Siddardha

we know that 1/2 CV2 is the energy stored in a capactor with capacitance C when connected across the voltage source V. 

the property of capacitor is it acquires charge when it is connected to voltage source.

after this was this connected it acts as a energy source untill the charge in it is dissipated or until an equal energy source is countered to it.

so in case 1: when it is connected to the 200V source 

 energy acquired by the 600pF capacitor is 1.2 * 10^-5 

that means the energy 1.2 *10^-5 is shared between two capacitors in equal amount 

that means energy lost is half of the intial total energy and that is equal to energy gained by the second capacitor = 0.6 *10^-5 joules  

you can do it by grouping two digits together form right like in this case 1369. now start division
step 1: choose the number such that its square is close to our left end pair (here 13)
    3)1369(3
      09  
      04 69
   step 2 : Now multiplie the divisor with 2 (3 *2 =6)
 
choose another number (here 7), to place on the right side of the multiplied divisor (here 6) such that both the digits combined and multiplied with the chosen number will give either the exact value (here 496) or close to our required value.
           67)496(7
              496  
               0
 
so our square root of 1369 is our first digit 3 and our second digit 7 =37
 
               or
for quick calculations follow this method
 
  we know the square of 30 =900
 and the square of 40 =1600
so the square of some number between 30 to 40 will be 1369
Now check the middle number, i.e. 35
sq of 35 =1225
that means our required number lies between 35 to 40
 
Now go for unit digit. Our unit digit is 9, which is given by 3 or 7 only when squared.
From 35 to 40 only 37 square will be 9 as a unit digit.
Our answer is 37.