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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

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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
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उत्तर

6 hours

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पाठ 2.6: Differential Equations - MCQ

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

If 1, `omega` and `omega^2` are the cube roots of unity, prove `(a + b omega + c omega^2)/(c + s omega +  b omega^2) =  omega^2`


\[\frac{d^3 x}{d t^3} + \frac{d^2 x}{d t^2} + \left( \frac{dx}{dt} \right)^2 = e^t\]

\[\sqrt[3]{\frac{d^2 y}{d x^2}} = \sqrt{\frac{dy}{dx}}\]

\[x + \left( \frac{dy}{dx} \right) = \sqrt{1 + \left( \frac{dy}{dx} \right)^2}\]

Show that the function y = A cos 2x − B sin 2x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + 4y = 0\].


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

Function y = log x


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

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

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

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

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

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

xy dy = (y − 1) (x + 1) dx


tan y \[\frac{dy}{dx}\] = sin (x + y) + sin (x − y) 

 


(y + xy) dx + (x − xy2) dy = 0


(y2 + 1) dx − (x2 + 1) dy = 0


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

Solve the following differential equation:
\[\left( 1 + y^2 \right) \tan^{- 1} xdx + 2y\left( 1 + x^2 \right)dy = 0\]


Find the solution of the differential equation cos y dy + cos x sin y dx = 0 given that y = \[\frac{\pi}{2}\], when x = \[\frac{\pi}{2}\] 

 


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

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

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

Solve the following differential equations:
\[\frac{dy}{dx} = \frac{y}{x}\left\{ \log y - \log x + 1 \right\}\]


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

 

Solve the following initial value problem:-

\[\frac{dy}{dx} + y\cot x = 2\cos x, y\left( \frac{\pi}{2} \right) = 0\]


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.


The equation of the curve whose slope is given by \[\frac{dy}{dx} = \frac{2y}{x}; x > 0, y > 0\] and which passes through the point (1, 1) is


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 = ex + 1            y'' − y' = 0


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). 


Find the differential equation whose general solution is

x3 + y3 = 35ax.


Solve the following differential equation.

y2 dx + (xy + x2 ) dy = 0


Solve the following differential equation.

`(x + a) dy/dx = – y + a`


Solve the following differential equation.

dr + (2r)dθ= 8dθ


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


Solve the differential equation:

`e^(dy/dx) = x`


Solve:

(x + y) dy = a2 dx


y dx – x dy + log x dx = 0


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

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


Solve the following differential equation

`x^2  ("d"y)/("d"x)` = x2 + xy − y2 


Choose the correct alternative:

Solution of the equation `x("d"y)/("d"x)` = y log y is


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 


Verify y = `a + b/x` is solution of `x(d^2y)/(dx^2) + 2 (dy)/(dx)` = 0

y = `a + b/x`

`(dy)/(dx) = square`

`(d^2y)/(dx^2) = square`

Consider `x(d^2y)/(dx^2) + 2(dy)/(dx)`

= `x square + 2 square`

= `square`

Hence y = `a + b/x` is solution of `square`


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


There are n students in a school. If r % among the students are 12 years or younger, which of the following expressions represents the number of students who are older than 12?


Solve the differential equation `dy/dx + xy = xy^2` and find the particular solution when y = 4, x = 1.


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