JEE Exam > JEE Questions > Direction: Read the following text and answe...
Start Learning for Free
Direction: Read the following text and answer the following questions on the basis of the same:
Polio drops are delivered to 50K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation dy/dx = k(50 - y) where x denotes the number of weeks and y the number of children who have been given the drops.
Q. The value of C in the particular solution given that y(0) = 0 and k = 0.049 is
- a)log 50
- b)log 1/50
- c)50
- d)-50
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Direction: Read the following text and answer the following questions...
Given,
View all questions of this test
y(0) = and k = 0.049
We have, -log|50 - y| = Kx + C
log |50 - y| = -Kx - C
log |50 - 0| = 0 - C
[∵ x = 0, K = 0.049, y(0) = 0]
log 50 = - C
C = log 1/50
Most Upvoted Answer
Direction: Read the following text and answer the following questions...
Given Information:
The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops.
By the end of the 2nd week, half the children have been given the polio drops.
Differential Equation:
We are given the differential equation dy/dx = k(50 - y), where x denotes the number of weeks and y denotes the number of children who have been given the drops.
Particular Solution:
To find the particular solution, we need to find the value of C.
Given y(0) = 0, which means at the beginning (x = 0), no children have been given the drops.
Substituting the given values:
Substituting x = 0 and y = 0 in the differential equation, we get:
dy/dx = k(50 - y)
0 = k(50 - 0)
0 = 50k
Solving for k:
From the above equation, we can see that k = 0.
Substituting the value of k:
Now, substituting the value of k = 0 in the differential equation, we get:
dy/dx = 0(50 - y)
dy/dx = 0
Integrating both sides:
∫dy = ∫0 dx
y = C
Substituting the value of y(0) = 0:
We know that y = C, so substituting the value of y(0) = 0, we get:
0 = C
Conclusion:
Therefore, the value of C in the particular solution is 0.
The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops.
By the end of the 2nd week, half the children have been given the polio drops.
Differential Equation:
We are given the differential equation dy/dx = k(50 - y), where x denotes the number of weeks and y denotes the number of children who have been given the drops.
Particular Solution:
To find the particular solution, we need to find the value of C.
Given y(0) = 0, which means at the beginning (x = 0), no children have been given the drops.
Substituting the given values:
Substituting x = 0 and y = 0 in the differential equation, we get:
dy/dx = k(50 - y)
0 = k(50 - 0)
0 = 50k
Solving for k:
From the above equation, we can see that k = 0.
Substituting the value of k:
Now, substituting the value of k = 0 in the differential equation, we get:
dy/dx = 0(50 - y)
dy/dx = 0
Integrating both sides:
∫dy = ∫0 dx
y = C
Substituting the value of y(0) = 0:
We know that y = C, so substituting the value of y(0) = 0, we get:
0 = C
Conclusion:
Therefore, the value of C in the particular solution is 0.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Direction: Read the following text and answer the following questions on the basis of the same:Polio drops are delivered to 50K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation dy/dx = k(50 - y) where x denotes the number of weeks and y the number of children who have been given the drops.Q. The value of C in the particular solution given that y(0) = 0 and k = 0.049 isa)log 50b)log 1/50c)50d)-50Correct answer is option 'B'. Can you explain this answer?
Question Description
Direction: Read the following text and answer the following questions on the basis of the same:Polio drops are delivered to 50K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation dy/dx = k(50 - y) where x denotes the number of weeks and y the number of children who have been given the drops.Q. The value of C in the particular solution given that y(0) = 0 and k = 0.049 isa)log 50b)log 1/50c)50d)-50Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Direction: Read the following text and answer the following questions on the basis of the same:Polio drops are delivered to 50K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation dy/dx = k(50 - y) where x denotes the number of weeks and y the number of children who have been given the drops.Q. The value of C in the particular solution given that y(0) = 0 and k = 0.049 isa)log 50b)log 1/50c)50d)-50Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: Read the following text and answer the following questions on the basis of the same:Polio drops are delivered to 50K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation dy/dx = k(50 - y) where x denotes the number of weeks and y the number of children who have been given the drops.Q. The value of C in the particular solution given that y(0) = 0 and k = 0.049 isa)log 50b)log 1/50c)50d)-50Correct answer is option 'B'. Can you explain this answer?.
Direction: Read the following text and answer the following questions on the basis of the same:Polio drops are delivered to 50K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation dy/dx = k(50 - y) where x denotes the number of weeks and y the number of children who have been given the drops.Q. The value of C in the particular solution given that y(0) = 0 and k = 0.049 isa)log 50b)log 1/50c)50d)-50Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Direction: Read the following text and answer the following questions on the basis of the same:Polio drops are delivered to 50K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation dy/dx = k(50 - y) where x denotes the number of weeks and y the number of children who have been given the drops.Q. The value of C in the particular solution given that y(0) = 0 and k = 0.049 isa)log 50b)log 1/50c)50d)-50Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: Read the following text and answer the following questions on the basis of the same:Polio drops are delivered to 50K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation dy/dx = k(50 - y) where x denotes the number of weeks and y the number of children who have been given the drops.Q. The value of C in the particular solution given that y(0) = 0 and k = 0.049 isa)log 50b)log 1/50c)50d)-50Correct answer is option 'B'. Can you explain this answer?.
Solutions for Direction: Read the following text and answer the following questions on the basis of the same:Polio drops are delivered to 50K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation dy/dx = k(50 - y) where x denotes the number of weeks and y the number of children who have been given the drops.Q. The value of C in the particular solution given that y(0) = 0 and k = 0.049 isa)log 50b)log 1/50c)50d)-50Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Direction: Read the following text and answer the following questions on the basis of the same:Polio drops are delivered to 50K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation dy/dx = k(50 - y) where x denotes the number of weeks and y the number of children who have been given the drops.Q. The value of C in the particular solution given that y(0) = 0 and k = 0.049 isa)log 50b)log 1/50c)50d)-50Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Direction: Read the following text and answer the following questions on the basis of the same:Polio drops are delivered to 50K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation dy/dx = k(50 - y) where x denotes the number of weeks and y the number of children who have been given the drops.Q. The value of C in the particular solution given that y(0) = 0 and k = 0.049 isa)log 50b)log 1/50c)50d)-50Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Direction: Read the following text and answer the following questions on the basis of the same:Polio drops are delivered to 50K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation dy/dx = k(50 - y) where x denotes the number of weeks and y the number of children who have been given the drops.Q. The value of C in the particular solution given that y(0) = 0 and k = 0.049 isa)log 50b)log 1/50c)50d)-50Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Direction: Read the following text and answer the following questions on the basis of the same:Polio drops are delivered to 50K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation dy/dx = k(50 - y) where x denotes the number of weeks and y the number of children who have been given the drops.Q. The value of C in the particular solution given that y(0) = 0 and k = 0.049 isa)log 50b)log 1/50c)50d)-50Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Direction: Read the following text and answer the following questions on the basis of the same:Polio drops are delivered to 50K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation dy/dx = k(50 - y) where x denotes the number of weeks and y the number of children who have been given the drops.Q. The value of C in the particular solution given that y(0) = 0 and k = 0.049 isa)log 50b)log 1/50c)50d)-50Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup