NCERT Solutions for Exercise 12.2 Class 12 Maths Chapter 12

NCERT Solutions for Exercise 12.2 Class 12 Maths Chapter 12 - Linear Programming

Edited By Ramraj Saini | Updated on Dec 04, 2023 11:08 AM IST | #CBSE Class 12th

NCERT Solutions For Class 12 Maths Chapter 12 Exercise 12.2

NCERT Solutions for Exercise 12.2 Class 12 Maths Chapter 12 Linear Programming are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. NCERT solutions for exercise 12.2 Class 12 Maths chapter 12 discuss a few types of linear programming problems. There are 11 practice questions given in exercise 12.2 Class 12 Maths. All these problems of NCERT solutions for Class 12 Maths chapter 12 exercise 12.2 are done using graphical methods. Manufacturing problems, diet problems, transportation problems are some of the linear programming problems given in the Class 12 Maths chapter 12 exercise 12.2. According to the given statements, the given objective functions and the constraints are formulated and then solved using graphical methods. Along with the Class 12 Maths chapter 12 exercise 12.2 solutions there are two more exercises.

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All these NCERT problems are solved by Mathematics expert faculties and NCERT solutions for Class 12 Maths chapter 12 exercise 12.2 can be used for the preparation of the CBSE Class 12 Board Exam. 12th class Maths exercise 12.2 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise enumerated in NCERT Book together using the link provided below.

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Access NCERT Solutions for Class 12 Maths Chapter 12 Exercise 12.2

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Linear Programming Class 12 Chapter 12-Exercise: 12.2

Question:1 Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60/kg and Food Q costs Rs.80/kg. Food P contains 3 units/kg of Vitamin A and 5 units/kg of Vitamin B while food Q contains 4 units/kg of Vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture.

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Answer:

Let mixture contain x kg of food P and y kg of food Q. Thus, $x\geq 0,y\geq 0$ .

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

$3x+4y\geq 8$

$5x+2y\geq 11$

Total cost is Z. $Z=60x+80y$

Subject to constraint,

$3x+4y\geq 8$

$5x+2y\geq 11$

$x\geq 0,y\geq 0$

The feasible region determined by constraints is as follows:

1627041171227

It can be seen that a feasible region is unbounded.

The corner points of the feasible region are $A(\frac{8}{3},0),B(2,\frac{1}{2}),C(0,\frac{11}{2})$

The value of Z at corner points is as shown :

corner points	$Z=60x+80y$
$A(\frac{8}{3},0)$	160	MINIMUM
$B(2,\frac{1}{2})$	160	minimum
$C(0,\frac{11}{2})$	440

Feasible region is unbounded, therefore 160 may or may not be the minimum value of Z.

For this, we draw $60x+80y< 160\, \, or \, \, \, 3x+4y< 8$ 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. $\, \, 3x+4y< 8$

Hence, Z has a minimum value 160 at line segment joining points $A(\frac{8}{3},0)$ and $B(2,\frac{1}{2})$ .

Question:2 One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.

Answer:

Let there be x cakes of first kind and y cakes of the second kind.Thus, $x\geq 0,y\geq 0$ .

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,

$200x+100y\leq 5000$

$\Rightarrow \, \, \, \, 2x+y\leq 50$

. $\, \, 25x+50y\leq 10000$

$\Rightarrow \, \, x+2y\leq 400$

The total number of cakes, Z. Z=X+Y

Subject to constraint,

$\Rightarrow \, \, \, \, 2x+y\leq 50$

$\Rightarrow \, \, x+2y\leq 400$

$x\geq 0,y\geq 0$

The feasible region determined by constraints is as follows:

1627041262324

The corner points of the feasible region are $A(25,0),B(20,10),C(0,20),D(0,0)$

The value of Z at corner points is as shown :

corner points	Z=X+Y
$A(25,0)$	25
$B(20,10)$	30	maximum
$C(0,20)$ $D(0,0)$	20 0	minimum

The maximum cake can be made 30 (20 of the first kind and 10 of the second kind).

Question:3 A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time.

(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. $1.5x+3y\leq 42$

craftsman’s time availability is 24 hours

i.e. $3x+y\leq 24$

The factory has to work at full capacity.

Hence, $1.5x+3y= 42...............1$

$3x+y= 24...............2$

Solving equation 1 and 2, we have

$x=4\, \, and\, \, \, y=12$

Thus, 4 rackets and 12 bats are to be made .

(ii) If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity.

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

$1.5x+3y\leq 42$

$3x+y\leq 24$

$x,y\geq 0$

The profit on the bat is 10 and on the racket is 20.

$Z=20x+10y$

The mathematical formulation is :

maximise $Z=20x+10y$

subject to constraints,

$1.5x+3y\leq 42$

$3x+y\leq 24$

$x,y\geq 0$

The feasible region determined by constraints is as follows:

1627370575766

The corner points are $A(8,0),B(4,12),C(0,14),D(0,0)$

The value of Z at corner points is as shown :

CORNER POINTS	$Z=20x+10y$
$A(8,0)$	160
$B(4,12)$	200	maximum
$C(0,14)$	140
$D(0,0)$	0

Thus, the maximum profit of the factory when it works at full capacity is 200.

Question:4 A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?

Answer:

Let packages of nuts be x and packages of bolts be y .Thus, $x\geq 0,y\geq 0$ .

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

$x+3y\leq 12$

$3x+y\leq 12$

$x\geq 0,y\geq 0$

$Z= 17.5x+7y$

The feasible region determined by constraints is as follows:

1627370632779

The corner points of feasible region are $A(4,0),B(3,3),C(0,4),D(0,0)$

The value of Z at corner points is as shown :

Corner points	$Z= 17.5x+7y$
$A(4,0)$	70
$B(3,3)$	73.5	maximum
$C(0,4)$	28
$D(0,0)$	0

The maximum value of z is 73.5 at $B(3,3)$ .

Thus, 3 packages of nuts and 3 packages of bolts should be manufactured everyday to get maximum profit.

Question:5 A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs 7 and screws B at a profit of Rs 10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximise his profit? Determine the maximum profit.

Answer:

Let factory manufactures screws of type A and factory manufactures screws of type B. Thus, $x\geq 0,y\geq 0$ .

The given information can be represented in the table as :

	screw A	screw B	availability
Automatic machine	4	6	$4\times 60=240$
hand operated machine	6	3	$4\times 60=240$

Profit on a package of screw A is Rs.7 and on the package of screw B is 10.

Therefore, the constraint is

$4x+6y\leq 240$

$6x+3y\leq 240$

$x\geq 0,y\geq 0$

$Z= 7x+10y$

The feasible region determined by constraints is as follows:

1627370732345

The corner points of the feasible region are $A(40,0),B(30,20),C(0,40),D(0,0)$

The value of Z at corner points is as shown :

Corner points	$Z= 7x+10y$
$A(40,0)$	280
$B(30,20)$	410	maximum
$C(0,40)$	400
$D(0,0)$	0

The maximum value of z is 410 at $B(30,20)$ .

Thus, 30 packages of screw A and 20 packages of screw B should be manufactured every day to get maximum profit.

Question:6 A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?

Answer:

Let the cottage industry manufactures x pedestal lamps and y wooden shades. Thus, $x\geq 0,y\geq 0$ .

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

$2x+y\leq 12$

$3x+2y\leq 20$

$x\geq 0,y\geq 0$

$Z= 5x+3y$

The feasible region determined by constraints is as follows:

1627370794134

The corner points of the feasible region are $A(6,0),B(4,4),C(0,10),D(0,0)$

The value of Z at corner points is as shown :

Corner points	$Z= 5x+3y$
$A(6,0)$	30
$B(4,4)$	32	maximum
$C(0,10)$	30
$D(0,0)$	0

The maximum value of z is 32 at $B(4,4)$ .

Thus, 4 shades and 4 pedestals lamps should be manufactured every day to get the maximum profit.

Question:7 A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximise the profit?

Answer:

Let x be Souvenirs of type A and y be Souvenirs of type B .Thus, $x\geq 0,y\geq 0$ .

The given information can be represented in table as :

	Type A	Type B	availability
cutting	5	8	$(3\times 60)+20=200$
asembling	10	8	$4\times 60=240$

Profit on type A Souvenirs is Rs. 5 and on type B Souvenirs is 6.

Therefore, constraint are

$5x+8y\leq 200$

$10x+8y\leq 240$

$x\geq 0,y\geq 0$

$Z=5x+6y$

The feasible region determined by constraints is as follows:

1627370879345

The corner points of feasible region are $A(24,0),B(8,20),C(0,25),D(0,0)$

The value of Z at corner points is as shown :

Corner points	$Z=5x+6y$
$A(24,0)$	120
$B(8,20)$	160	maximum
$C(0,25)$	150
$D(0,0)$	0

The maximum value of z is 160 at $B(8,20)$ .

Thus,8 Souvenirs of type A and 20 Souvenirs of type B should be manufactured everyday to get maximum profit.

Question:8 A merchant plans to sell two types of personal computers – a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000.

Answer:

Let merchant plans has personal computers x desktop model and y portable model

.Thus, $x\geq 0,y\geq 0$ .

The cost of desktop model is cost Rs 25000 and portable model is Rs 40000.

Merchant can invest Rs 70 lakhs maximum.

$25000x+40000y\leq 7000000$

$5x+8y\leq 1400$

the total monthly demand of computers will not exceed 250 units.

$x+y\leq 250$

profit on the desktop model is Rs 4500 and on portable model is Rs 5000.

Total profit = Z , $Z=4500x+5000y$

The mathematical formulation of given problem is :
$5x+8y\leq 1400$

$x+y\leq 250$

$x\geq 0,y\geq 0$

$Z=4500x+5000y$

The feasible region determined by constraints is as follows:

1627377288762

The corner points of feasible region are $A(250,0),B(200,50),C(0,175),D(0,0)$

The value of Z at corner points is as shown :

Corner points	$Z=4500x+5000y$
$A(250,0)$	1125000
$B(200,50)$	1150000	maximum
$C(0,175)$	875000
$D(0,0)$	0

The maximum value of z is 1150000 at $B(200,50)$ .

Thus, merchant should stock 200 desktop models and 50 portable models to get maximum profit.

Question:9 A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods F1 and F2 are available. Food F1 costs Rs 4 per unit food and F2 costs Rs 6 per unit. One unit of food F1 contains 3 units of vitamin A and 4 units of minerals. One unit of food F2 contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.

Answer:

Let diet contain x unit of food F1 and y unit of foof F2 .Thus, $x\geq 0,y\geq 0$ .

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

$3x+4y\geq 4$

$6x+3y\geq 6$

$x\geq 0,y\geq 0$

$Z= 4x+6y$

The feasible region determined by constraints is as follows: 1627377385273

We can see feasible region is unbounded.

The corner points of feasible region are $A(\frac{80}{3},0),B(24,\frac{4}{3}),C(0,\frac{100}{3})$

The value of Z at corner points is as shown :

Corner points	$Z= 4x+6y$
$A(\frac{80}{3},0)$	106.67
$B(24,\frac{4}{3}),$	104	minimum
$C(0,\frac{100}{3})$	200	maximum

Feasible region is unbounded , therefore 104 may or may not be minimum value of Z .

For this we draw $4x+6y< 104$ or $2x+3y< 52$ 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 $2x+3y< 52$ .

Hence , Z has minimum value 104.

Question:10 There are two types of fertilisers F1 and F2 . F1 consists of 10% nitrogen and 6% phosphoric acid and F2 consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs atleast 14 kg of nitrogen and 14 kg of phosphoric acid for her crop. If F1 costs Rs 6/kg and F2 costs Rs 5/kg, determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?

Answer:

Let farmer buy x kg of fertilizer F1 and y kg of F2 .Thus, $x\geq 0,y\geq 0$ .

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

$10\%x+5\%y\geq 14$

$\frac{x}{10}+\frac{y}{20}\geq 14$

$2x+y\geq 280$

F1 contain 6% phophoric acid and F2 contain 10% phosphoric acid .Farmer requires atleast 14 kg of nitrogen

$6\%x+10\%y\geq 14$

$\frac{6x}{100}+\frac{y}{20}\geq 14$

$3x+56y\geq 700$

Total cost is Z . $Z=6x+5y$

Subject to constraint ,

$2x+y\geq 280$

$3x+56y\geq 700$

$x\geq 0,y\geq 0$

$Z=6x+5y$

The feasible region determined by constraints is as follows:

1627377453836

It can be seen that feasible region is unbounded.

The corner points of feasible region are $A(\frac{700}{3},0),B(100,80),C(0,280)$

The value of Z at corner points is as shown :

corner points	$Z=6x+5y$
$A(\frac{700}{3},0)$	1400
$,B(100,80)$	1000	minimum
$C(0,280)$	1400

Feasible region is unbounded , therefore 1000 may or may not be minimum value of Z .

For this we draw $6x+5y< 1000$ 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 $6x+5y< 1000$ .

Hence , Z has minimum value 1000 at point $,B(100,80)$

Question:11 The corner points of the feasible region determined by the following system of linear inequalities:

$2x+y \leq 10,x+3y \leq 15,x,y\geq 0$ are $(0,0),(5,0),(3,4)$ and $(0,5)$ . Let $Z=px+qy,$ where $p,q > 0.$ Condition on p and q so that the maximum of Z occurs at both $(3,4)$ and $(0,5)$ is

Answer:

The maximum value of Z is unique.

It is given that maximum value of Z occurs at two points $(3,4)\, \, and\, \, \, (0,5)$ .

$\therefore$ Value of Z at $(3,4)$ =value of Z at $(0,5)$

$\Rightarrow \, \, \, p(3)+q(4)=p(0)+q(5)$

$\Rightarrow \, \, \, 3p+4q=5q$

$\Rightarrow \, \, \, q=3p$

Hence, D is correct option.

Benefits of NCERT Solutions for Class 12 Maths Chapter 12 Exercise 12.2

For CBSE board exams students can expect one similar question as discussed in NCERT book exercise 12.2 Class 12 Maths
The Class 12 Maths chapter 12 exercise 12.2 solutions are available for free and can be downloaded using any downloading tools
These solutions will help students to improve their conceptual understanding

Key Features Of NCERT Solutions for Exercise 12.2 Class 12 Maths Chapter 12

Comprehensive Coverage: The solutions encompass all the topics covered in ex 12.2 class 12, ensuring a thorough understanding of the concepts.
Step-by-Step Solutions: In this class 12 maths ex 12.2, each problem is solved systematically, providing a stepwise approach to aid in better comprehension for students.
Accuracy and Clarity: Solutions for class 12 ex 12.2 are presented accurately and concisely, using simple language to help students grasp the concepts easily.
Conceptual Clarity: In this 12th class maths exercise 12.2 answers, emphasis is placed on conceptual clarity, providing explanations that assist students in understanding the underlying principles behind each problem.
Inclusive Approach: Solutions for ex 12.2 class 12 cater to different learning styles and abilities, ensuring that students of various levels can grasp the concepts effectively.
Relevance to Curriculum: The solutions for class 12 maths ex 12.2 align closely with the NCERT curriculum, ensuring that students are prepared in line with the prescribed syllabus.

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Frequently Asked Questions (FAQs)

1. What are the benefits of solving exercise 12.2 Class 12 Maths?

By solving the Class 12 Maths NCERT syllabus chapter 12 exercise 2 problems students will be able to clarify their doubts in the concepts covered in the chapter and will be helpful for exams also

2. List out a few types of linear programming problems?

Some of the linear programming problems are diet problems, manufacturing problems, allocation problems and transportation problems

3. What is the manufacturing problems discussed in the Class 12 NCERT Maths chapter 12?

The number of products which should be produced and sold is determined here subjected to some constraints like manpower, machines, labour etc

4. What is diet problems in linear programming?

Diet problems minimise the cost of diet subjected to the amount of different nutrients required

5. What is the significance of linear programming problems in the CBSE board exam point of view?

Students may get up to 5 marks questions from the Class 12 NCERT chapter linear programming

6. Can we solve Class 12 maths chapter 12 exercise 12.2 directly without solving exercise 12.1 Class 12 Maths?

No, exercise 12.1 explains the method of solving linear programming problems using graphs. Once students are through with the first exercise they can move to the second one. The concepts covered in the first exercise are used to solve the second exercise.

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quartely question paper for mathematics cbse

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Ah, you're looking for CBSE quarterly question papers for mathematics, right? Those can be super helpful for exam prep.

Unfortunately, CBSE doesn't officially release quarterly papers - they mainly put out sample papers and previous years' board exam papers. But don't worry, there are still some good options to help you practice!

Have you checked out the CBSE sample papers on their official website? Those are usually pretty close to the actual exam format. You could also look into previous years' board exam papers - they're great for getting a feel for the types of questions that might come up.

If you're after more practice material, some textbook publishers release their own mock papers which can be useful too.

Let me know if you need any other tips for your math prep. Good luck with your studies!

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Jefferson 25 September,2024

i have taken admission in clg after my campartment exam in chemistry along with the neet 2025 preperation but unfortunately i again got campartment after doing all this preparation i got 15 marks only now I can't able to think what should I do next.

It's understandable to feel disheartened after facing a compartment exam, especially when you've invested significant effort. However, it's important to remember that setbacks are a part of life, and they can be opportunities for growth.

Possible steps:

Re-evaluate Your Study Strategies:
- Identify Weak Areas: Pinpoint the specific topics or concepts that caused difficulties.
- Seek Clarification: Reach out to teachers, tutors, or online resources for additional explanations.
- Practice Regularly: Consistent practice is key to mastering chemistry.
Consider Professional Help:
- Tutoring: A tutor can provide personalized guidance and support.
- Counseling: If you're feeling overwhelmed or unsure about your path, counseling can help.
Explore Alternative Options:
- Retake the Exam: If you're confident in your ability to improve, consider retaking the chemistry compartment exam.
- Change Course: If you're not interested in pursuing chemistry further, explore other academic options that align with your interests.
Focus on NEET 2025 Preparation:
- Stay Dedicated: Continue your NEET preparation with renewed determination.
- Utilize Resources: Make use of study materials, online courses, and mock tests.
Seek Support:
- Talk to Friends and Family: Sharing your feelings can provide comfort and encouragement.
- Join Study Groups: Collaborating with peers can create a supportive learning environment.

Remember: This is a temporary setback. With the right approach and perseverance, you can overcome this challenge and achieve your goals.

I hope this information helps you.

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Kanishka kaushikii 17 September,2024

i scored 84 percent in cbse 2 years ago.Am i eligible for medhavi scholarship if give 12th again after 2 drop years and will got 75+ in mpboard

Hi,

Qualifications:
Age: As of the last registration date, you must be between the ages of 16 and 40.
Qualification: You must have graduated from an accredited board or at least passed the tenth grade. Higher qualifications are also accepted, such as a diploma, postgraduate degree, graduation, or 11th or 12th grade.
How to Apply:
Get the Medhavi app by visiting the Google Play Store.
Register: In the app, create an account.
Examine Notification: Examine the comprehensive notification on the scholarship examination.
Sign up to Take the Test: Finish the app's registration process.
Examine: The Medhavi app allows you to take the exam from the comfort of your home.
Get Results: In just two days, the results are made public.
Verification of Documents: Provide the required paperwork and bank account information for validation.
Get Scholarship: Following a successful verification process, the scholarship will be given. You need to have at least passed the 10th grade/matriculation scholarship amount will be transferred directly to your bank account.

Scholarship Details:

Type A: For candidates scoring 60% or above in the exam.

Type B: For candidates scoring between 50% and 60%.

Type C: For candidates scoring between 40% and 50%.

Cash Scholarship:

Scholarships can range from Rs. 2,000 to Rs. 18,000 per month, depending on the marks obtained and the type of scholarship exam (SAKSHAM, SWABHIMAN, SAMADHAN, etc.).

Since you already have a 12th grade qualification with 84%, you meet the qualification criteria and are eligible to apply for the Medhavi Scholarship exam. Make sure to prepare well for the exam to maximize your chances of receiving a higher scholarship.

Hope you find this useful!

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Yuvan 30 August,2024

i upload 12th board result screenshot in ncweb form from the cbse site so it is valid

hello mahima,

If you have uploaded screenshot of your 12th board result taken from CBSE official website,there won,t be a problem with that.If the screenshot that you have uploaded is clear and legible. It should display your name, roll number, marks obtained, and any other relevant details in a readable forma.ALSO, the screenshot clearly show it is from the official CBSE results portal.

hope this helps.

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Ashvadha 12 July,2024

Kya mujhe class 12 ka important question milega jo exam mai per year puche jate hai

Hello Akash,

If you are looking for important questions of class 12th then I would like to suggest you to go with previous year questions of that particular board. You can go with last 5-10 years of PYQs so and after going through all the questions you will have a clear idea about the type and level of questions that are being asked and it will help you to boost your class 12th board preparation.

You can get the Previous Year Questions (PYQs) on the official website of the respective board.

I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.

Thank you and wishing you all the best for your bright future.

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kumardurgesh1802 10 July,2024

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Central Board of Secondary Education Class 12th Examination

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Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

Option 1) less than 3	Option 2) more than 3 but less than 6
Option 3) more than 6 but less than 9	Option 4) more than 9

NCERT Solutions for Exercise 12.2 Class 12 Maths Chapter 12 - Linear Programming

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