The kinetic energy of an electron and a proton is $10^{-32} \ J$. Then the relation between their de-Broglie wavelengths is

$Fe_2Cr_2O_4 + Na_2CO_3 + O_2$ $\xrightarrow{\text{Fusion}} [X]$ $\xrightarrow{H^+ / H_2O} [Y]$ $\xrightarrow{H_2O_2 / H^+} [Z]$
Which of the following statements is true for the compounds $[X], [Y],$ and $[Z]$?

$A$ current $I$ flows in an infinitely long wire with a cross-section in the form of a semicircular ring of radius $R$. The magnitude of the magnetic induction along its axis is

If $\vec{a}=\frac{1}{\sqrt{10}}(3 \hat{i}+\hat{k})$ and $\vec b = \frac{1}{7}(2 \hat{i} + 3 \hat{j} - 6 \hat{k})$,then the value of $(2\vec a - \vec b) \cdot [(\vec a \times \vec b) \times (\vec a + 2\vec b)]$ is

$A$ neutron moving with velocity $u$ collides elastically with an atom of mass number $A$. If the collision is head-on and the initial kinetic energy of the neutron is $E$,then the final kinetic energy of the neutron after the collision is

If $f(x)=|x|+|\sin x|$ for $x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, then its left hand derivative at $x=0$ is