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If $\overline{a}$ and $\overline{b}$ are two unit vectors such that $5 \overline{a} + 4 \overline{b}$ and $\overline{a} - 2 \overline{b}$ are perpendicular to each other,then the angle between $\overline{a}$ and $\overline{b}$ is

The ammonia prepared by treating ammonium sulphate with calcium hydroxide is completely used by $NiCl _2 \cdot 6 H _2 O$ to form a stable coordination compound. Assume that both the reactions are $100 \%$ complete. If $1584 g$ of ammonium sulphate and $952 g$ of $NiCl _2 \cdot 6 H _2 O$ are used in the preparation, the combined weight (in grams) of gypsum and the nickelammonia coordination compound thus produced is. . . . (Atomic weights in $g mol ^{-1}: H =1, N =14, O =16, S =32,{ Cl =35.5}, Ca =40, Ni =59$ )

Archaeopteryx,a transitional fossil between birds and reptiles,was discovered from rocks of which of the following periods?

$\int \left(1+x-\frac{1}{x}\right) e^{x+\frac{1}{x}} ~d x$ is equal to

$A$ particle moves with a velocity $\vec{v} = 5\hat{i} - 3\hat{j} + 6\hat{k} \text{ m/s}$ under the influence of a constant force $\vec{F} = 10\hat{i} + 10\hat{j} + 20\hat{k} \text{ N}$. The instantaneous power will be ............... $\text{J/s}$.

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