$A$ 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 major product of the following reaction is

$A$ uniform rod of mass $m$ and length $l$ is moving with velocity $u$ in a direction perpendicular to its length. $A$ blow of impulse $J$ is given perpendicular to its length at a distance $\frac{l}{4}$ from its centre at point $P$ such that the instantaneous velocity of point $P$ becomes $2u$. Then the velocity of its centre of mass will be:

If $A$ and $B$ are events of a random experiment such that $P(A \cup B) = \frac{4}{5}$,$P(\bar{A} \cup \bar{B}) = \frac{7}{10}$ and $P(B) = \frac{2}{5}$,then $P(A)$ equals

The electron in a hydrogen atom makes a transition from an excited state to the ground state. Which of the following statements is true?

The venous system of a frog differs from that of a mammal due to the presence of: