Ionic radius (in $\mathring{A}$) of $As^{3+}$,$Sb^{3+}$ and $Bi^{3+}$ follow the order

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 Gattermann reaction,a diazonium group is replaced by $\underline{X}$ using $\underline{Y}$. $\underline{X}$ and $\underline{Y}$ are:
$\underline{X} \quad \underline{Y}$

If $A+B+C=270^{\circ}$,then $\cos 2A+\cos 2B+\cos 2C$ is equal to:

There is a horizontal film of soap solution. On it,a thread is placed in the form of a loop. The film is pierced inside the loop,and the thread becomes a circular loop of radius $R$. If the surface tension of the soap solution is $T$,then what will be the tension in the thread?

If $A(2,-1)$ and $B(6,5)$ are two points,the ratio in which the foot of the perpendicular from $P(4,1)$ to $AB$ divides $AB$ is: