Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 1>Q 44

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A spherical rain drop evaporates at a rate proportional to its surface area at that instant. The radius of the drop initially is $3 mm$ and after one hour it is found to be $2 mm$ . If $r (t)$ represents the radius of the drop at time $t$ , then

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Important Questions on Differential Equations

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Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 1>Q 45

An object falling from rest in air is subject not only to the gravitational force but also to air resistance. Assume that the air resistance is proportional to the velocity with constant of proportionality as

k > 0,

and acts in a direction opposite to motion

(g = 9.8 m / s^{2}) .

Then velocity cannot exceed

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Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 1>Q 46

The rate of growth of bacteria is proportional to the number present. If initially, there are

1000

bacteria and the number doubles in

1

hour, the number of bacteria after

2 \frac{1}{2}

hours will be

(\sqrt{2} = 1.414)

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Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 1>Q 47

A population grows at the rate of

10 %

of the population per year. How long does it take for the population to double?

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Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 2>Q 1

The differential equation satisfied by $\sqrt{1 + x^{2}} + \sqrt{1 + y^{2}} = k (x \sqrt{1 + y^{2}} - y \sqrt{1 + x^{2}}), k \in R$ is

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Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 2>Q 2

The solution of the equation

\frac{d y}{d x} = \frac{1}{x + y + 1}

is

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Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 2>Q 3

Let

y = f (x)

be a curve which passes through

(3, 1)

and is such that normal at any point on it passes through

(1, 1)

. Then,

y = f (x)

describes

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Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 2>Q 4

The general solution of the differential equation $\frac{d y}{d x} + \sin (\frac{x + y}{2}) = \sin (\frac{x - y}{2})$

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Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 2>Q 5

The equation of the curve passing through the point

(0, \frac{π}{4})

and satisfying the differential equation

(e^{x} \tan y) d x + ((1 + e^{x}) \sec^{2} y) d y = 0

is given by