$A$ conducting rod $AC$ of length $4l$ is rotated about a point $O$ in a uniform magnetic field $\vec B$ directed into the paper. $AO = l$ and $OC = 3l$. Then:

If the pair of straight lines given by $Ax^2 + 2Hxy + By^2 = 0$ $(H^2 > AB)$ forms an equilateral triangle with the line $ax + by + c = 0$,then $(A + 3B)(3A + B)$ is equal to:

$A$ sample of a radioactive element has a mass of $10 \, g$ at an instant $t=0$. The approximate mass of this element in the sample after two mean lives is ........ $g$.

The refractive index of a material of a plano-concave lens is $5/3$,and the radius of curvature is $0.3 ~m$. The focal length of the lens in air is (in $~m$)

When the gap is closed without placing any object in the screw gauge whose least count is $0.005 \ mm$,the $5^{th}$ division on its circular scale coincides with the reference line on the main scale. When a small sphere is placed,the reading on the main scale advances by $4$ divisions,whereas the circular scale reading advances by five times the corresponding reading when no object was placed. There are $200$ divisions on the circular scale. The radius of the sphere is .......... $mm$.

In angiosperms,the functional megaspore develops into which of the following?