If $I_n = \int \sin^n x \, dx$,then $n I_n - (n-1) I_{n-2}$ equals

If $I_n = \int_0^{\pi / 4} \tan^n x \, dx$, then $I_2+I_4, I_3+I_5, I_4+I_6, \ldots$ are in

Phytochrome is a

Two slabs $A$ and $B$ of equal surface area are placed one over the other such that their surfaces are completely in contact. The thickness of slab $A$ is twice that of $B$. The coefficient of thermal conductivity of slab $A$ is twice that of $B$. The first surface of slab $A$ is maintained at $100^{\circ} C$,while the second surface of slab $B$ is maintained at $25^{\circ} C$. The temperature at the contact of their surfaces is (in $^{\circ} C$)

$A$ crystal is made up of metal ions $M_1$ and $M_2$ and oxide ions. Oxide ions form a $ccp$ lattice structure. The cation $M_1$ occupies $50 \%$ of octahedral voids and the cation $M_2$ occupies $12.5 \%$ of tetrahedral voids of the oxide lattice. The oxidation numbers of $M_1$ and $M_2$ are,respectively:

$(\sqrt{3}+i)^7+(\sqrt{3}-i)^7$ is equal to (in $\sqrt{3}$)