HSC Commerce (English Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find `(d^2y)/dx^2` if, `y = e^((2x + 1))`

Find `(d^2y)/dx^2` if, `y = e^((2x + 1))`

Solve the differential equation `dy/dx+2xy=x` by completing the following activity.

Solution: `dy/dx+2xy=x`       ...(1)

This is the linear differential equation of the form `dy/dx +Py =Q,"where"`

`P=square` and Q = x

∴ `I.F. = e^(intPdx)=square`

The solution of (1) is given by

`y.(I.F.)=intQ(I.F.)dx+c=intsquare  dx+c`

∴ `ye^(x^2) = square`

This is the general solution.

Find `(d^2y)/(dx^2)` if, y = `e^((2x+1))`

Find `(d^2y)/dx^2` if, y = `e^((2x + 1))`

Find `(d^2y)/dx^2  "if,"  y= e^((2x+1))`

Find `(d^2y)/dx^2` if, `y = e^((2x + 1))`

Find `(d^2y)/dx^2` if, y = `e^(2x +1)`

Find `(d^2y)/dx^2, "if"  y = e^((2x+1))`

Find `(d^2y)/dx^2` if, `y = e^((2x+1))`

Find `(d^2y)/(dx^2)  "if", y = e^((2x + 1))`

In a certain culture of bacteria, the rate of increase is proportional to the number present. If it is found that the number doubles in 4 hours, find the number of times the bacteria are increased in 12 hours.

If the population of a country doubles in 60 years, in how many years will it be triple (treble) under the assumption that the rate of increase is proportional to the number of inhabitants?
(Given log 2 = 0.6912, log 3 = 1.0986)

If a body cools from 80°C to 50°C at room temperature of 25°C in 30 minutes, find the temperature of the body after 1 hour.

If a body cools from 80°C to 50°C at room temperature of 25°C in 30 minutes, find the temperature of the body after 1 hour.

The rate of growth of bacteria is proportional to the number present. If initially, there were 1000 bacteria and the number doubles in 1 hour, find the number of bacteria after `2 1/2` hours.
[Take `sqrt2 = 1.414`]

The rate of disintegration of a radioactive element at any time t is proportional to its mass at that time. Find the time during which the original mass of 1.5 gm will disintegrate into its mass of 0.5 gm.

The rate of decay of certain substances is directly proportional to the amount present at that instant. Initially, there is 25 gm of certain substance and two hours later it is found that 9 gm are left. Find the amount left after one more hour.

Find the population of a city at any time t, given that the rate of increase of population is proportional to the population at that instant and that in a period of 40 years, the population increased from 30,000 to 40,000.

A body cools according to Newton’s law from 100° C to 60° C in 20 minutes. The temperature of the surrounding being 20° C. How long will it take to cool down to 30° C?