Given:
Step 1: Understanding Electrostatic Induction
When a charged object (glass rod) is brought near a conductor (metal sphere), it induces charge separation. The negative charges in the metal sphere move towards the glass rod, while the positive charges move away.
Step 2: What Happens When the Glass Rod is Removed?
Since the metal sphere is not grounded and no charge transfer has occurred, the charge redistribution disappears after removing the glass rod. The net charge on the sphere remains zero.
Answer: The correct option is A (Zero).
When a positively charged glass rod is brought near an uncharged metal sphere, it causes the electrons in the metal sphere to move due to electrostatic induction. Since the glass rod is positively charged, it will attract the free electrons in the metal sphere, causing a slight negative charge to accumulate on the side of the sphere nearest to the rod, while the far side becomes slightly positively charged. However, because the metal sphere is mounted on an insulated stand and no charge is allowed to flow in or out, once the glass rod is removed, the sphere remains neutral.
Thus, the net charge on the metal sphere will be zero after the glass rod is removed, as no charge is transferred to or from the sphere.
\(\textbf{Correct Answer:}\) (A) Zero
Match List-I with List-II.
Choose the correct answer from the options given below :}
There are three co-centric conducting spherical shells $A$, $B$ and $C$ of radii $a$, $b$ and $c$ respectively $(c>b>a)$ and they are charged with charges $q_1$, $q_2$ and $q_3$ respectively. The potentials of the spheres $A$, $B$ and $C$ respectively are:
Two resistors $2\,\Omega$ and $3\,\Omega$ are connected in the gaps of a bridge as shown in the figure. The null point is obtained with the contact of jockey at some point on wire $XY$. When an unknown resistor is connected in parallel with $3\,\Omega$ resistor, the null point is shifted by $22.5\,\text{cm}$ towards $Y$. The resistance of unknown resistor is ___ $\Omega$. 
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