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NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming provided here. These NCERT solutions are prepared by expert team at Careers360 considering the latest syllabus of CBSE 2023-24. This ch 12 maths class 12 helps solving and finding optimal solutions to problems related to maximising profit or minimising cost. NCERT linear programming class 12 solutions will help in formulating these real life problems into a mathematical model. You should practise linear programming problems (lpp class 12) for getting command of concepts and in depth understanding of this linear programming class 12 chapter.
In this linear programming class 12 solutions, you are going to deal with problems on linear programming like maximisation and minimization of equations, mathematical and graphical methods to solve problems of linear programming. You can also refer to linear programming class 12 ncert solutions for better understanding of concepts. Below we have given complete Class 12 maths chapter 12 NCERT solutions. Check all NCERT solutions from class 6 to 12 at a single place to prepare better for exams.
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Also read:
>> Feasible Region: The feasible region, or solution region, of a linear programming problem is the common area determined by all the constraints, including the non-negativity constraints (x ≥ 0, y ≥ 0).
>> Infeasible Solution: Any point within or on the boundary of the feasible region represents a feasible solution to the constraints. Points outside the feasible region are considered infeasible solutions.
>> Optimal Solution: An optimal solution is any point within the feasible region that provides the optimal value (maximum or minimum) of the objective function.
Fundamental Theorems in Linear Programming:
>> Optimality at Corner Points: For a linear programming problem with a feasible region represented as a convex polygon, if the objective function Z = ax + by has an optimal value, this optimal value must occur at one of the corner points (vertices) of the feasible region.
>> Existence of Maxima and Minima: If the feasible region R is bounded, then the objective function Z has both a maximum and a minimum value on R, and each of these values occurs at a corner point (vertex) of R. If R is unbounded, a maximum or minimum may not exist. However, if it does exist, it must occur at a corner point of R.
>> Corner Point Method: The corner point method is used to solve a linear programming problem and consists of the following steps:
Find the feasible region of the linear programming problem and determine its corner points (vertices).
Evaluate the objective function Z = ax + by at each corner point. Let M and m represent the largest and smallest values obtained at these points.
If the feasible region is bounded, M and m respectively represent the maximum and minimum values of the objective function.
If the feasible region is unbounded, then:
M is the maximum value of the objective function if the open half-plane determined by ax + by > M has no points in common with the feasible region.
m is the minimum value of the objective function if the open half-plane determined by ax + by < M has no points in common with the feasible region.
Free download NCERT Class 12 Maths Chapter 12 Question Answer for CBSE Exam.
NCERT linear programming class 12 solutions - Exercise: 12.1
Answer:
The region determined by constraints, is as follows,
The region A0B represents the feasible region
The corner points of the feasible region are
Maximize
The value of these points at these corner points are :
Corner points | ||
12 | ||
0 | ||
16 | maximum |
The maximum value of Z is 16 at
Answer:
The region determined by constraints, is as follows,
The corner points of feasible region are
The value of these points at these corner points are :
Corner points | ||
6 | ||
-12 | Minimum | |
0 | ||
16 |
The minimum value of Z is -12 at
Answer:
The region determined by constraints, , , is as follows :
The corner points of feasible region are
The value of these points at these corner points are :
Corner points | ||
9 | ||
0 | ||
10 | ||
Maximum |
The maximum value of Z is at
Answer:
The region determined by constraints is as follows,
The feasible region is unbounded as shown.
The corner points of the feasible region are
The value of these points at these corner points are :
Corner points | ||
9 | ||
7 | Minimum | |
10 | ||
The feasible region is unbounded, therefore 7 may or may not be the minimum value of Z .
For this, we draw and check whether resulting half plane has a point in common with the feasible region or not.
We can see a feasible region has no common point with.
Hence, Z has a minimum value of 7 at
Answer:
The region determined by constraints, is as follows,
The corner points of feasible region are
The value of these points at these corner points are :
Corner points | ||
15 | ||
18 | Maximum | |
10 | ||
The maximum value of Z is 18 at
Question:6 Solve the following Linear Programming Problems graphically: Minimise Subject to
Show that the minimum of Z occurs at more than two points.
Answer:
The region determined by constraints is as follows,
The corner points of the feasible region are
The value of these points at these corner points are :
Corner points | |
6 | |
6 |
Value of Z is the same at both points.
If we take any other point like on line , then Z=6.
Thus the minimum value of Z occurs at more than 2 points .
Therefore, the value of Z is minimum at every point on the line .
Answer:
The region determined by constraints, is as follows,
The corner points of feasible region are
The value of these points at these corner points are :
Corner points | ||
400 | ||
600 | Maximum | |
300 | Minimum | |
600 | maximum |
The minimum value of Z is 300 at and maximum value is 600 at all points joing line segment and
Answer:
The region determined by constraints is as follows,
The corner points of the feasible region are
The value of these points at these corner points are :
Corner points | ||
100 | Minimum | |
100 | Minimum | |
250 | ||
400 | Maximum |
The minimum value of Z is 100 at all points on the line segment joining points and .
The maximum value of Z is 400 at .
Answer:
The region determined by constraints is as follows,
The corner points of the feasible region are
The value of these points at these corner points are :
Corner points | ||
- 6 | minimum | |
-2 | ||
1 | maximum | |
The feasible region is unbounded, therefore 1 may or may not be the maximum value of Z.
For this, we draw and check whether resulting half plane has a point in common with a feasible region or not.
We can see the resulting feasible region has a common point with a feasible region.
Hence , Z =1 is not maximum value , Z has no maximum value.
Answer:
The region determined by constraints is as follows,
There is no feasible region and thus, Z has no maximum value.
NCERT linear programming class 12 solutions - Exercise: 12.2
Answer:
Let mixture contain x kg of food P and y kg of food Q. Thus, .
The given information can be represented in the table as :
Vitamin A | Vitamin B | Cost | |
Food P | 3 | 5 | 60 |
Food Q | 4 | 2 | 80 |
requirement | 8 | 11 |
The mixture must contain 8 units of Vitamin A and 11 units of Vitamin B.
Therefore, we have
Total cost is Z.
Subject to constraint,
The feasible region determined by constraints is as follows:
It can be seen that a feasible region is unbounded.
The corner points of the feasible region are
The value of Z at corner points is as shown :
corner points | ||
160 | MINIMUM | |
160 | minimum | |
440 |
Feasible region is unbounded, therefore 160 may or may not be the minimum value of Z.
For this, we draw and check whether resulting half plane has a point in common with the feasible region or not.
We can see a feasible region has no common point with.
Hence, Z has a minimum value 160 at line segment joining points and .
Answer:
Let there be x cakes of first kind and y cakes of the second kind.Thus, .
The given information can be represented in the table as :
Flour(g) | fat(g) | |
Cake of kind x | 200 | 25 |
Cake of kind y | 100 | 50 |
Availability | 5000 | 1000 |
Therefore,
.
The total number of cakes, Z. Z=X+Y
Subject to constraint,
The feasible region determined by constraints is as follows:
The corner points of the feasible region are
The value of Z at corner points is as shown :
corner points | Z=X+Y | |
25 | ||
30 | maximum | |
20 0 | minimum |
The maximum cake can be made 30 (20 of the first kind and 10 of the second kind).
(i) What number of rackets and bats must be made if the factory is to work at full capacity?
Answer:
Let number of rackets be x and number of bats be y.
the machine time availability is not more than 42 hours.
i.e.
craftsman’s time availability is 24 hours
i.e.
The factory has to work at full capacity.
Hence,
Solving equation 1 and 2, we have
Thus, 4 rackets and 12 bats are to be made .
Answer:
Let the number of rackets is x and the number of bats is y.
the machine time availability is not more than 42 hours.
craftsman’s time availability is 24 hours
The given information can be repreented in table as shown :
racket | bat | availability | |
machine time | 1.5 | 3 | 42 |
craftman's time | 3 | 1 | 24 |
The profit on the bat is 10 and on the racket is 20.
The mathematical formulation is :
maximise
subject to constraints,
The feasible region determined by constraints is as follows:
The corner points are
The value of Z at corner points is as shown :
CORNER POINTS | ||
160 | ||
200 | maximum | |
140 | ||
0 |
Thus, the maximum profit of the factory when it works at full capacity is 200.
Answer:
Let packages of nuts be x and packages of bolts be y .Thus, .
The given information can be represented in table as :
bolts | nuts | availability | |
machine A | 1 | 3 | 12 |
machine B | 3 | 1 | 12 |
Profit on a package of nuts is Rs. 17.5 and on package of bolt is 7.
Therefore, constraint are
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
Corner points | ||
70 | ||
73.5 | maximum | |
28 | ||
0 |
The maximum value of z is 73.5 at .
Thus, 3 packages of nuts and 3 packages of bolts should be manufactured everyday to get maximum profit.
Answer:
Let factory manufactures screws of type A and factory manufactures screws of type B. Thus, .
The given information can be represented in the table as :
screw A | screw B | availability | |
Automatic machine | 4 | 6 | |
hand operated machine | 6 | 3 | |
Profit on a package of screw A is Rs.7 and on the package of screw B is 10.
Therefore, the constraint is
The feasible region determined by constraints is as follows:
The corner points of the feasible region are
The value of Z at corner points is as shown :
Corner points | ||
280 | ||
410 | maximum | |
400 | ||
0 |
The maximum value of z is 410 at .
Thus, 30 packages of screw A and 20 packages of screw B should be manufactured every day to get maximum profit.
Answer:
Let the cottage industry manufactures x pedestal lamps and y wooden shades. Thus, .
The given information can be represented in the table as :
lamps | shades | availability | |
machine (h) | 2 | 1 | 12 |
sprayer (h) | 3 | 2 | 20 |
Profit on a lamp is Rs. 5 and on the shade is 3.
Therefore, constraint is
The feasible region determined by constraints is as follows:
The corner points of the feasible region are
The value of Z at corner points is as shown :
Corner points | ||
30 | ||
32 | maximum | |
30 | ||
0 |
The maximum value of z is 32 at .
Thus, 4 shades and 4 pedestals lamps should be manufactured every day to get the maximum profit.
Answer:
Let x be Souvenirs of type A and y be Souvenirs of type B .Thus, .
The given information can be represented in table as :
Type A | Type B | availability | |
cutting | 5 | 8 | |
asembling | 10 | 8 | |
Profit on type A Souvenirs is Rs. 5 and on type B Souvenirs is 6.
Therefore, constraint are
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
Corner points | ||
120 | ||
160 | maximum | |
150 | ||
0 |
The maximum value of z is 160 at .
Thus,8 Souvenirs of type A and 20 Souvenirs of type B should be manufactured everyday to get maximum profit.
Answer:
Let merchant plans has personal computers x desktop model and y portable model
.Thus, .
The cost of desktop model is cost Rs 25000 and portable model is Rs 40000.
Merchant can invest Rs 70 lakhs maximum.
the total monthly demand of computers will not exceed 250 units.
profit on the desktop model is Rs 4500 and on portable model is Rs 5000.
Total profit = Z ,
The mathematical formulation of given problem is :
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
Corner points | ||
1125000 | ||
1150000 | maximum | |
875000 | ||
0 |
The maximum value of z is 1150000 at .
Thus, merchant should stock 200 desktop models and 50 portable models to get maximum profit.
Answer:
Let diet contain x unit of food F1 and y unit of foof F2 .Thus, .
The given information can be represented in table as :
Vitamin | minerals | cost per unit | |
foof F1 | 3 | 4 | 4 |
food F2 | 6 | 3 | 6 |
80 | 100 |
Cost of food F1 is Rs 4 per unit and Cost of food F2 is Rs 6 per unit
Therefore, constraint are
The feasible region determined by constraints is as follows:
We can see feasible region is unbounded.
The corner points of feasible region are
The value of Z at corner points is as shown :
Corner points | ||
106.67 | ||
104 | minimum | |
200 | maximum | |
Feasible region is unbounded , therefore 104 may or may not be minimum value of Z .
For this we draw or and check whether resulting half plane has point in common with feasible region or not.
We can see feasible region has no common point with .
Hence , Z has minimum value 104.
Answer:
Let farmer buy x kg of fertilizer F1 and y kg of F2 .Thus, .
The given information can be represented in table as :
Nitrogen | phosphoric acid | Cost | |
F1 | 10 | 6 | 6 |
F2 | 5 | 10 | 5 |
requirement | 14 | 14 |
F1 contain 10% nitrogen and F2 contain 5% nitrogen .Farmer requires atleast 14 kg of nitrogen
F1 contain 6% phophoric acid and F2 contain 10% phosphoric acid .Farmer requires atleast 14 kg of nitrogen
Total cost is Z .
Subject to constraint ,
The feasible region determined by constraints is as follows:
It can be seen that feasible region is unbounded.
The corner points of feasible region are
The value of Z at corner points is as shown :
corner points | ||
1400 | ||
1000 | minimum | |
1400 |
Feasible region is unbounded , therefore 1000 may or may not be minimum value of Z .
For this we draw and check whether resulting half plane has point in common with feasible region or not.
We can see feasible region has no common point with .
Hence , Z has minimum value 1000 at point
Question:11 The corner points of the feasible region determined by the following system of linear inequalities:
are and . Let where Condition on p and q so that the maximum of Z occurs at both and is
Answer:
The maximum value of Z is unique.
It is given that maximum value of Z occurs at two points .
Value of Z at =value of Z at
Hence, D is correct option.
NCERT solutions for class 12 maths chapter 12 linear programming-Miscellaneous Exercise
Question:1 Reference of Example 9 (Diet problem): A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30 g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q contains 3 units of calcium, 20 units of iron, 4 units of cholesterol and 3 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and at most 300 units of cholesterol.
Answer:
Let diet contain x packets of food P and y packets of food Q. Thus, .
The mathematical formulation of the given problem is as follows:
Total cost is Z .
Subject to constraint,
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
corner points | ||
150 | MINIMUM | |
285 | maximum | |
228 |
Hence, Z has a maximum value of 285 at the point .
to maximise the amount of vitamin A in the diet, 40 packets of food P and 15 packets of food Q should be used. The maximum amount of vitamin A is 285 units.
Answer:
Let farmer mix x bags of brand P and y bags of brand Q. Thus, .
The given information can be represented in the table as :
Vitamin A | Vitamin B | Cost | |
Food P | 3 | 5 | 60 |
Food Q | 4 | 2 | 80 |
requirement | 8 | 11 |
The given problem can be formulated as follows:
Therefore, we have
Subject to constraint,
The feasible region determined by constraints is as follows:
The corner points of the feasible region are
The value of Z at corner points is as shown :
corner points | ||
4500 | ||
2650 | ||
1950 | minimum | |
2400 |
Feasible region is unbounded, therefore 1950 may or may not be a minimum value of Z. For this, we draw and check whether resulting half plane has a point in common with the feasible region or not.
We can see a feasible region has no common point with .
Hence, Z has a minimum value 1950 at point .
Answer:
Let mixture contain x kg of food X and y kg of food Y.
Mathematical formulation of given problem is as follows:
Minimize :
Subject to constraint ,
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
corner points | ||
160 | ||
112 | minimum | |
116 | ||
160 |
The feasible region is unbounded , therefore 112 may or may not be minimum value of Z .
For this we draw and check whether resulting half plane has point in common with feasible region or not.
We can see feasible region has no common point with .
Hence , Z has minimum value 112 at point
Answer:
Let x and y toys of type A and type B.
Mathematical formulation of given problem is as follows:
Minimize :
Subject to constraint ,
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
corner points | ||
150 | ||
250 | ||
262.5 | maximum | |
200 |
Therefore 262.5 may or may not be maximum value of Z .
Hence , Z has maximum value 262.5 at point
Answer:
Let airline sell x tickets of executive class and y tickets of economy class.
Mathematical formulation of given problem is as follows:
Minimize :
Subject to constraint ,
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
corner points | ||
68000 | ||
136000 | maximum | |
128000 | ||
therefore 136000 is maximum value of Z .
Hence , Z has maximum value 136000 at point
Answer:
Let godown A supply x and y quintals of grain to shops D and E respectively. Then , (100-x-y) will be supplied to shop F. Requirements at shop D is 60 since godown A supply x .Therefore remaining (60-x) quintals of grain will be transported from godown B.
Similarly, (50-y) quintals and 40-(100-x-y)=(x+y-60) will be transported from godown B to shop E and F respectively. The problem can be represented diagrammatically as follows:
and
and
Total transportation cost z is given by ,
Mathematical formulation of given problem is as follows:
Minimize :
Subject to constraint ,
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
corner points | ||
560 | ||
620 | ||
610 | ||
510 | minimum |
therefore 510 may or may not be minimum value of Z .
Hence , Z has miniimum value 510 at point
Answer:
Let x and y litres of oil be supplied from A to petrol pump,D and E. Then , (7000-x-y) will be supplied from A to petrol pump F.
Requirements at petrol pump D is 4500 L. since x L A are transported from depot A,remaining 4500-x L will be transported from petrol pump B
Similarly, (3000-y)L and 3500-(7000-x-y)=(x+y-3500) L will be transported from depot B to petrol E and F respectively.
The problem can be represented diagrammatically as follows:
and
and
Cost of transporting 10 L petrol =Re 1
Cost of transporting 1 L petrol
Total transportation cost z is given by ,
Mathematical formulation of given problem is as follows:
Minimize :
Subject to constraint ,
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
corner points | ||
5000 | ||
5300 | ||
5550 | ||
4400 | minimum | |
5450 |
Hence , Z has miniimum value 4400 at point
Answer:
Let fruit grower use x bags of brand P and y bags of brand Q.
Mathematical formulation of given problem is as follows:
Minimize :
Subject to constraint ,
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
corner points | ||
595 | ||
550 | ||
470 | minimum | |
Therefore 470 is minimum value of Z .
Hence , Z has minimum value 470 at point
Question:9 Reference of Que 8 : A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine.
Kg per bag | ||
Brand A | Brand P | |
Nitrogen | 3 | 3.5 |
Phosphoric Acid | 1 | 2 |
Potash | 3 | 1.5 |
Chlorine | 1.5 | 2 |
Answer:
Let fruit grower use x bags of brand P and y bags of brand Q.
Mathematical formulation of given problem is as follows:
Maximize :
Subject to constraint ,
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
corner points | ||
595 | maximum | |
550 | ||
470 | minimum | |
therefore 595 is maximum value of Z .
Hence , Z has minimum value 595 at point
Answer:
Let x and y be number of dolls of type A abd B respectively that are produced per week.
Mathematical formulation of given problem is as follows:
Maximize :
Subject to constraint ,
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
corner points | ||
7200 | ||
15000 | ||
16000 | Maximum | |
Therefore 16000 is maximum value of Z .
Hence , Z has minimum value 16000 at point
If you are looking for ncert exercise solutions of linear programming class 12 then they are listed below.
In this article, you will get NCERT solutions for class 12 and you can also use the webpage pdf downloader tool to download NCERT Solutions for Class 12 maths chapter 12 PDF from here. Generally, one five marks question is asked from Linear programming class 12 in the final examination. This chapter has around 21 lpp class 12 questions, here you will find all solutions very easily. These NCERT Class 12 maths solutions chapter 12 are explained in a detailed manner that will help you in scoring high scores.
Let's take an NCERT problem - A furniture dealer deals in only two items–chairs and tables. Has storage space of at most 60 pieces and He has Rs 50,000 to invest. A chair costs Rs 500 and A table costs Rs 2500. He estimates that from the sale of one chair, he can make a profit of Rs 75 and that from the sale of one table a profit of Rs 250. He wants to know how many chairs and tables he should buy from the available money so as to maximise his total profit, assuming that he can sell all the items which he buys.
The problems that involve maximising cost and minimising profit are called optimization problems. This ch 12 maths class 12 is quite important because it includes such concepts. The above given problem is an example of linear programming.
Also read,
12.1 Introduction
12.2 Linear Programming Problem and its Mathematical Formulation
12.2.1 Mathematical formulation of the problem
12.2.2 Graphical method of solving linear programming problems
12.3 Different Types of Linear Programming Problems
Detailed explanations: The class 12 maths ch 12 question answer provided in NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming are explained in a detailed and step-by-step manner. This helps students to understand the concepts better and makes it easy for them to solve similar problems.
Easy to understand: The maths chapter 12 class 12 solutions are written in simple language, making it easy for students to understand and learn the concepts. The solutions are designed to cater to the needs of students of all learning levels.
Covers all the topics: The class 12 linear programming solutions cover all the topics in Chapter 12 Linear Programming of Class 12 Maths. This helps students to have a comprehensive understanding of the chapter.
As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
NCERT Class 12 maths solutions chapter 12 are prepared and explained in detailed form. It makes these Class 12 maths chapter 12 NCERT solutions easy to understand.
NCERT Solutions for Class 12 maths chapter 12 PDF is very helpful for the preparation of this chapter.
These NCERT Solutions for Class 12 maths chapter 12 will give you a new way to solve questions.
Miscellaneous exercise is quite important, so to develop a grip on the concepts. In NCERT Class 12 maths solutions chapter 12 linear programming, you will get solutions for miscellaneous exercise too.
Happy Reading!
As most the questions in CBSE board exam are asked directly from NCERT textbook, so one must know the NCERT well but only knowing the answer is not guaranteed to score good marks in the exam. One should know how to answer in board exams in order to get good marks. NCERT solutions are provided by the experts who know how best to write answers in the board exam in order to get good marks. Interested students can study linear programming class 12 solutions pdf both online and offline.
Yes, linear programming is useful in formulating these real-life problems into a mathematical model and then solving them. Some optimisation problems like maximizing the profits and minimizing the cost can be solved by linear programming. concepts of liner programming important in board and engineering exam therefore this chapter is very important. you should solve ncert exercise to get command on concepts.
No, CBSE doesn’t provide NCERT solutions for any class or subject. but you can find solutions free from careers360 official website. these solutions are explained in details by our expert team in very simple format so that students can understand these very easily.
Here, you will get the detailed NCERT solutions for class 12 maths by clicking on the links that are listed above in this article, for comfortability of students these are listed subjects as well as chapter wise. or you can find these solutions from careers360 official website.
Generally, one question of 5 marks is asked from this chapter in the CBSE 12th board final exam. if you want to score five out of five then it demand practice and in depth understanding of concepts therefore it ncert solutions and ncert exercise are recommended to students.
Linear programming problem and its mathematical formulation, graphical method of solving linear programming problems are the important topics of this chapter. you can refer NCERT solutions to get in depth understanding and getting hold on concepts.
hello,
Yes you can appear for the compartment paper again since CBSE gives three chances to a candidate to clear his/her exams so you still have two more attempts. However, you can appear for your improvement paper for all subjects but you cannot appear for the ones in which you have failed.
I hope this was helpful!
Good Luck
Hello dear,
If you was not able to clear 1st compartment and now you giving second compartment so YES, you can go for your improvement exam next year but if a student receives an improvement, they are given the opportunity to retake the boards as a private candidate the following year, but there are some requirements. First, the student must pass all of their subjects; if they received a compartment in any subject, they must then pass the compartment exam before being eligible for the improvement.
As you can registered yourself as private candidate for giving your improvement exam of 12 standard CBSE(Central Board of Secondary Education).For that you have to wait for a whole year which is bit difficult for you.
Positive side of waiting for whole year is you have a whole year to preparing yourself for your examination. You have no distraction or something which may causes your failure in the exams. In whole year you have to stay focused on your 12 standard examination for doing well in it. By this you get a highest marks as a comparison of others.
Believe in Yourself! You can make anything happen
All the very best.
Hello Student,
I appreciate your Interest in education. See the improvement is not restricted to one subject or multiple subjects and we cannot say if improvement in one subject in one year leads to improvement in more subjects in coming year.
You just need to have a revision of all subjects what you have completed in the school. have a revision and practice of subjects and concepts helps you better.
All the best.
If you'll do hard work then by hard work of 6 months you can achieve your goal but you have to start studying for it dont waste your time its a very important year so please dont waste it otherwise you'll regret.
Yes, you can take admission in class 12th privately there are many colleges in which you can give 12th privately.
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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 Investment Banking career involves the invention and generation of capital for other organizations, governments, and other entities. Individuals who opt for a career as Investment Bankers are the head of a team dedicated to raising capital by issuing bonds. Investment bankers are termed as the experts who have their fingers on the pulse of the current financial and investing climate. Students can pursue various Investment Banker courses, such as Banking and Insurance, and Economics to opt for an Investment Banking career path.
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.
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
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