Platinum crystallizes in a face-centered cubic $(FCC)$ crystal with a unit cell length $a$. The distance between nearest neighbors is

$A$ ball is thrown on a lawn in such a way that it initially slides with a speed $v_0$ without rolling. It gradually picks up rotational motion. Find the speed of the ball at which there will be rolling without slipping.

Breeding crops with higher levels of vitamins,minerals,and proteins is known as ..........

Give the number of electrons in the species $H_{2}^{+}$,$H_{2}$,and $O_{2}^{+}$.

Let $f: R-\{3\} \rightarrow R-\{1\}$ be defined by $f(x) = \frac{x-2}{x-3}$. Let $g: R \rightarrow R$ be given as $g(x) = 2x-3$. Then, the sum of all the values of $x$ for which $f^{-1}(x) + g^{-1}(x) = \frac{13}{2}$ is equal to

If $f: R \rightarrow R$ is an even function which is twice differentiable on $R$ and $f^{\prime \prime}(\pi)=1$,then $f^{\prime \prime}(-\pi)$ is equal to