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

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

Find the differential equation of all the parabolas with latus rectum '4a' and whose axes are parallel to x-axis.


Show that the differential equation of which y = 2(x2 − 1) + \[c e^{- x^2}\] is a solution, is \[\frac{dy}{dx} + 2xy = 4 x^3\]


Verify that \[y = e^{m \cos^{- 1} x}\] satisfies the differential equation \[\left( 1 - x^2 \right)\frac{d^2 y}{d x^2} - x\frac{dy}{dx} - m^2 y = 0\]


For the following differential equation verify that the accompanying function is a solution:

Differential equation Function
\[x + y\frac{dy}{dx} = 0\]
\[y = \pm \sqrt{a^2 - x^2}\]

For the following differential equation verify that the accompanying function is a solution:

Differential equation Function
\[x^3 \frac{d^2 y}{d x^2} = 1\]
\[y = ax + b + \frac{1}{2x}\]

Differential equation \[\frac{dy}{dx} + y = 2, y \left( 0 \right) = 3\] Function y = e−x + 2


Differential equation \[\frac{d^2 y}{d x^2} - y = 0, y \left( 0 \right) = 2, y' \left( 0 \right) = 0\] Function y = ex + ex


\[\frac{dy}{dx} = \log x\]

\[\frac{dy}{dx} = x \log x\]

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

(1 + x2) dy = xy dx


\[\frac{dy}{dx} = \left( e^x + 1 \right) y\]

x cos2 y  dx = y cos2 x dy


\[\frac{dy}{dx} = \frac{e^x \left( \sin^2 x + \sin 2x \right)}{y\left( 2 \log y + 1 \right)}\]

y (1 + ex) dy = (y + 1) ex dx


Solve the following differential equation: 
(xy2 + 2x) dx + (x2 y + 2y) dy = 0


\[\frac{dy}{dx} = y \tan 2x, y\left( 0 \right) = 2\] 

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.


In a culture the bacteria count is 100000. The number is increased by 10% in 2 hours. In how many hours will the count reach 200000, if the rate of growth of bacteria is proportional to the number present.


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

x2 dy + y (x + y) dx = 0


(x + 2y) dx − (2x − y) dy = 0


\[\left[ x\sqrt{x^2 + y^2} - y^2 \right] dx + xy\ dy = 0\]

Solve the following initial value problem:-

\[x\frac{dy}{dx} - y = \left( x + 1 \right) e^{- x} , y\left( 1 \right) = 0\]


The population of a city increases at a rate proportional to the number of inhabitants present at any time t. If the population of the city was 200000 in 1990 and 250000 in 2000, what will be the population in 2010?


The tangent at any point (x, y) of a curve makes an angle tan−1(2x + 3y) with x-axis. Find the equation of the curve if it passes through (1, 2).


At every point on a curve the slope is the sum of the abscissa and the product of the ordinate and the abscissa, and the curve passes through (0, 1). Find the equation of the curve.


The normal to a given curve at each point (x, y) on the curve passes through the point (3, 0). If the curve contains the point (3, 4), find its equation.


Radium decomposes at a rate proportional to the quantity of radium present. It is found that in 25 years, approximately 1.1% of a certain quantity of radium has decomposed. Determine approximately how long it will take for one-half of the original amount of  radium to decompose?


Find the equation of the curve passing through the point (0, 1) if the slope of the tangent to the curve at each of its point is equal to the sum of the abscissa and the product of the abscissa and the ordinate of the point.


The slope of a curve at each of its points is equal to the square of the abscissa of the point. Find the particular curve through the point (−1, 1).


The integrating factor of the differential equation \[x\frac{dy}{dx} - y = 2 x^2\]


If xmyn = (x + y)m+n, prove that \[\frac{dy}{dx} = \frac{y}{x} .\]


In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-

`y=sqrt(a^2-x^2)`              `x+y(dy/dx)=0`


Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.


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.


Form the differential equation from the relation x2 + 4y2 = 4b2


For  the following differential equation find the particular solution.

`dy/ dx = (4x + y + 1),

when  y = 1, x = 0


Solve the following differential equation.

`dy /dx +(x-2 y)/ (2x- y)= 0`


The solution of `dy/ dx` = 1 is ______.


The integrating factor of the differential equation `dy/dx - y = x` is e−x.


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

The differential equation of y = Ae5x + Be–5x is


Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`


The solution of differential equation `x^2 ("d"^2y)/("d"x^2)` = 1 is ______


Solve the differential equation `"dy"/"dx"` = 1 + x + y2 + xy2, when y = 0, x = 0.


Which of the following defines a differential equation?


What distinguishes an ordinary differential equation from other types of differential equations?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×