The structural formula of $2$-methyl-$2$-butene is:

$A$ spherical surface of radius of curvature $R$ separates air (refractive index $1.0$) from glass (refractive index $1.5$). The centre of curvature is in the glass. $A$ point object $P$ placed in air is found to have a real image $Q$ in the glass. The line $PQ$ cuts the surface at the point $O$,and $PO = OQ$. The distance $PO$ is equal to: (in $,R$)

$A$ plane passes through the point $(3, 5, 7)$. If the direction ratios of its normal are equal to the intercepts made by the plane $x + 3y + 2z = 9$ with the coordinate axes,then the equation of that plane is

If $x=p+q$,$y=p \omega+q \omega^2$,and $z=p \omega^2+q \omega$,where $\omega$ is a complex cube root of unity,then $xyz$ is equal to:

The input resistance of a common emitter transistor amplifier,if the output resistance is $500 \, k\Omega$,the current gain $\alpha = 0.98$ and power gain is $6.0625 \times 10^6$,is....$\Omega$

$A$ small square loop of wire of side $l$ is placed inside a large square loop of side $L$ $(L \gg l)$. If the loops are coplanar and their centres coincide,the mutual inductance of the system is directly proportional to :