If $\omega$ is a complex cube root of unity,then $\sin \left\{\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right\}$ is equal to

$A$ bag contains $5$ black balls,$4$ white balls and $3$ red balls. If a ball is selected at random,the probability that it is a black or a red ball is:

The area (in square units) bounded by the curves $y^2=4x$ and $x^2=4y$ in the plane is

Which of the following is the correct sequence of the various steps of Herbarium formation?
$1$ Drying $2$ Poisoning $3$ Collection $4$ Labelling $5$ Mounting $6$ Deposition $7$ Stitching

$A$ coil of wire of radius $r$ has $600$ turns and a self-inductance of $108 \ mH$. The self-inductance of a coil with the same radius and $500$ turns is: (in $mH$)

Two Carnot engines $A$ and $B$ are operated in succession. The first one,$A$,receives heat from a source at $T_1 = 800\, K$ and rejects heat to a sink at $T_2\, K$. The second engine,$B$,receives the heat rejected by the first engine and rejects heat to another sink at $T_3 = 300\, K$. If the work outputs of the two engines are equal,then the value of $T_2$ is ...... $K$.