$\left|\begin{array}{ccc} \log e & \log e^2 & \log e^3 \\ \log e^2 & \log e^3 & \log e^4 \\ \log e^3 & \log e^4 & \log e^5 \end{array}\right|$ is equal to :

Let $n = 1! + 4! + 7! + \ldots + 400!$. Then the ten's digit of $n$ is

For a plane electromagnetic wave propagating in the $x$-direction,which one of the following combinations gives the correct possible directions for the electric field $(\vec{E})$ and magnetic field $(\vec{B})$ respectively?

$A$ student records $\Delta Q, \Delta U$ and $\Delta W$ for a thermodynamic cycle $A \to B \to C \to A$. Certain entries are missing. Find the correct entry from the following options.

Process	$AB$	$BC$	$CA$
$\Delta W$	$40 \ J$	$ $	$30 \ J$
$\Delta U$	$ $	$50 \ J$	$ $
$\Delta Q$	$150 \ J$	$10 \ J$	$ $

Three blocks $A, B$ and $C$ of masses $4\, kg$,$2\, kg$ and $1\, kg$ respectively,are in contact on a frictionless surface,as shown. If a force of $14\, N$ is applied on the $4\, kg$ block,then the contact force between $A$ and $B$ is .......... $N$.

One mole of the complex compound $Co(NH_3)_5Cl_3$ gives $3$ moles of ions on dissolution in water. One mole of the same complex reacts with two moles of $AgNO_3$ solution to yield two moles of $AgCl_{(s)}$. The structure of the complex is :-