If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors and $\lambda$ is a real number, then the vectors $\vec{a}+2 \vec{b}+3 \vec{c}$, $\lambda \vec{b}+4 \vec{c}$, and $(2 \lambda-1) \vec{c}$ are non-coplanar for:

Which one of the following elements reacts with steam?

If $\alpha = \frac{5}{2! 3} + \frac{5 \cdot 7}{3! 3^2} + \frac{5 \cdot 7 \cdot 9}{4! 3^3} + \ldots$,then $\alpha^2 + 4\alpha$ is equal to

Keto-enol tautomerism is not observed in

Two long conductors,separated by a distance $d$,carry currents $I_1$ and $I_2$ in the same directions. They exert a force $F$ on each other. Now,the current in one of them is increased to two times its original value and its direction is reversed. The distance is also increased to $3d$. The new value of the force between them is:

The cathode of a photoelectric cell is changed such that the work function changes from $W_1$ to $W_2$ $(W_2 > W_1)$. If the current before and after the change are $I_1$ and $I_2$ respectively,with all other conditions remaining unchanged,then (assuming $h\nu > W_2$):