If

then $$|\overrightarrow{\mathrm{u}} \times \overrightarrow{\mathrm{v}}| \text { is }$$

Three fair coins with faces numbered 1 and 0 are tossed simultaneously. Then variance (X) of the probability distribution of random variable $$\mathrm{X}$$, where $$\mathrm{X}$$ is the sum of numbers on the upper most faces, is

If $$\mathrm{f}(x)=x^2+1$$ and $$\mathrm{g}(x)=\frac{1}{x}$$, then the value of $$\mathrm{f}(\mathrm{g}(\mathrm{g}(\mathrm{f}(x))))$$ at $$x=1$$ is

A glass prism deviates the red and violet rays through $$9^{\circ}$$ and $$11^{\circ}$$ respectively. A second prism of equal angle deviates them through $$11^{\circ}$$ and $$13^{\circ}$$ respectively. The ratio of dispersive power of second prism to first prism is