मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Bacterial increases at the rate proportional to the number present. If original number M doubles in 3 hours, then number of bacteria will be 4M in

Advertisements
Advertisements

प्रश्न

Select and write the correct alternative from the given option for the question

Bacterial increases at the rate proportional to the number present. If original number M doubles in 3 hours, then number of bacteria will be 4M in

पर्याय

  • 4 hours

  • 6 hours

  • 8 hours

  • 10 hours

MCQ
Advertisements

उत्तर

6 hours

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2.6: Differential Equations - MCQ

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

\[\frac{d^4 y}{d x^4} = \left\{ c + \left( \frac{dy}{dx} \right)^2 \right\}^{3/2}\]

Assume that a rain drop evaporates at a rate proportional to its surface area. Form a differential equation involving the rate of change of the radius of the rain drop.

 

Show that y = e−x + ax + b is solution of the differential equation\[e^x \frac{d^2 y}{d x^2} = 1\]

 


Differential equation \[x\frac{dy}{dx} = 1, y\left( 1 \right) = 0\]

Function y = log x


\[\frac{dy}{dx} = x^2 + x - \frac{1}{x}, x \neq 0\]

\[\frac{dy}{dx} + 2x = e^{3x}\]

\[\frac{dy}{dx} + \frac{1 + y^2}{y} = 0\]

\[\frac{dy}{dx} = \frac{1 + y^2}{y^3}\]

\[\frac{dy}{dx} = \frac{1 - \cos 2y}{1 + \cos 2y}\]

\[\left( x - 1 \right)\frac{dy}{dx} = 2 xy\]

\[\left( x - 1 \right)\frac{dy}{dx} = 2 x^3 y\]

xy dy = (y − 1) (x + 1) dx


\[x\frac{dy}{dx} + \cot y = 0\]

(1 − x2) dy + xy dx = xy2 dx


tan y dx + sec2 y tan x dy = 0


(y + xy) dx + (x − xy2) dy = 0


\[\left( x - 1 \right)\frac{dy}{dx} = 2 x^3 y\]

\[\frac{dr}{dt} = - rt, r\left( 0 \right) = r_0\]

\[\frac{dy}{dx} = y \tan x, y\left( 0 \right) = 1\]

The volume of a spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of the balloon after `t` seconds.


(x2 − y2) dx − 2xy dy = 0


\[xy\frac{dy}{dx} = x^2 - y^2\]

(x + 2y) dx − (2x − y) dy = 0


Solve the following initial value problem:-

\[\frac{dy}{dx} + 2y \tan x = \sin x; y = 0\text{ when }x = \frac{\pi}{3}\]


A population grows at the rate of 5% per year. How long does it take for the population to double?


The slope of the tangent at a point P (x, y) on a curve is \[\frac{- x}{y}\]. If the curve passes through the point (3, −4), find the equation of the curve.


Find the equation of the curve which passes through the point (2, 2) and satisfies the differential equation
\[y - x\frac{dy}{dx} = y^2 + \frac{dy}{dx}\]


Define a differential equation.


The differential equation satisfied by ax2 + by2 = 1 is


Solve the following differential equation : \[\left( \sqrt{1 + x^2 + y^2 + x^2 y^2} \right) dx + xy \ dy = 0\].


Verify that the function y = e−3x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + \frac{dy}{dx} - 6y = 0.\]


The price of six different commodities for years 2009 and year 2011 are as follows: 

Commodities A B C D E F

Price in 2009 (₹)

35 80 25 30 80 x
Price in 2011 (₹) 50 y 45 70 120 105

The Index number for the year 2011 taking 2009 as the base year for the above data was calculated to be 125. Find the values of x andy if the total price in 2009 is ₹ 360.


The differential equation `y dy/dx + x = 0` represents family of ______.


Choose the correct option from the given alternatives:

The solution of `1/"x" * "dy"/"dx" = tan^-1 "x"` is


Find the differential equation whose general solution is

x3 + y3 = 35ax.


Solve the following differential equation.

dr + (2r)dθ= 8dθ


The differential equation of `y = k_1e^x+ k_2 e^-x` is ______.


The solution of `dy/dx + x^2/y^2 = 0` is ______


Solve the differential equation:

`e^(dy/dx) = x`


Solve the following differential equation

`yx ("d"y)/("d"x)` = x2 + 2y2 


For the differential equation, find the particular solution

`("d"y)/("d"x)` = (4x +y + 1), when y = 1, x = 0


Solve the following differential equation y2dx + (xy + x2) dy = 0


Solve the following differential equation

`x^2  ("d"y)/("d"x)` = x2 + xy − y2 


A solution of differential equation which can be obtained from the general solution by giving particular values to the arbitrary constant is called ______ solution


The function y = ex is solution  ______ of differential equation


The function y = cx is the solution of differential equation `("d"y)/("d"x) = y/x`


Solve: ydx – xdy = x2ydx.


lf the straight lines `ax + by + p` = 0 and `x cos alpha + y sin alpha = p` are inclined at an angle π/4 and concurrent with the straight line `x sin alpha - y cos alpha` = 0, then the value of `a^2 + b^2` is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×