For a gas $\frac{R}{C_v} = 0.4$,where $R$ is the universal gas constant and $C_v$ is the molar specific heat at constant volume. The gas is made up of molecules which are

If $a$ and $b$ are two non-zero perpendicular vectors, then a vector $y$ satisfying the equations $a \cdot y = c$ (where $c$ is a scalar) and $a \times y = b$ is

The species having tetrahedral shape is

Mosses and ferns are found in moist and shady places because both

$A$ small ball of mass $m$ is released at a height $R$ above the Earth's surface,as shown in the figure. The ball enters a narrow groove and reaches a maximum depth of $R/2$ inside the Earth before coming to rest momentarily. The groove contains an ideal spring of spring constant $K$ and natural length $R$. Find the value of $K$. ($R$ is the radius of the Earth and $M$ is the mass of the Earth).

$\lim _{x \rightarrow \infty}\left(\frac{x+5}{x+2}\right)^{x+3}$ equals