$A$ radioactive material decays by simultaneous emission of two particles with respective half-lives $1620 \ years$ and $810 \ years$. The time (in years) after which one-fourth of the material remains is

The bond length of $HCl$ molecule is $1.275 \ \mathring{A}$ and its dipole moment is $1.03 \ D$. The ionic character of the molecule (in percent) (charge of the electron $= 4.8 \times 10^{-10} \ esu$) is

Which of the following is related to genetic engineering?

$A$ rod $P$ of length $1 \ m$ is hinged at one end $A$ and there is a ring attached to the other end. Another long rod $Q$ is hinged at $B$ and it passes through the ring. The rod $P$ is rotated about an axis which is perpendicular to the plane in which both the rods are present and the variation between the angles $\theta$ and $\phi$ are plotted as shown. The distance between the hinges $A$ and $B$ is ....... $m$.

The figure shows a plot of binding energy per nucleon $E_b$ against the nuclear mass $M$. $A, B, C, D, E, F$ correspond to different nuclei. Consider four reactions:
$(i)$ $A + B \to C + \varepsilon$
$(ii)$ $C \to A + B + \varepsilon$
$(iii)$ $D + E \to F + \varepsilon$
$(iv)$ $F \to D + E + \varepsilon$
where $\varepsilon$ is the energy released. In which reactions is $\varepsilon$ positive?

$A$ parallel plate capacitor is charged and then disconnected from the charging battery. If the plates are now moved farther apart by pulling at them by means of insulating handles, then