to a pair of linear equations:
Given Equations,
Let,
Now, our equation becomes
And
Multiplying (1) by 3 we get
Now, adding (2) and (3) we get
Putting this in (2)
Now,
Hence,
Q1 Solve the following pairs of equations by reducing them to a pair of linear equations: (v)
Given Equations,
Let,
Now, our equation becomes
And
By Cross Multiplication method,
And Hence,
Q1 Solve the following pairs of equations by reducing them to a pair of linear equations:
Given Equations,
Let,
Now, our equation becomes
And
By Cross Multiplication method,
And Hence,
Q1 Solve the following pairs of equations by reducing them to a pair of linear equations:
(vii)
Given Equations,
Let,
Now, our equation becomes
And
By Cross Multiplication method,
Now,
And,
Adding (3) and (4) we get,
Putting this value in (3) we get,
And Hence,
Q1 Solve the following pairs of equations by reducing them to a pair of linear equations:
Given Equations,
Let,
Now, our equation becomes
And
Now, Adding (1) and (2), we get
Putting this value in (1)
Now,
And
Now, Adding (3) and (4), we get
Putting this value in (3),
Hence,
Let the speed of Ritu in still water be x and speed of current be y,
Let's solve this problem by using relative motion concept,
the relative speed when they are going in the same direction (downstream)= x +y
the relative speed when they are going in the opposite direction (upstream)= x - y
Now, As we know,
Relative distance = Relative speed * time .
So, According to the question,
And,
Now, Adding (1) and (2), we get
Putting this in (2)
Hence,
Hence Speed of Ritu in still water is 6 km/hour and speed of the current is 4 km/hour
Let the number of days taken by woman and man be x and y respectively,
The proportion of Work done by a woman in a single day
The proportion of Work done by a man in a single day
Now, According to the question,
Also,
Let,
Now, our equation becomes
And
By Cross Multiplication method,
So,
Let the speed of the train and bus be u and v respectively
Now According to the question,
And
Let,
Now, our equation becomes
And
By Cross Multiplication method,
And Hence,
Hence the speed of the train and bus are 60 km/hour and 80 km/hour respectively.
Class 10 math chapter 3 solutions Pair of Linear Equations in Two Variables Excercise: 3.7
Answer:
Let the age of Ani be , age of Biju be ,
Case 1: when Ani is older than Biju
age of Ani's father Dharam:
and
age of his sister Cathy :
Now According to the question,
Also,
Now subtracting (1) from (2), we get,
putting this in (1)
Hence the age of Ani and Biju is 19 years and 16 years respectively.
Case 2:
And
Now Adding (3) and (4), we get,
putting it in (3)
Hence the age of Ani and Biju is 21 years and 24 years respectively.
Answer:
Let the amount of money the first person and the second person having is x and y respectively
Noe, According to the question.
Also
Multiplying (2) by 2 we get,
Now adding (1) and (3), we get
Putting this value in (1)
Thus two friends had 40 Rs and 170 Rs respectively.
Answer:
Let the speed of the train be v km/h and the time taken by train to travel the given distance be t hours and the distance to travel be d km.
Now As we Know,
Now, According to the question,
Now, Using equation (1), we have
Also,
Adding equations (2) and (3), we obtain:
Substituting the value of x in equation (2), we obtain:
Putting this value in (1) we get,
Hence the distance covered by train is 600km.
Answer:
Let the number of rows is x and the number of students in a row is y.
Total number of students in the class = Number of rows * Number of students in a row
Now, According to the question,
Also,
Subtracting equation (2) from (1), we get:
Substituting the value of y in equation (1), we obtain:
Hence,
The number of rows is 4 and the Number of students in a row is 9.
Total number of students in a class
:
Hence there are 36 students in the class.
Q5 In a , . Find the three angles.
Answer:
Given,
Also, As we know that the sum of angles of a triangle is 180, so
Now From (1) we have
Putting this value in (2) we have
Putting this in (3)
And
Hence three angles of triangles
Answer:
Given two equations,
And
Points(x,y) which satisfies equation (1) are:
X | 0 | 1 | 5 |
Y | -5 | 0 | 20 |
Points(x,y) which satisfies equation (1) are:
X | 0 | 1 | 2 |
Y | -3 | 0 | 3 |
GRAPH:
As we can see from the graph, the three points of the triangle are, (0,-3),(0,-5) and (1,0).
Q7 Solve the following pair of linear equations: (i)
Answer:
Given Equations,
Now By Cross multiplication method,
Q7 Solve the following pair of linear equations: (ii)
Answer:
Given two equations,
Now By Cross multiplication method,
Q7 Solve the following pair of linear equations: (iii)
Answer:
Given equation,
Now By Cross multiplication method,
Q7 Solve the following pair of linear equations: (iv)
Answer:
Given,
And
Now, Subtracting (1) from (2), we get
Substituting this in (1), we get,
.
Hence,
Q7 Solve the following pair of linear equations: (v)
Answer:
Given Equations,
As we can see by adding and subtracting both equations we can make our equations simple to solve.
So,
Adding (1) and )2) we get,
Subtracting (2) from (1) we get,
Now, Adding (3) and (4) we get,
Putting this value in (3)
Hence,
Q8 ABCD is a cyclic quadrilateral (see Fig. 3.7). Find the angles of the cyclic quadrilateral.
Answer:
As we know that in a quadrilateral the sum of opposite angles is 180 degrees.
So, From Here,
Also,
Multiplying (1) by 3 we get,
Now,
Subtracting, (2) from (3) we get,
Substituting this value in (1) we get,
Hence four angles of a quadrilateral are :
Solving a linear equation with two variables.
Representation of linear equation in a graph.
Solutions of linear equations using the graph.
Algebraic interpretation of linear equations.
Formation of linear equations using statements.
Also get the solutions exercise wise-
Many real-life situations can be formulated using Mathematical equations given in this chapter 3 NCERT Class 10 Maths solutions.
For example, consider the statement "cost of 1 Kg Apple and 2Kg orange is 120 and the cost of 3 Kg Apple and 1 Kg orange is 210". The statement can be formulated using the Mathematical equation, for this consider the cost of Apple as x and that of orange as y. Then we can write two equations as x+2y=120 and 3x+y=210.
Solution Link |
NCERT solutions for class 10 maths chapter 3 |
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NCERT solutions Class 10 Maths Chapter 3 are the most important tool when you are appearing for board examinations. 90% paper of CBSE board examinations, directly come from the NCERT.
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After covering Linear Equations in Two Variables Class 10 solutions you should target the past year papers of CBSE board examinations. The previous year papers will cover the rest 10% part of the Class 10 board exams.
In Class 10 Maths, a pair of linear equations in two variables is a set of two linear equations that contain two variables, typically represented by x and y. Linear equations are equations of the form ax + by = c, where a, b, and c are constants.
Students can find NCERT solutions for maths to class 10 linear equations in two variables above in this article. Our experts in simple and easy format develop these maths class 10 chapter 3 pair of linear equations in two variables class 10 solutions. These will be very helpful for students.
It is very important to go through Class 10 maths linear equations in two variables questions as they are designed to help you understand the material and practice your problem-solving skills. Students can find ch 3 maths class 10 ncert solutions at careers360 official website. However, it is not necessarily required to work through class 10 chapter 3 maths solutions by every question in order to understand the concepts covered in the chapter.
NCERT class chapter 3 pair of linear equations in two variables class 10 solutions
Contains the concepts of pairs of linear equations and solving them using methods like graphing method, substitution method, elimination method, Consistency and inconsistency of a pair of linear equations, and Dependent and independent linear equations. As Class 10 linear equations in two variables questions are used to solve real-world problems.
In chapter 3 Pair of linear equations class 10 Exercise 3.1, Question 1 is important. All questions in Exercise 3.2 are important. In Exercise 3.3, Question 1 (parts iv, v, vi), Question 2, and Question 3 are important. Exercise 3.4's Question 2 is important, and Exercise 3.5's Questions 2 and 4 are important. All questions in Exercise 3.6 are important. All questions in the optional Exercise 3.7 are important. Students can download a pair of linear equations in two variables class 10 pdf.
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The eligibility age criteria for class 10th CBSE is 14 years of age. Since your son will be 15 years of age in 2024, he will be eligible to give the exam.
According to CBSE norms, a student must be 14 years old by the end of the year in which the exam will be held in order to sit for the 10th board exam. If your age is greater than 14, however, there are no limits. Therefore, based on your DOB, you will be 12 years and 6 months old by the end of December 2022. After the actual 16 June 2024, you'll be qualified to take your 10th board.
Hello aspirant,
Central Board Of Secondary Education(CBSE) is likely to declare class 10 and 12 terms 2 board result 2022 by July 15. The evaluation process is underway. Students are demanding good results and don't want to lack behind. They are requesting the board to use their best scores in Term 1 and Term 2 exams to prepare for the results.
CBSE concluded board exams 2022 for 10, and 12 on June 15 and May 24. Exams for both classes began on April 26. A total of 35 lakh students including 21 lakh class 10 students and 14 lakh class 12 students appeared in exams and are awaiting their results.
You can look for your results on websites- cbse.gov (//cbse.gov) .in, cbseresults.nic.in
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The field of biomedical engineering opens up a universe of expert chances. An Individual in the biomedical engineering career path work in the field of engineering as well as medicine, in order to find out solutions to common problems of the two fields. The biomedical engineering job opportunities are to collaborate with doctors and researchers to develop medical systems, equipment, or devices that can solve clinical problems. Here we will be discussing jobs after biomedical engineering, how to get a job in biomedical engineering, biomedical engineering scope, and salary.
Database professionals use software to store and organise data such as financial information, and customer shipping records. Individuals who opt for a career as data administrators ensure that data is available for users and secured from unauthorised sales. DB administrators may work in various types of industries. It may involve computer systems design, service firms, insurance companies, banks and hospitals.
A career as ethical hacker involves various challenges and provides lucrative opportunities in the digital era where every giant business and startup owns its cyberspace on the world wide web. Individuals in the ethical hacker career path try to find the vulnerabilities in the cyber system to get its authority. If he or she succeeds in it then he or she gets its illegal authority. Individuals in the ethical hacker career path then steal information or delete the file that could affect the business, functioning, or services of the organization.
The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.
Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.
Individuals who opt for a career as geothermal engineers are the professionals involved in the processing of geothermal energy. The responsibilities of geothermal engineers may vary depending on the workplace location. Those who work in fields design facilities to process and distribute geothermal energy. They oversee the functioning of machinery used in the field.
Individuals who opt for a career as a remote sensing technician possess unique personalities. Remote sensing analysts seem to be rational human beings, they are strong, independent, persistent, sincere, realistic and resourceful. Some of them are analytical as well, which means they are intelligent, introspective and inquisitive.
Remote sensing scientists use remote sensing technology to support scientists in fields such as community planning, flight planning or the management of natural resources. Analysing data collected from aircraft, satellites or ground-based platforms using statistical analysis software, image analysis software or Geographic Information Systems (GIS) is a significant part of their work. Do you want to learn how to become remote sensing technician? There's no need to be concerned; we've devised a simple remote sensing technician career path for you. Scroll through the pages and read.
The role of geotechnical engineer starts with reviewing the projects needed to define the required material properties. The work responsibilities are followed by a site investigation of rock, soil, fault distribution and bedrock properties on and below an area of interest. The investigation is aimed to improve the ground engineering design and determine their engineering properties that include how they will interact with, on or in a proposed construction.
The role of geotechnical engineer in mining includes designing and determining the type of foundations, earthworks, and or pavement subgrades required for the intended man-made structures to be made. Geotechnical engineering jobs are involved in earthen and concrete dam construction projects, working under a range of normal and extreme loading conditions.
How fascinating it is to represent the whole world on just a piece of paper or a sphere. With the help of maps, we are able to represent the real world on a much smaller scale. Individuals who opt for a career as a cartographer are those who make maps. But, cartography is not just limited to maps, it is about a mixture of art, science, and technology. As a cartographer, not only you will create maps but use various geodetic surveys and remote sensing systems to measure, analyse, and create different maps for political, cultural or educational purposes.
Budget analysis, in a nutshell, entails thoroughly analyzing the details of a financial budget. The budget analysis aims to better understand and manage revenue. Budget analysts assist in the achievement of financial targets, the preservation of profitability, and the pursuit of long-term growth for a business. Budget analysts generally have a bachelor's degree in accounting, finance, economics, or a closely related field. Knowledge of Financial Management is of prime importance in this career.
The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.
Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
An underwriter is a person who assesses and evaluates the risk of insurance in his or her field like mortgage, loan, health policy, investment, and so on and so forth. The underwriter career path does involve risks as analysing the risks means finding out if there is a way for the insurance underwriter jobs to recover the money from its clients. If the risk turns out to be too much for the company then in the future it is an underwriter who will be held accountable for it. Therefore, one must carry out his or her job with a lot of attention and diligence.
Individuals in the operations manager jobs are responsible for ensuring the efficiency of each department to acquire its optimal goal. They plan the use of resources and distribution of materials. The operations manager's job description includes managing budgets, negotiating contracts, and performing administrative tasks.
An investment director is a person who helps corporations and individuals manage their finances. They can help them develop a strategy to achieve their goals, including paying off debts and investing in the future. In addition, he or she can help individuals make informed decisions.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.
An expert in plumbing is aware of building regulations and safety standards and works to make sure these standards are upheld. Testing pipes for leakage using air pressure and other gauges, and also the ability to construct new pipe systems by cutting, fitting, measuring and threading pipes are some of the other more involved aspects of plumbing. Individuals in the plumber career path are self-employed or work for a small business employing less than ten people, though some might find working for larger entities or the government more desirable.
Individuals who opt for a career as construction managers have a senior-level management role offered in construction firms. Responsibilities in the construction management career path are assigning tasks to workers, inspecting their work, and coordinating with other professionals including architects, subcontractors, and building services engineers.
Urban Planning careers revolve around the idea of developing a plan to use the land optimally, without affecting the environment. Urban planning jobs are offered to those candidates who are skilled in making the right use of land to distribute the growing population, to create various communities.
Urban planning careers come with the opportunity to make changes to the existing cities and towns. They identify various community needs and make short and long-term plans accordingly.
Highway Engineer Job Description: A Highway Engineer is a civil engineer who specialises in planning and building thousands of miles of roads that support connectivity and allow transportation across the country. He or she ensures that traffic management schemes are effectively planned concerning economic sustainability and successful implementation.
Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems.
A Naval Architect is a professional who designs, produces and repairs safe and sea-worthy surfaces or underwater structures. A Naval Architect stays involved in creating and designing ships, ferries, submarines and yachts with implementation of various principles such as gravity, ideal hull form, buoyancy and stability.
Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.
A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.
Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth.
An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.
The audiologist career involves audiology professionals who are responsible to treat hearing loss and proactively preventing the relevant damage. Individuals who opt for a career as an audiologist use various testing strategies with the aim to determine if someone has a normal sensitivity to sounds or not. After the identification of hearing loss, a hearing doctor is required to determine which sections of the hearing are affected, to what extent they are affected, and where the wound causing the hearing loss is found. As soon as the hearing loss is identified, the patients are provided with recommendations for interventions and rehabilitation such as hearing aids, cochlear implants, and appropriate medical referrals. While audiology is a branch of science that studies and researches hearing, balance, and related disorders.
The hospital Administrator is in charge of organising and supervising the daily operations of medical services and facilities. This organising includes managing of organisation’s staff and its members in service, budgets, service reports, departmental reporting and taking reminders of patient care and services.
For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs.
Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.
Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.
Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.
Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.
A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.
The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.
A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.
A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.
In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.
Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.
For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.
In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion.
Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article.
Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.
Linguistic meaning is related to language or Linguistics which is the study of languages. A career as a linguistic meaning, a profession that is based on the scientific study of language, and it's a very broad field with many specialities. Famous linguists work in academia, researching and teaching different areas of language, such as phonetics (sounds), syntax (word order) and semantics (meaning).
Other researchers focus on specialities like computational linguistics, which seeks to better match human and computer language capacities, or applied linguistics, which is concerned with improving language education. Still, others work as language experts for the government, advertising companies, dictionary publishers and various other private enterprises. Some might work from home as freelance linguists. Philologist, phonologist, and dialectician are some of Linguist synonym. Linguists can study French, German, Italian.
The career of a travel journalist is full of passion, excitement and responsibility. Journalism as a career could be challenging at times, but if you're someone who has been genuinely enthusiastic about all this, then it is the best decision for you. Travel journalism jobs are all about insightful, artfully written, informative narratives designed to cover the travel industry. Travel Journalist is someone who explores, gathers and presents information as a news article.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.
A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans.
A metallurgical engineer is a professional who studies and produces materials that bring power to our world. He or she extracts metals from ores and rocks and transforms them into alloys, high-purity metals and other materials used in developing infrastructure, transportation and healthcare equipment.
An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems.
An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party.
Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack