For the parabola $y^2+6y-2x+5=0$:
$(I)$ The vertex is $(-2,-3)$
$(II)$ The directrix is $y+3=0$
Which of the following is correct?

$A$ body is executing simple harmonic motion. At a displacement $x$ its potential energy is $E_1$ and at a displacement $y$ its potential energy is $E_2$. The potential energy $(E)$ at displacement $(x+y)$ is

The correct output for the given logic circuit and inputs is:

What is $Z$ in the following reaction sequence?
$C_6H_5NH_2$ $\xrightarrow[(i) NaNO_2 + HCl / 273 \ K]{(ii) H_3PO_2 + H_2O}$ $\xrightarrow[(iii) CO, HCl, \text{anhydrous } AlCl_3/CuCl]{} Z$

$A$ $500\,\mu F$ capacitor is charged at a steady rate of $100\,\mu C/s$. The potential difference across the capacitor will be $10\,V$ after an interval of $......\,s$.

An inductor $(L = 100 \, mH)$,a resistor $(R = 100 \, \Omega)$,and a battery $(E = 100 \, V)$ are initially connected in series as shown in the figure. After a long time,the battery is disconnected by short-circuiting the points $A$ and $B$. The current in the circuit $1 \, ms$ after the short circuit is: