Charges are uniformly spread on the surface of a conducting sphere. The electric field from the center of the sphere in a point outside the sphere varies with distance \( r \) from the center as 
Match the following types of nuclei with examples shown: 

Electrical as well as gravitational effects can be thought to be caused by fields. Which of the following is true for an electrical and gravitational field ?
Match the following:
In the following, \( [x] \) denotes the greatest integer less than or equal to \( x \). 
Choose the correct answer from the options given below:
For x < 0:
f(x) = ex + ax
For x ≥ 0:
f(x) = b(x - 1)2
Electromagnetic Induction is a current produced by the voltage production due to a changing magnetic field. This happens in one of the two conditions:-
The electromagnetic induction is mathematically represented as:-
e=N × d∅.dt
Where