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

One junction of a certain thermoelectric couple is at a fixed temperature $T_r$ and the other junction is at temperature $T$. The thermo-electromotive force for this is expressed by $E=k(T-T_r)[T_0-\frac{1}{2}(T+T_r)]$. At temperature $T=\frac{1}{2} T_0$,the thermoelectric power is

Which science presents the changes in the internal and external structure of plants from the perspective of evolution and phylogeny?

If $\int \frac{dx}{x^2+2x+2} = f(x) + c$, then $f(x)$ is equal to :

$A$ ray of light of intensity $I$ is incident on a parallel glass slab at point $A$ as shown in the diagram. It undergoes partial reflection and refraction. At each reflection, $25\%$ of incident energy is reflected. The rays $AB$ and $A'B'$ undergo interference. The ratio of $I_{max}$ and $I_{min}$ is (in $: 1$)

The Henry's law constant for the solubility of $N_2$ gas in water at $298 \ K$ is $1.0 \times 10^5 \ atm$. The mole fraction of $N_2$ in air is $0.8$. The number of moles of $N_2$ from air dissolved in $10 \ moles$ of water at $298 \ K$ and $5 \ atm$ pressure is