If $P$ is the set of all real numbers $\alpha$ such that the product of the lengths of perpendiculars from $(\alpha, 1)$ to the pair of straight lines $3x^2+7xy+2y^2=0$ is $\frac{\sqrt{2}}{5}$,then the sum of the elements in $P$ is

$A$ thin prism $P_1$ with angle $4^o$ and made from glass of refractive index $1.54$ is combined with another thin prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without deviation. The angle of prism $P_2$ is (in $^o$)

The figure shows three resistor configurations $R_1, R_2$,and $R_3$ connected to a $3 \, V$ battery. If the power dissipated by the configurations $R_1, R_2$,and $R_3$ is $P_1, P_2$,and $P_3$ respectively,then:

What is the meaning of the word 'ease' in French?

$A$ homogeneous solid cylinder of length $L$ $(L < H/2)$,cross-sectional area $A/5$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L/4$ in the denser liquid as shown in the figure. The lower density liquid is open to the atmosphere having pressure $P_0$. Then,the density $D$ of the solid is given by:

Calculate the strength of $20 \, V \, H_2O_2$ in $g/L$.