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NCERT Solutions for Exercise 9.4 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 9.4 Class 12 Maths chapter 9 gives an idea about how to solve differential equations of variable separable type. The given differential equations are converted to variable separable forms and are solved using integration. The NCERT solutions for Class 12 Maths chapter 9 exercise 9.4 presents such 23 questions. In Class 12 Maths chapter 9 exercise 9.4 certain cases are discussed where the differential equations are to be formed using the given data and then solve using the variable separable method. Two more methods were discussed in the coming exercises to solve the differential equations.
12th class Maths exercise 9.4 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.
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Question:1 Find the general solution:
Answer:
Given,
Question:5 Find the general solution:
Answer:
Given, in the question
Let,
This is the general solution
Question:7 Find the general solution:
Answer:
Given,
let logy = t
=> 1/ydy = dt
This is the general solution
Question:8 Find the general solution:
Answer:
Given, in the question
This is the required general equation.
Question:11 Find a particular solution satisfying the given condition:
Answer:
Given, in the question
Now,
Now comparing the coefficients
A + B = 2; B + C = 1; A + C = 0
Solving these:
Putting the values of A,B,C:
Therefore,
Now, y= 1 when x = 0
c = 1
Putting the value of c, we get:
Question:12 Find a particular solution satisfying the given condition:
Answer:
Given, in the question
Let,
Now comparing the values of A,B,C
A + B + C = 0; B-C = 0; A = -1
Solving these:
Now putting the values of A,B,C
Given, y =0 when x =2
Therefore,
Question:13 Find a particular solution satisfying the given condition:
Answer:
Given,
Now, y =1 when x =0
1 = 0 + c
Therefore, c = 1
Putting the value of c:
Question:14 Find a particular solution satisfying the given condition:
Answer:
Given,
Now, y=1 when x =0
1 = ksec0
k = 1
Putting the vlue of k:
y = sec x
Question:15 Find the equation of a curve passing through the point (0, 0) and whose differential equation is .
Answer:
We first find the general solution of the given differential equation
Given,
Now, Since the curve passes through (0,0)
y = 0 when x =0
Putting the value of c, we get:
Question:16 For the differential equation , find the solution curve passing through the point (1, –1).
Answer:
We first find the general solution of the given differential equation
Given,
Now, Since the curve passes through (1,-1)
y = -1 when x = 1
Putting the value of C:
Answer:
According to the question,
Now, Since the curve passes through (0,-2).
x =0 and y = -2
Putting the value of c, we get
Answer:
Slope m of line joining (x,y) and (-4,-3) is
According to the question,
Now, Since the curve passes through (-2,1)
x = -2 , y =1
Putting the value of k, we get
Answer:
Volume of a sphere,
Given, Rate of change is constant.
Now, at t=0, r=3 and at t=3 , r =6
Putting these value:
Also,
Putting the value of c and k:
Answer:
Let p be the principal amount and t be the time.
According to question,
Now, at t =0 , p = 100
and at t =10, p = 200
Putting these values,
Also,
,
So value of r = 6.93%
Answer:
Let p be the principal amount and t be the time.
According to question,
Now, at t =0 , p = 1000
Putting these values,
Also, At t=10
,
After 10 years, the total amount would be Rs.1648
Answer:
Let n be the number of bacteria at any time t.
According to question,
Now, at t=0, n = 100000
Again, at t=2, n= 110000
Using these values, for n= 200000
There are 23 questions in the NCERT syllabus exercise 9.4 Class 12 Maths. The first 10 questions of NCERT solutions for Class 12 Maths chapter 9 exercise 9.4 is to find the general solutions. Next 12 questions of Class 12 Maths chapter 9 exercise 9.4 is to find particular solutions using the variable separable method. And last one question of Class 12th Maths chapter 6 exercise 9.4 is of objective type and is to find the general solution.
The differential equations of order 1 and degree 1 are handled.
Differential equations of variable separable type are solved in the NCERT solutions for Class 12 Maths chapter 9 exercise 9.4.
Six example problems and their solutions are given under topic 9.5.1.
Twenty-three questions are explained in the Class 12th Maths chapter 6 exercise 9.4.
One question is of objective type with 4 choices.
Three subtopics are discussed in topic 9.5.
3 methods are discussed.
The topics discussed are listed below
Differential equations of variable separable type, homogeneous and linear differential equations.
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!
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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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