The thermo emf of a thermocouple is given by $E = aT + bT^2$,where $\frac{a}{b} = -200^{\circ}C$. If the cold junction is kept at $30^{\circ}C$,then the inversion temperature is ($\varepsilon$ in volt,$T$ in centigrade). (in $K$)

The value of $\lim_{n \rightarrow \infty} \frac{1}{n^3} \sum_{k=1}^n (k^2 x)$ is

The electric field associated with an $e.m.$ wave in vacuum is given by $\vec E = \hat i\,40\,\cos \left( {kz - 6 \times {{10}^8}\,t} \right)$,where $E$,$z$,and $t$ are in $V/m$,$m$,and $s$ respectively. The value of the wave vector $k$ is ....... $m^{-1}$.

The point of intersection of the line $\frac{x - 1}{3} = \frac{y + 2}{4} = \frac{z - 3}{-2}$ and the plane $2x - y + 3z - 1 = 0$ is

If the length of the tangent from $(h, k)$ to the circle $x^2+y^2=16$ is twice the length of the tangent from the same point to the circle $x^2+y^2+2x+2y=0$,then

If $A=35^{\circ}, B=15^{\circ}$ and $C=40^{\circ}$,then $\tan A \cdot \tan B+\tan B \cdot \tan C+\tan C \cdot \tan A$ is equal to