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Easy

Question

# A sphere of mass M and Radius R_{2} has a concentric cavity of Radius R_{1} as shown in figure. The force exerted by the shpere on a particle of mass located at a distance from the center of shhere varies as

## The correct answer is:

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### is decreasing in

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### The interval of increase of the function is

The given function is

A function is said to be increasing when it’s first order derivative is positive.

It means f’(x) > 0

We will use this condition to find the answer.

Taking the first order derivative of the given function.

f(x) =

f’(x) = 1 – e

Now for the function to be increasing,

f'(x) > 0

1 - e

1 > e

e

Taking log

xlog

x < 0 ...{ log

x can have any value less than zero.

There is no lower limit on x.

So, the interval will be (-∞,0)

A function is said to be increasing when it’s first order derivative is positive.

It means f’(x) > 0

We will use this condition to find the answer.

Taking the first order derivative of the given function.

f(x) =

f’(x) = 1 – e

^{x}+ 0Now for the function to be increasing,

f'(x) > 0

1 - e

^{x}> 01 > e

^{x}e

^{x }< 1Taking log

_{e}of both the sides. It means we are taking natural log on both the sides.xlog

_{e}e < log_{e}1x < 0 ...{ log

_{e}e = 1 and log_{e}1 = 0}x can have any value less than zero.

There is no lower limit on x.

So, the interval will be (-∞,0)

### The interval of increase of the function is

Maths-General

The given function is

A function is said to be increasing when it’s first order derivative is positive.

It means f’(x) > 0

We will use this condition to find the answer.

Taking the first order derivative of the given function.

f(x) =

f’(x) = 1 – e

Now for the function to be increasing,

f'(x) > 0

1 - e

1 > e

e

Taking log

xlog

x < 0 ...{ log

x can have any value less than zero.

There is no lower limit on x.

So, the interval will be (-∞,0)

A function is said to be increasing when it’s first order derivative is positive.

It means f’(x) > 0

We will use this condition to find the answer.

Taking the first order derivative of the given function.

f(x) =

f’(x) = 1 – e

^{x}+ 0Now for the function to be increasing,

f'(x) > 0

1 - e

^{x}> 01 > e

^{x}e

^{x }< 1Taking log

_{e}of both the sides. It means we are taking natural log on both the sides.xlog

_{e}e < log_{e}1x < 0 ...{ log

_{e}e = 1 and log_{e}1 = 0}x can have any value less than zero.

There is no lower limit on x.

So, the interval will be (-∞,0)

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### In experiment of the potentiometer wire of length 100 cm has a resistance of 10, It is connected in series with a resistance R and a cell of emf 2 volts and of negligible internal resistance. A Source of emf 10mV is balanced against a length of 40 cm of the potentiometer wire. What is the value of the external resistance?

### In experiment of the potentiometer wire of length 100 cm has a resistance of 10, It is connected in series with a resistance R and a cell of emf 2 volts and of negligible internal resistance. A Source of emf 10mV is balanced against a length of 40 cm of the potentiometer wire. What is the value of the external resistance?

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Maths-

### The function is

The given function is f(x) =

We will take the first order derivative of the function.

The quantity x

And all other values are postive constants.

So, the total value of the first order derivative is positive.

It means f'(x) > 0

It means the given function is strictly increasing.

We will take the first order derivative of the function.

The quantity x

^{2}is always positive.And all other values are postive constants.

So, the total value of the first order derivative is positive.

It means f'(x) > 0

It means the given function is strictly increasing.

### The function is

Maths-General

The given function is f(x) =

We will take the first order derivative of the function.

The quantity x

And all other values are postive constants.

So, the total value of the first order derivative is positive.

It means f'(x) > 0

It means the given function is strictly increasing.

We will take the first order derivative of the function.

The quantity x

^{2}is always positive.And all other values are postive constants.

So, the total value of the first order derivative is positive.

It means f'(x) > 0

It means the given function is strictly increasing.

maths-

### If the function is decreasing in its domain then

### If the function is decreasing in its domain then

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