$A$ rope of mass $5\,kg$ is moving vertically in a vertical position with an upwards force of $100\,N$ acting at the upper end and a downwards force of $70\,N$ acting at the lower end. The tension at the midpoint of the rope is $............\,N$.

Which of the following reactions defines $\Delta H_f^o$?

The condition that $f(x)=a x^3+b x^2+c x+d$ has no extreme value,is

If $m$ and $M$ respectively denote the minimum and maximum of $f(x)=(x-1)^2+3$ for $x \in [-3, 1]$,then the ordered pair $(m, M)$ is equal to

Two blocks of masses $1 \ kg$ and $2 \ kg$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{40}{3 \pi} \times 10^6 \ N m^{-2}$. What should be the minimum radius of the wire used if it should not break (in $mm$)? $\left(g = 10 \ m s^{-2}\right)$

If the lines $3x + 4y - 14 = 0$ and $6x + 8y + 7 = 0$ are both tangents to a circle,then its radius is