$S_1, S_2, \ldots, S_{10}$ are the speakers in a conference. If $S_1$ addresses only after $S_2$,then the number of ways the speakers address is

If $(x, y, z)$ is an arbitrary point lying on a plane $P$ which passes through the points $(42, 0, 0)$,$(0, 42, 0)$,and $(0, 0, 42)$,then the value of the expression $3 + \frac{x-11}{(y-19)^2(z-12)^2} + \frac{y-19}{(x-11)^2(z-12)^2} + \frac{z-12}{(x-11)^2(y-19)^2} - \frac{x+y+z}{14(x-11)(y-19)(z-12)}$ is:

$A$ $20 \, cm$ length of a certain solution causes right-handed rotation of $38^\circ$. $A$ $30 \, cm$ length of another solution causes left-handed rotation of $24^\circ$. The optical rotation caused by a $30 \, cm$ length of a mixture of the above solutions in the volume ratio $1 : 2$ is:

If $P_1, P_2, P_3$ are the perimeters of the three circles $x^2+y^2+8x-6y=0$,$4x^2+4y^2-4x-12y-186=0$,and $x^2+y^2-6x+6y-9=0$ respectively,then

The human body does not produce

If the circles $x^2+y^2-2 \lambda x-2 y-7=0$ and $3(x^2+y^2)-8 x+29 y=0$ are orthogonal,then $\lambda$ is equal to