हिंदी

Choose the correct alternative. Bacteria increases at the rate proportional to the number present. If the original number M doubles in 3 hours, then the number of bacteria will be 4M in - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Choose the correct alternative.

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

विकल्प

  • 4 hours

  • 6 hours

  • 8 hours

  • 10 hours

MCQ
Advertisements

उत्तर

Bacteria increases at the rate proportional to the number present. If the original number M doubles in 3 hours, then the number of bacteria will be 4M in 6 hours

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 8: Differential Equation and Applications - Miscellaneous Exercise 8 [पृष्ठ १७२]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 8 Differential Equation and Applications
Miscellaneous Exercise 8 | Q 1.08 | पृष्ठ १७२

संबंधित प्रश्न

Verify that y = cx + 2c2 is a solution of the differential equation 

\[2 \left( \frac{dy}{dx} \right)^2 + x\frac{dy}{dx} - y = 0\].

\[\left( x + 2 \right)\frac{dy}{dx} = x^2 + 3x + 7\]

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

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

\[\cos x \cos y\frac{dy}{dx} = - \sin x \sin y\]

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

\[\frac{dy}{dx} = 2 e^{2x} y^2 , y\left( 0 \right) = - 1\]

Find the particular solution of edy/dx = x + 1, given that y = 3, when x = 0.


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

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

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

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

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

3x2 dy = (3xy + y2) dx


(x + 2y) dx − (2x − y) dy = 0


Solve the following initial value problem:-

\[\left( 1 + y^2 \right) dx + \left( x - e^{- \tan^{- 1} y} \right) dx = 0, y\left( 0 \right) = 0\]


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


In a simple circuit of resistance R, self inductance L and voltage E, the current `i` at any time `t` is given by L \[\frac{di}{dt}\]+ R i = E. If E is constant and initially no current passes through the circuit, prove that \[i = \frac{E}{R}\left\{ 1 - e^{- \left( R/L \right)t} \right\}.\]


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.


The slope of the tangent at each point of a curve is equal to the sum of the coordinates of the point. Find the curve that passes through the origin.


Find the solution of the differential equation
\[x\sqrt{1 + y^2}dx + y\sqrt{1 + x^2}dy = 0\]


Integrating factor of the differential equation cos \[x\frac{dy}{dx} + y \sin x = 1\], is


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


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


Find the equation of the plane passing through the point (1, -2, 1) and perpendicular to the line joining the points A(3, 2, 1) and B(1, 4, 2). 


Determine the order and degree of the following differential equations.

Solution D.E
y = aex + be−x `(d^2y)/dx^2= 1`

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


State whether the following statement is True or False:

The integrating factor of the differential equation `("d"y)/("d"x) - y` = x is e–x 


Solve the following differential equation

`y log y ("d"x)/("d"y) + x` = log y


Solve `x^2 "dy"/"dx" - xy = 1 + cos(y/x)`, x ≠ 0 and x = 1, y = `pi/2`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×