Practice Test

Q1) Bacteria increases at the rate proportional to the number present. If the original number N doubles in 3 hours, then the number of bacteria will be 4N in Show Answer

Q2) The decay rate of certain substance is directly proportional to the amount present at that instant. Initially there are 27 grams of the substance and three hours later it is found that 8 grams are left. The amount left after one more hour is Show Answer

Q3) The rate of growth of bacteria is proportional to the number of bacteria present. If the original number N doubles in 3 hours, the number in 6 hours, will be Show Answer

Q4) Assume that a spherical raindrop evaporates at a rate proportional to the surface areas. Differential equation involving rate of change of radius of rain drop is (r = radius, t= time, k = constant) Show Answer

Q5) The rate of decay of the mass of a radioactive substance at any instant is time its mass at that instant. The differential equations satisfied by the mass of the substance is Show Answer

Q6) The decay rate of a radioactive substance is proportional to its mass present at that instant. If the original quantity 50 gms reduces to 25 gms in 2 hours. Then the time when the quantity left is 12.5 gms is Show Answer

Q7) Order and degree of a differential equation are always positive integers. Show Answer

Q8) The degree of a differential equation is the power of the highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any. Show Answer

Q9) The order of highest derivative occurring in the differential equation is called degree of the differential equation. Show Answer

Q10) The power of the highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any is called order of the differential equation. Show Answer