Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Target Exercises>Q 36

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IMPORTANT

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Water is drained from a vertical cylindrical tank by opening a valve at the base of the tank. It is known that the rate at which the water level drops, is proportional to the square root of water depth $y$ where the constant of proportionality $k > 0$ depends on the acceleration due to gravity and the geometry of the hole. If $t$ is measured in minutes and $k = \frac{1}{15}$ , then the time to drain the tank, if the water is $4 m$ deep to start with, is

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Important Questions on Differential Equations

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Target Exercises>Q 37

The general solution of the differential equation

y (x^{2} y + e^{x}) d x - e^{x} d y = 0

is

HARD

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Target Exercises>Q 38

The solution of the equation

x^{2} y - x^{3} \frac{d y}{d x} = y^{4} \cos x,

when

y (0) = 1,

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Target Exercises>Q 40

A normal is drawn at a point $P (x, y)$ of a curve. It meets the $X$ -axis at $Q .$ If $P Q$ is of constant length $k$ , then the differential equation describing such a curve is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Target Exercises>Q 41

Which one of the following curves represents the solution of the initial value problem

D y = 100 - y

where

y (0) = 50 ?

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Target Exercises>Q 42

If a population grows at the rate of

5 %

per year. Then, the population will be doubled in

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Target Exercises>Q 43

The line 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),

then its equation is