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Questions Related to physics

The value of $\displaystyle anti\log _5\left [\frac {\tan^2\left (\frac {\pi}{5}\right )+\tan^2\left (\frac {2\pi}{5}\right )+20}{\cot^2\left (\frac {\pi}{5}\right )+\cot^2\left (\frac {2\pi}{5}\right )+28}\right ]$ is equal to

logarithm and its uses basic mathematical concepts physics

  1. odd number

  2. even number

  3. prime number

  4. composite number

Show answer
Correct Option: A,C
Explanation:
$\frac { { tan }^{ 2 }(\frac { \Pi  }{ 5 } )+{ tan }^{ 2 }(\frac { 2\Pi  }{ 5 } )+20 }{ { cot }^{ 2 }(\frac { \Pi  }{ 5 } )+{ cot }^{ 2 }(\frac { 2\Pi  }{ 5 } )+28 } \\ =\frac { { (\sqrt { 5-2\sqrt { 5 }  } ) }^{ 2 }+(\sqrt { \frac { 5 }{ 5-2\sqrt { 5 }  }  } )^{ 2 }+20 }{ { (\frac { 1 }{ \sqrt { 5-2\sqrt { 5 }  }  } ) }^{ 2 }+{ (\sqrt { \frac { 5-2\sqrt { 5 }  }{ 5 } ) }  }^{ 2 }+28 } \\ =\frac { 5-2\sqrt { 5 } +\frac { 5 }{ 5-2\sqrt { 5 }  } +20 }{ \frac { 1 }{ 5-2\sqrt { 5 }  } +\frac { 5-2\sqrt { 5 }  }{ 5 } +28 } \\ =\frac { 5[(5-{ 2\sqrt { 5 } ) }^{ 2 }+5+20(5-2\sqrt { 5 } )] }{ 5+(5-{ 2\sqrt { 5 } ) }^{ 2 }+140(5-2\sqrt { 5 } ) } \\ =\frac { 5(45-20\sqrt { 5 } +5+100-40\sqrt { 5 } ) }{ 5+45-20\sqrt { 5 } +700-200\sqrt { 5 }  } \\ =\frac { 750-300\sqrt { 5 }  }{ 750-300\sqrt { 5 }  } \\ antilog _{ 5 }[\frac { { tan }^{ 2 }(\frac { \Pi  }{ 5 } +{ tan }^{ 2 }(\frac { 2\Pi  }{ 5 } )+20 }{ { cot }^{ 2 }(\frac { \Pi  }{ 5 } )+{ cot }^{ 2 }(\frac { 2\Pi  }{ 5 } )+28 } ]={ 5 }^{ 1 }\quad =5$

Evaluate using logarithm table: $\dfrac {28.45 \times \sqrt [3] {0.3254}}{32.43 \times \sqrt [5] {0.3046}}$

logarithm and its uses basic mathematical concepts physics

  1. $0.7666$

  2. $0.7656$

  3. $0.5686$

  4. $0.2936$

Show answer
Correct Option: B
Explanation:

Let $y=\dfrac { 28.45\times \sqrt [ 3 ]{ .3254 }  }{ 32.43\times \sqrt [ 3 ]{ .3046 }  } $

$ \ln { y } =\ln { 28.45 } +\ln { \sqrt [ 3 ]{ .3254 }  } -(\ln { 32.43 } +\ln { \sqrt [ 5 ]{ .3046 }  } )\ \ln { y } =\ln { 25.45 } +\dfrac { 1 }{ 3 } \ln { .3245- } \ln { 32.43 } -\dfrac { 1 }{ 5 } \ln { .4046 } \ \ln { y } =3.236+(-.375)-3.479-(-.237)\ \ln { y } =-.381$
$ y=$ anti $\ln { (-.381) } $

$ y=.7656$
So, option B is correct.

If $\log _{10} 2 = 0.3010$, then the number of digits in $2^{64}$ is

logarithm and its uses basic mathematical concepts physics

  1. $18$

  2. $24$

  3. $22$

  4. $20$

Show answer
Correct Option: D
Explanation:

Given $\log _{ 10 }{ 2 } =0.301$

$\log _{ 10 }{ 2^{64} } =64 \times \log _{ 10 }{ 2 } =64 \times 0.3010=19.264$
$\Rightarrow 2^{64}=10^{19.264}$
The number of digits in $10^{19}$ is $20$ , there will be $21$ digits from $10^{21}$
The number $10^{19.264}$ lies between them
Therefore the number of digits in $10^{19.264}$ is $20$
Therefore the correct option is $D$

If $\log _{10} 3 = 0.4771$, then the number of zeros after the decimal in $3^{-100}$ is

logarithm and its uses basic mathematical concepts physics

  1. $47$

  2. $48$

  3. $49$

  4. $50$

Show answer
Correct Option: A
Explanation:

The number of zeroes will be
$=|log _{10}(3^{-100})|$
$=|-100(log _{10}(3))|$
$=|-47.71|$
$=47.71$
Taking the integral part (since number of zeroes has to be an integer, there will be $47$ zeros.

Approximate of $\log _{11}21$ is

logarithm and its uses basic mathematical concepts physics

  1. 1.27

  2. 1.21

  3. 1.18

  4. 1.15

  5. 1.02

Show answer
Correct Option: A
Explanation:

Approximate value of $\log _{ 11 }{ 21 } $

$=\log _{ 11 }{ (7\times 3) } $
$=\log _{ 11 }{ 7 } +\log _{ 11 }{ 3 }$
$ =0.8115+0.4581$
$=1.27$

The temperature of the biodigester is kept around $35^{\circ}C$, so as to sustain the fermentation of animal during slurry.

physics energy management solar power plant production of electricity from solar energy solar energy and its applications

  1. True

  2. False

  3. Ambiguous

  4. Data insufficient

Show answer
Correct Option: A
Explanation:

Answer is A.

This is a complex process by which organic matter is decomposed by anaerobic bacteria. The decomposition process produces a gaseous byproduct often called biogas, which consists primarily of methane, carbon dioxide, and hydrogen sulfide. It occurs in nature and can be used to produce biogas from biomass in an anaerobic digestor. 
To optimize the digestion process, the biodigester must be kept at a consistent temperature, as rapid changes will upset bacterial activity. In most areas of the United States, digestion vessels require some level of insulation and/or heating. Some installations circulate the coolant from their biogas-powered engines in or around the digester to keep it warm, while others burn part of the biogas to heat the digester. In a properly designed system, heating generally results in an increase in biogas production during colder periods.
Hence, the statement is true.

The ................ animal dung left after the production of biogas is an excellent manure.

physics energy management solar power plant production of electricity from solar energy solar energy and its applications

  1. spent

  2. coal

  3. methane

  4. pesticides

Show answer
Correct Option: A
Explanation:

The dried manure left after the biogas process is even richer than ordinary muck and makes a fantastic organic fertilizer.
Hence, The spent animal dung left after the production of biogas is an excellent manure.

When solar dryer is placed in a sunlight, then :

physics energy management solar power plant production of electricity from solar energy solar energy and its applications

  1. Air inside it is cooled

  2. Air inside it is heated

  3. Air remain as such

  4. None of these

Show answer
Correct Option: B
Explanation:

When solar dryer is placed in sunlight then it convert solar energy into heat energy and heat the air inside the solar dryer to a constant temperature.

State whether true or false :
In solar dryer, we can keep dried fruits for longer duration of time.

physics energy management solar power plant production of electricity from solar energy solar energy and its applications

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

 Solar dryer is one of the oldest methods of preserving food for later use.  Foods can  be dried in the sun, in an oven or in a food dehydrator by using the right. So we can dried fruits for longer duration of time.

State whether true or false :
Solar dryer works on the principle of conversion of solar energy into heat energy.

physics energy management solar power plant production of electricity from solar energy solar energy and its applications

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

The basic function of a solar dryer is to heat air to a constant temperature with solar energy hence Solar dryer works on the principle of conversion of solar energy into heat energy.