If $a = \hat{i} + \hat{j} + t \hat{k}$ and $b = \hat{i} + 2 \hat{j} + 3 \hat{k}$,then the values of $t$ for which $(a+b)$ and $(a-b)$ are perpendicular are:

When the temperature of a body increases from $T$ to $T+\Delta T$,its moment of inertia increases from $I$ to $I+\Delta I$. If $\alpha$ is the coefficient of linear expansion of the material of the body,then $\frac{\Delta I}{I}$ is (neglect higher orders of $\alpha$ ).

$A$ vertical spring with force constant $k$ is fixed on a table. $A$ ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is

The particles emitted during the sequential radioactive decay of ${}^{238}U_{92}$ to ${}^{206}Pb_{82}$ are

Which layer of the uterus undergoes cyclical changes during the menstrual cycle?

If the difference between the roots of $x^2+ax+b=0$ and $x^2+bx+a=0$ is the same,and $a \neq b$,then: