The polar equation $\cos \theta + 7 \sin \theta = \frac{1}{r}$ represents a

The equation of the pair of lines passing through the origin whose sum and product of slopes are respectively the arithmetic mean and geometric mean of $4$ and $9$ is

The major product of the following reaction is

Two oxides of nitrogen,$NO$ and $NO_2$,react together at $253 \ K$ to form a compound of nitrogen $X$. $X$ reacts with water to yield another compound of nitrogen $Y$. The shape of the anion of $Y$ molecule is:

Identify the correct gland on the basis of the following characteristics:
$(I)$ It is located on the dorsal side of the forebrain.
$(II)$ It plays a very important role in the regulation of the $24$-hour rhythm of our body.
$(III)$ It helps in maintaining the body temperature.
$(IV)$ Its hormone influences metabolism as well as defense capability.

If the temperature of the sun were to increase from $T$ to $2T$ and its radius from $R$ to $2R$,then the ratio of the radiant energy received on earth to what it was previously will be