If $x_n = \cos \left(\frac{\pi}{4^n}\right) + i \sin \left(\frac{\pi}{4^n}\right)$,then the product $x_1 x_2 x_3 \ldots \infty$ is equal to

How many integuments surround the ovule in $Pinus$ and $Cycas$?

$A$ $10 \ kW$ transmitter emits radio waves of wavelength $500 \ m$. The number of photons emitted per second by the transmitter is of the order of:

The integral $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x \, dx$ is equal to

Consider an ionic solid $M X$ with $NaCl$ structure. Construct a new structure $( Z )$ whose unit cell is constructed from the unit cell of $M X$ following the sequential instructions given below. Neglect the charge balance.

$(i)$ Remove all the anions ( $X$ ) except the central one

$(ii)$ Replace all the face centered cations $(M)$ by anions $(X)$

$(iii)$ Remove all the corner cations $(M)$

$(iv)$ Replace the central anion ( $X$ ) with cation $(M)$

The value of $\left(\frac{\text { number of anions }}{\text { number of cations }}\right)$ in $Z$ is. . . . .

Among the bromides $(I)-(III)$ given below,the order of reactivity in $S_N1$ reaction is: