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NCERT Solutions for Exercise 9.3 Class 12 Maths Chapter 9 Differential Equations 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 9.3 Class 12 Maths chapter 9 comes under topic 9.4 of NCERT Class 12 Mathematics Book. The questions in exercise 9.3 Class 12 Maths are related to the concepts of forming a Differential Equation that represents a given family of curves. Differential equations related to the family of lines, parabolas, ellipse, circles etc are discussed. The procedures to form the differential equation that represents the family of a curve are detailed before the Class 12th Maths chapter 6 exercise 9.3. The other concepts discussed in the unit are detailed in the following exercises.
12th class Maths exercise 9.3 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 together using the link provided below.
Also read -
Answer:
Given equation is
Differentiate both the sides w.r.t x
Now, again differentiate it w.r.t x
Therefore, the required differential equation is or
Answer:
Given equation is
Differentiate both the sides w.r.t x
-(i)
Now, again differentiate it w.r.t x
-(ii)
Now, divide equation (i) and (ii)
Therefore, the required differential equation is
Answer:
Given equation is
-(i)
Differentiate both the sides w.r.t x
-(ii)
Now, again differentiate w.r.t. x
-(iii)
Now, multiply equation (i) with 2 and add equation (ii)
-(iv)
Now, multiply equation (i) with 3 and subtract from equation (ii)
-(v)
Now, put values from (iv) and (v) in equation (iii)
Therefore, the required differential equation is
Answer:
Given equation is
-(i)
Now, differentiate w.r.t x
-(ii)
Now, again differentiate w.r.t x
-(iii)
Now, multiply equation (ii) with 2 and subtract from equation (iii)
-(iv)
Now,put the value in equation (iii)
Therefore, the required equation is
Answer:
Given equation is
-(i)
Now, differentiate w.r.t x
-(ii)
Now, again differentiate w.r.t x
-(iii)
Now, multiply equation (i) with 2 and multiply equation (ii) with 2 and add and subtract from equation (iii) respectively
we will get
Therefore, the required equation is
Question:6 Form the differential equation of the family of circles touching the y-axis at origin.
Answer:
If the circle touches y-axis at the origin then the centre of the circle lies at the x-axis
Let r be the radius of the circle
Then, the equation of a circle with centre at (r,0) is
-(i)
Now, differentiate w.r.t x
-(ii)
Put equation (ii) in equation (i)
Therefore, the required equation is
Answer:
Equation of perabola having vertex at origin and axis along positive y-axis is
(i)
Now, differentiate w.r.t. c
-(ii)
Put value from equation (ii) in (i)
Therefore, the required equation is
Question:8 Form the differential equation of the family of ellipses having foci on y-axis and centre at origin.
Answer:
Equation of ellipses having foci on y-axis and centre at origin is
-
Now, differentiate w..r.t. x
-(i)
Now, again differentiate w.r.t. x
-(ii)
Put value from equation (ii) in (i)
Our equation becomes
Therefore, the required equation is
Answer:
Equation of hyperbolas having foci on x-axis and centre at the origin
Now, differentiate w..r.t. x
-(i)
Now, again differentiate w.r.t. x
-(ii)
Put value from equation (ii) in (i)
Our equation becomes
Therefore, the required equation is
Question:10 Form the differential equation of the family of circles having centre on y-axis and radius 3 units.
Answer:
Equation of the family of circles having centre on y-axis and radius 3 units
Let suppose centre is at (0,b)
Now, equation of circle with center (0,b) an radius = 3 units
Now, differentiate w.r.t x
we get,
Put value fro equation (ii) in (i)
Therefore, the required differential equation is
Question:11 Which of the following differential equations has as the general solution?
(A)
(B)
(C)
(D)
Answer:
Given general solution is
Differentiate it w.r.t x
we will get
Again, Differentiate it w.r.t x
Therefore, (B) is the correct answer
Question:12 Which of the following differential equations has as one of its particular solution?
(A)
(B)
(C)
(D)
Answer:
Given equation is
Now, on differentiating it w.r.t x
we get,
and again on differentiating it w.r.t x
we get,
Now, on substituting the values of in all the options we will find that only option c which is satisfies
Therefore, the correct answer is (C)
Examples 4 to 8 are given before the exercise 9.3 Class 12 Maths to get an idea of the concepts discussed in the NCERT Book of Class 12 Maths chapter topic 9.4. And 12 questions are given in the Class 12 Maths chapter 9 exercise 9.3 for practice and these are solved here by mathematics expert faculties. It is better to try to solve the questions without looking for solutions. If any doubts arise while solving use NCERT solutions for Class 12 Maths chapter 9 exercise 9.3.
12 questions are explained through exercise 9.3 Class 12 Maths.
Two objective questions with 4 choices are given in the Class 12th Maths chapter 6 exercise 9.3.
Ellipse.
Students must be able to differentiate the given function. For this students should be aware of basic differentiation.
Yes, as NCERT is followed by CBSE students it is important to cover this chapter.
Yes, to solve certain problems or to represent a certain type of motions differential equations are used.
The concepts of order and degree of differential equations and general and particular solutions are covered.
The NCERT Class 12 exercise 9.3 covers the topic of forming differential equations of a family of curves.
Application Date:09 September,2024 - 14 November,2024
Application Date:09 September,2024 - 14 November,2024
Admit Card Date:04 October,2024 - 29 November,2024
Admit Card Date:04 October,2024 - 29 November,2024
Hello there! Thanks for reaching out to us at Careers360.
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!
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:
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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.
Hi,
Qualifications:
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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.
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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.
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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