Mass of living matter at a trophic level in an area at any time is called

If $y = a \sin x + b \cos x$,then $y^2 + \left( \frac{dy}{dx} \right)^2$ is a

Two rigid boxes containing different ideal gases are placed on a table. Box $A$ contains one mole of nitrogen at temperature $T_0$,while box $B$ contains one mole of helium at temperature $(7/3) T_0$. The boxes are then put into thermal contact with each other,and heat flows between them until the gases reach a common final temperature (Ignore the heat capacity of boxes). Then,the final temperature of gases,$T_f$,in terms of $T_0$ is

An inductor $L$,a resistance $R$ and two identical bulbs $B_1$ and $B_2$ are connected to a battery through a switch $S$ as shown in the figure. The resistance of the coil having inductance $L$ is also $R$. Which of the following statements gives the correct description of the happenings when the switch $S$ is closed?

In $YDSE$,how many maxima can be obtained on the screen if the wavelength of light used is $200 \, nm$ and $d = 700 \, nm$?

In a $\triangle ABC$,if $\angle C = 90^{\circ}$,then $\frac{a^2-b^2}{a^2+b^2}$ is equal to