If the volume of a parallelepiped with coterminous edges $4 \hat{i} + 5 \hat{j} + \hat{k}$,$-\hat{j} + \hat{k}$,and $3 \hat{i} + 9 \hat{j} + p \hat{k}$ is $34$ cubic units,then $p$ is equal to:

$A$ sphere of mass $m$ moving with velocity $v$ collides head-on with another sphere of the same mass which is at rest. The ratio of the final velocity of the second sphere to the initial velocity of the first sphere is ($e$ is the coefficient of restitution and the collision is inelastic).

$A$ bimetallic strip consists of metals $A$ and $B$. It is mounted rigidly at the base as shown. The metal $A$ has a higher coefficient of expansion than that of metal $B$. When the bimetallic strip is placed in a cold bath,it will:

Assertion : In recombinant $DNA$ technology human genes are often transferred into bacteria (prokaryotes) or yeast (eukaryote).
Reason : Both bacteria and yeast multiply very fast to form huge population which expresses the desired gene.

$\int_{-\pi / 2}^{\pi / 2} \sin ^4 x \cos ^6 x \, dx$ is equal to

Electrons with a kinetic energy of $6.023 \times 10^4 \ J/mol$ are evolved from the surface of a metal when it is exposed to radiation of wavelength $600 \ nm$. The minimum amount of energy required to remove an electron from the metal atom is