Log_2aa=x    then, a=(2a)^x  ......(1)

Log_3a2a=y    then,2a=(3a)^y ......(2)

Log_4a 3a=z  then, 3a=(4a)^z ......(3)

So, 

a=(2a)^x  [from (1)]

Or, a=(3a)^xy    [from(2)]

Or, a=(4a)^xyz     [from(3)]

Multiplying both sides by 4a,

4a.a=4a.(4a)^xyz  

Or,(2a)² =(4a)^{xyz + 1} 

Or,(3a)^2y =(4a)^xyz+1 

Or,(4a)^2yz =(4a)^xyz+1 

Or, 2yz = xyz+1 .proved.

In benzene molecule, carbon and carbon bond can't have polarity because there is not any electronegativity difference and the carbon hydrogen is also not much polar because the electronegativity difference is almost zero and also the small pull due to small difference in Electronegativity is balanced due to even pull from all directions.

In chlorobenzene the electronegativity difference between carbon and chlorine is very high so, it is polar.

(to compare polarity first check electronegativity...

Yes, a physical quantity can have magnitude and direction but still be a scalar if it doesn't obey the vector addition. An example is Electric Current which has magnitude and a fixed direction, but it does not follow vector laws of addition.

1.ans:  No the tension in the string of a simple pendulum is not constant throughout the motion                                     

v is velocity of the bob and theta is the angle made by the string with vertical axis.

as v and θ both are variable T is also variable.

T is maximum at mean position as at mean position v is max and the angle is minimum.

2.ans: If the amplitude of the simple...