Assertion $A$: Barium is not required in the normal biological processes of the human body.
Reason $R$: Barium does not exhibit more than one oxidation state.

The coefficient of $x^3 y^4 z^5$ in the expansion of $(x y+y z+x z)^6$ is

$x = \log \left( \frac{1}{y} + \sqrt{1 + \frac{1}{y^2}} \right) \Rightarrow y$ is equal to

Consider the following statements $A$ and $B$ and identify the correct answer.
$A$. In an elastic collision,if a body suffers a head-on collision with another of the same mass at rest,then the first body comes to rest while the other starts moving with the velocity of the first one.
$B$. Two bodies of equal mass suffering a head-on elastic collision merely exchange their velocities.

The roots of the equation $x^3-14x^2+56x-64=0$ are in

The transformed equation of $3x^2 - 4xy = r^2$ when the coordinate axes are rotated about the origin through an angle of $\operatorname{Tan}^{-1}(2)$ in the positive direction is: