If $\overrightarrow{E}$ and $\overrightarrow{B}$ are the electric and magnetic field vectors of electromagnetic waves,then the direction of propagation of the electromagnetic wave is along the direction of

The perimeter of a sector is a constant. If its area is to be maximum,the sectorial angle is:

If $f: \mathbb{R} \rightarrow \mathbb{R}$ is such that $f(x+y) = f(x) + f(y)$ for all $x, y \in \mathbb{R}$,$f(1) = 7$,and $\sum_{r=1}^n f(r) = 14112$,then $n = $

An object $2.4 \, m$ in front of a lens forms a sharp image on a film $12 \, cm$ behind the lens. $A$ glass plate $1 \, cm$ thick,of refractive index $1.50$,is interposed between the lens and the film with its plane faces parallel to the film. At what distance (from the lens) should the object be shifted to be in sharp focus on the film? (in $m$)

$A$ non-uniformly shaped conductor is charged. Then,at its sharpest point:

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 $K$)