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Questions Related to physics

Multiple choice logarithm and its uses basic mathematical concepts 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

  1. odd number

  2. even number

  3. prime number

  4. composite number
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation
$\frac { { tan }^{ 2 }(\frac { \Pi  }{ 5 } )+{ tan }^{ 2 }(\frac { 2\Pi  }{ 5 } )+20 }{ { cot }^{ 2 }(\frac { \Pi  }{ 5 } )+{ cot }^{ 2 }(\frac { 2\Pi  }{ 5 } )+28 } \\ =\frac { { (\sqrt { 5-2\sqrt { 5 }  } ) }^{ 2 }+(\sqrt { \frac { 5 }{ 5-2\sqrt { 5 }  }  } )^{ 2 }+20 }{ { (\frac { 1 }{ \sqrt { 5-2\sqrt { 5 }  }  } ) }^{ 2 }+{ (\sqrt { \frac { 5-2\sqrt { 5 }  }{ 5 } ) }  }^{ 2 }+28 } \\ =\frac { 5-2\sqrt { 5 } +\frac { 5 }{ 5-2\sqrt { 5 }  } +20 }{ \frac { 1 }{ 5-2\sqrt { 5 }  } +\frac { 5-2\sqrt { 5 }  }{ 5 } +28 } \\ =\frac { 5[(5-{ 2\sqrt { 5 } ) }^{ 2 }+5+20(5-2\sqrt { 5 } )] }{ 5+(5-{ 2\sqrt { 5 } ) }^{ 2 }+140(5-2\sqrt { 5 } ) } \\ =\frac { 5(45-20\sqrt { 5 } +5+100-40\sqrt { 5 } ) }{ 5+45-20\sqrt { 5 } +700-200\sqrt { 5 }  } \\ =\frac { 750-300\sqrt { 5 }  }{ 750-300\sqrt { 5 }  } \\ antilog _{ 5 }[\frac { { tan }^{ 2 }(\frac { \Pi  }{ 5 } +{ tan }^{ 2 }(\frac { 2\Pi  }{ 5 } )+20 }{ { cot }^{ 2 }(\frac { \Pi  }{ 5 } )+{ cot }^{ 2 }(\frac { 2\Pi  }{ 5 } )+28 } ]={ 5 }^{ 1 }\quad =5$
Multiple choice logarithm and its uses basic mathematical concepts physics

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

  1. $0.7666$

  2. $0.7656$

  3. $0.5686$

  4. $0.2936$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

Multiple choice logarithm and its uses basic mathematical concepts physics

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

  1. $18$

  2. $24$

  3. $22$

  4. $20$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $D$

Multiple choice logarithm and its uses basic mathematical concepts physics

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

  1. $47$

  2. $48$

  3. $49$

  4. $50$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice logarithm and its uses basic mathematical concepts physics

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

  1. 1.27

  2. 1.21

  3. 1.18

  4. 1.15

  5. 1.02
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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

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

  1. True

  2. False

  3. Ambiguous

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. spent

  2. coal

  3. methane

  4. pesticides
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
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.