If $a = 2i + j - k, b = i + 2j + k$ and $c = i - j + 2k,$ then $a \cdot (b \times c) = $

$2 \pi - (\sin^{-1} \frac{4}{5} + \sin^{-1} \frac{5}{13} + \sin^{-1} \frac{16}{65})$ is equal to

If the point $P(\alpha, \beta, \gamma)$ lies on the plane $2x+y+z=1$ and $[\alpha \ \beta \ \gamma] \begin{bmatrix} 1 & 9 & 1 \\ 8 & 2 & 1 \\ 7 & 3 & 1 \end{bmatrix} = [0 \ 0 \ 0]$,then $\alpha^2+\beta^2+\gamma^2=$

Schwann cells are found around:

In a fission reaction $_{92}^{236}U \to ^{117}X + ^{117}Y + n + n$,the binding energy per nucleon of $X$ and $Y$ is $8.5\, MeV$,whereas that of $^{236}U$ is $7.6\, MeV$. The total energy liberated will be about:

The graph in the figure shows how the count-rate $A$ of a radioactive source as measured by a Geiger counter varies with time $t$. The relationship between $A$ and $t$ is: (Assume $\ln 12 = 2.6$)