The number of common tangent$(s)$ to the circles $x^2 + y^2 + 2x + 8y - 23 = 0$ and $x^2 + y^2 - 4x - 10y + 19 = 0$ is:

In the $Hoop$ process for the refining of $Al$,the molten materials form three different layers and remain separate during electrolysis because ..........

In which of the following reactions,the concentration of product is higher than the concentration of reactant at equilibrium? $(K = \text{equilibrium constant})$

At $527 \, ^oC$,the reaction given below has $K_c = 4$:
$NH_{3(g)} \rightleftharpoons \frac{1}{2} N_{2(g)} + \frac{3}{2} H_{2(g)}$
What is the $K_P$ for the following reaction?
$N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$

$A$ block of mass $1\, kg$ lies on a horizontal surface in a truck. The coefficient of static friction between the block and the surface is $0.6$. If the acceleration of the truck is $5\, m\, s^{-2}$,the frictional force acting on the block is ........ $N$.

The lanthanide contraction is responsible for the fact that