Changes in $GnRH$ pulse frequency in females is controlled by circulating levels of

Match the following columns:

Column-$I$	Column-$II$
$(a)$ Gymnosperms	$(p)$ Trimerous flowers
$(b)$ Monocots	$(q)$ Absence of flowers
$(c)$ Dicots	$(r)$ Primitive flowers
$(d)$ Pteridophytes	$(s)$ Tetramerous or pentamerous flowers

$A$ block rests on a rough inclined plane making an angle of $30^o$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8.$ If the frictional force on the block is $10\,N,$ the mass of the block (in $kg$) is (take $g = 10\,m/s^2$)

The angular magnification of a simple microscope can be increased by increasing

If the angle $\theta$ between the vectors $\overrightarrow{a}=2 x^2 \hat{i}+4 x \hat{j}+\hat{k}$ and $\overrightarrow{b}=7 \hat{i}-2 \hat{j}+x \hat{k}$ is such that $90^{\circ} < \theta < 180^{\circ}$, then $x$ lies in the interval

$A$ spherical black body of radius $12 \, cm$ radiates $450 \, W$ of power at $500 \, K$. If the radius is halved and the temperature is doubled,the power radiated will be ........ $W$.