The transfer of energy from organism to organism in a natural community establishes

The perpendicular distance of the straight line $12x + 5y = 7$ from the origin is given by

$A$ ping-pong ball of mass $m$ is floating in air by a jet of water emerging out of a nozzle. If the water strikes the ping-pong ball with a speed $v$ and just after collision the water falls dead,the mass flow rate of water in the nozzle is equal to

One mole of $N_2H_4$ loses $10$ moles of electrons to form a new compound $Z$. Assuming that all the nitrogen atoms appear in the new compound,what is the oxidation state of nitrogen in $Z$? (There is no change in the oxidation state of hydrogen.)

$A$ bimetallic strip is formed out of two identical strips,one of copper and the other of brass. The coefficients of linear expansion of the two metals are $\alpha_C$ and $\alpha_B$. On heating,the temperature of the strip increases by $\Delta T$ and the strip bends to form an arc of radius $R$. Then $R$ is proportional to

$A$ lead bullet of mass $10 \ g$ travelling at $300 \ m/s$ strikes against a block of wood and comes to rest. Assuming $50\%$ of heat is absorbed by the bullet,the increase in its temperature is (Specific heat of lead $= 150 \ J/kg \cdot ^{\circ}C$) (in $^{\circ}C$)