Question 2 - Case Based Questions (MCQ) - Chapter 9 Class 12 Differential Equations

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.

Question 1

State the order of the above given differential equation.

Question 2

Which method of solving a differential equation can be used to solve dy/dx=k(50-y) ?

(a) Variable separable method

(b) Solving Homogeneous differential equation

(c) Solving Linear differential equation

(d) all of the above

Question 3

The solution of the differential equation dy / dx=k(50-y) is given by,

(a) log⁡ |50-y| =kx+C

(b) –log⁡ |50-y| =k x +C

(c) log⁡ |50-y| =log⁡ |kx| +C

(d) 50-y=kx+ C

Question 4

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

Question 5

Which of the following solutions may be used to find the number of children who

have been given the polio drops?

(a) y = 50 – e ^kx

(b) y = 50 – e ^-kx

(c) y = 50 (1-e- ^kx )

(d) y = 50 (e- ^kx -1)