$\int \cos^3 x \, e^{\log(\sin x)} \, dx$ is equal to

When $22.4 \ L$ of $H_{2(g)}$ is mixed with $11.2 \ L$ of $Cl_{2(g)}$,each at $S.T.P.$,the moles of $HCl_{(g)}$ formed is equal to

$A$ diverging lens with a focal length of magnitude $25 \, cm$ is placed at a distance of $15 \, cm$ from a converging lens with a focal length of magnitude $20 \, cm$. $A$ beam of parallel light falls on the diverging lens. The final image formed is:

What is the gametophytic stage of Pteridophytes?

Two slabs $A$ and $B$ of different materials but of the same thickness are joined end to end to form a composite slab. The thermal conductivities of $A$ and $B$ are $k_1$ and $k_2$ respectively. $A$ steady temperature difference of $12^{\circ} C$ is maintained across the composite slab. If $k_1 = \frac{k_2}{2}$,the temperature difference across slab $A$ is (in $^{\circ} C$)

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