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 solution of the differential equation dy/dx = k(50 - y) is given by,
  • a)
    log |50 – y| = kx + C
  • b)
    –log |50 – y| = kx + C
  • c)
    log |50 – y| = log|kx|+ C
  • d)
    50 – y = kx + C
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Direction: Read the following text and answer the following questions...
Dy/dx = k(50 - y)
View all questions of this test
Most Upvoted Answer
Direction: Read the following text and answer the following questions...
The given differential equation is 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. We need to find the solution to this differential equation.

To solve this differential equation, we can separate the variables and integrate both sides.

- Separate the variables:

dy/(50 - y) = kdx

- Integrate both sides:

∫(dy/(50 - y)) = ∫kdx

To integrate the left side, we can use the substitution u = 50 - y. Then, du = -dy.

- Substitute the values:

-∫(du/u) = ∫kdx

- Solve the integrals:

- ln|u| = kx + C1

- Substitute back u = 50 - y:

- ln|50 - y| = kx + C1

Now, we need to find the value of the constant C1. The given information states that by the end of the 2nd week, half the children have been given the polio drops. This means that when x = 2, y = 50K/2 = 25K.

- Substitute the values:

ln|50 - 25K| = 2k + C1

Since the natural logarithm of a negative number is undefined, we can take the absolute value of the equation:

ln|25K - 50| = 2k + C1

Now, we can simplify the equation further. Since ln|a - b| = -ln|b - a|, we can rewrite the equation as:

-ln|50 - 25K| = 2k + C1

Comparing this with the given options, we can see that the solution of the differential equation dy/dx = k(50 - y) is given by:

-ln|50 - y| = kx + Cb (option B)

Therefore, the correct answer is option B.
Explore Courses for JEE exam

Similar JEE Doubts

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 solution of the differential equation dy/dx = k(50 - y) is given by,a)log |50 – y| = kx + Cb)–log |50 – y| = kx + Cc)log |50 – y| = log|kx|+ Cd)50 – y = kx + CCorrect 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 solution of the differential equation dy/dx = k(50 - y) is given by,a)log |50 – y| = kx + Cb)–log |50 – y| = kx + Cc)log |50 – y| = log|kx|+ Cd)50 – y = kx + CCorrect 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 solution of the differential equation dy/dx = k(50 - y) is given by,a)log |50 – y| = kx + Cb)–log |50 – y| = kx + Cc)log |50 – y| = log|kx|+ Cd)50 – y = kx + CCorrect 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 solution of the differential equation dy/dx = k(50 - y) is given by,a)log |50 – y| = kx + Cb)–log |50 – y| = kx + Cc)log |50 – y| = log|kx|+ Cd)50 – y = kx + CCorrect 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 solution of the differential equation dy/dx = k(50 - y) is given by,a)log |50 – y| = kx + Cb)–log |50 – y| = kx + Cc)log |50 – y| = log|kx|+ Cd)50 – y = kx + CCorrect 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 solution of the differential equation dy/dx = k(50 - y) is given by,a)log |50 – y| = kx + Cb)–log |50 – y| = kx + Cc)log |50 – y| = log|kx|+ Cd)50 – y = kx + CCorrect 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 solution of the differential equation dy/dx = k(50 - y) is given by,a)log |50 – y| = kx + Cb)–log |50 – y| = kx + Cc)log |50 – y| = log|kx|+ Cd)50 – y = kx + CCorrect 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 solution of the differential equation dy/dx = k(50 - y) is given by,a)log |50 – y| = kx + Cb)–log |50 – y| = kx + Cc)log |50 – y| = log|kx|+ Cd)50 – y = kx + CCorrect 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 solution of the differential equation dy/dx = k(50 - y) is given by,a)log |50 – y| = kx + Cb)–log |50 – y| = kx + Cc)log |50 – y| = log|kx|+ Cd)50 – y = kx + CCorrect 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 solution of the differential equation dy/dx = k(50 - y) is given by,a)log |50 – y| = kx + Cb)–log |50 – y| = kx + Cc)log |50 – y| = log|kx|+ Cd)50 – y = kx + CCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
Explore Courses for JEE exam

Top Courses for JEE

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev