An ideal gas is taken around the cycle $ABCA$ as shown in the $P-V$ diagram. The work done during the cycle is

If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors and $\lambda$ is a real number,then the vectors $\vec{a}+2 \vec{b}+3 \vec{c}$,$\lambda \vec{b}+4 \vec{c}$,and $(2 \lambda-1) \vec{c}$ are non-coplanar for:

$A$ particle of mass $m$ and charge $q$ is placed at rest in a uniform electric field $E$ and then released. The $KE$ attained by the particle after moving a distance $y$ is

Platinum crystallizes in a face-centered cubic $(FCC)$ crystal with a unit cell edge length $a$. The distance between nearest neighbours is

If $a>0$,then $\int_{-\pi}^\pi \frac{\sin ^2 x}{1+a^x} d x$ is equal to

If $m$ and $M$ respectively denote the minimum and maximum of $f(x)=(x-1)^2+3$ for $x \in [-3, 1]$,then the ordered pair $(m, M)$ is equal to