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Maths-General
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does not exist Extreme Values; 
does not exist Extreme Values; 
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For all values of
,the values of
lie in the interval
For all values of
,the values of
lie in the interval
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If 
If 
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The minimum and maximum values of
are
The minimum and maximum values of
are
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The minimum and maximum values of
are
The minimum and maximum values of
are
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physics-
A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is
is

In a closed organ pipe in which length of air-column can be increased or decreased, the first resonance occurs at
and second resonance occurs at 
Thus, at first resonance

And a second resonance



Subtracting Eq.(i) from Eq.(ii), we have



Hence, frequency of tuning fork

Thus, at first resonance
And a second resonance


Subtracting Eq.(i) from Eq.(ii), we have
Hence, frequency of tuning fork
A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is
is

physics-General
In a closed organ pipe in which length of air-column can be increased or decreased, the first resonance occurs at
and second resonance occurs at 
Thus, at first resonance

And a second resonance



Subtracting Eq.(i) from Eq.(ii), we have



Hence, frequency of tuning fork

Thus, at first resonance
And a second resonance


Subtracting Eq.(i) from Eq.(ii), we have
Hence, frequency of tuning fork
physics-
In a sine wave, position of different particles at time
is shown in figure. The equation for this wave travelling along positive
can be

As is clear from figure, at
, displacement
. Therefore, option (a)or (d)may be correct.
In case of (d);




.
And slope at
and
is positive, in figure. Therefore, particle velocity is in negative y-direction.
In case of (d);
And slope at
In a sine wave, position of different particles at time
is shown in figure. The equation for this wave travelling along positive
can be

physics-General
As is clear from figure, at
, displacement
. Therefore, option (a)or (d)may be correct.
In case of (d);




.
And slope at
and
is positive, in figure. Therefore, particle velocity is in negative y-direction.
In case of (d);
And slope at
maths-
The function 
is
The function 
is
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and the equation
has at least one solution then the value of (a+b)
and the equation
has at least one solution then the value of (a+b)
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If 
If 
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The period of the function
where [.] de-notes the greatest integer function, is
The period of the function
where [.] de-notes the greatest integer function, is
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